If you cite multiple chapters or works from the same book, include a separate Works Cited entry for each chapter.
An appendix contains information that supplements the reader’s understanding of your research but is not essential to it. For example:
Something is only worth including as an appendix if you refer to information from it at some point in the text (e.g. quoting from an interview transcript). If you don’t, it should probably be removed.
The arithmetic mean is the most commonly used mean. It’s often simply called the mean or the average. But there are some other types of means you can calculate depending on your research purposes:
An essay is a focused piece of writing that explains, argues, describes, or narrates.
In high school, you may have to write many different types of essays to develop your writing skills.
The “hook” is the first sentence of your essay introduction. It should lead the reader into your essay, giving a sense of why it’s interesting.
To write a good hook, avoid overly broad statements or long, dense sentences. Try to start with something clear, concise and catchy that will spark your reader’s curiosity.
Your essay introduction should include three main things, in this order:
The length of each part depends on the length and complexity of your essay.
The median is the most informative measure of central tendency for skewed distributions or distributions with outliers. For example, the median is often used as a measure of central tendency for income distributions, which are generally highly skewed.
Because the median only uses one or two values, it’s unaffected by extreme outliers or non-symmetric distributions of scores. In contrast, the mean and mode can vary in skewed distributions.
A data set can often have no mode, one mode or more than one mode – it all depends on how many different values repeat most frequently.
Your data can be:
To find the mode:
Then you simply need to identify the most frequently occurring value.
There are three key steps in systematic sampling:
Each of these sentences expresses one main idea – by listing them in order, we can see the overall structure of the essay at a glance. Each paragraph will expand on the topic sentence with relevant detail, evidence, and arguments.
The two most common methods for calculating interquartile range are the exclusive and inclusive methods.
The exclusive method excludes the median when identifying Q1 and Q3, while the inclusive method includes the median as a value in the data set in identifying the quartiles.
For each of these methods, you’ll need different procedures for finding the median, Q1 and Q3 depending on whether your sample size is even- or odd-numbered. The exclusive method works best for even-numbered sample sizes, while the inclusive method is often used with odd-numbered sample sizes.
This is because it can be easier to introduce your paper once you’ve already written the body; you may not have the clearest idea of your arguments until you’ve written them, and things can change during the writing process.
The way you present your research problem in your introduction varies depending on the nature of your research paper. A research paper that presents a sustained argument will usually encapsulate this argument in a thesis statement.
A research paper designed to present the results of empirical research tends to present a research question that it seeks to answer. It may also include a hypothesis—a prediction that will be confirmed or disproved by your research.
Homoscedasticity, or homogeneity of variances, is an assumption of equal or similar variances in different groups being compared.
This is an important assumption of parametric statistical tests because they are sensitive to any dissimilarities. Uneven variances in samples result in biased and skewed test results.
Yes, you can create a stratified sample using multiple characteristics, but you must ensure that every participant in your study belongs to one and only one subgroup. In this case, you multiply the numbers of subgroups for each characteristic to get the total number of groups.
For example, if you were stratifying by location with three subgroups (urban, rural, or suburban) and marital status with five subgroups (single, divorced, widowed, married, or partnered), you would have 3 x 5 = 15 subgroups.
You should use stratified sampling when your sample can be divided into mutually exclusive and exhaustive subgroups that you believe will take on different mean values for the variable that you’re studying.
Using stratified sampling will allow you to obtain more precise (with lower variance) statistical estimates of whatever you are trying to measure.
For example, say you want to investigate how income differs based on educational attainment, but you know that this relationship can vary based on race. Using stratified sampling, you can ensure you obtain a large enough sample from each racial group, allowing you to draw more precise conclusions.
Without a clear thesis, an essay can end up rambling and unfocused, leaving your reader unsure of exactly what you want to say.
The structure of an essay is divided into an introduction that presents your topic and thesis statement, a body containing your in-depth analysis and arguments, and a conclusion wrapping up your ideas.
The structure of the body is flexible, but you should always spend some time thinking about how you can organize your essay to best serve your ideas.
Although the units of variance are harder to intuitively understand, variance is important in statistical tests.
The empirical rule, or the 68-95-99.7 rule, tells you where most of the values lie in a normal distribution:
The empirical rule is a quick way to get an overview of your data and check for any outliers or extreme values that don’t follow this pattern.
In normal distributions, a high standard deviation means that values are generally far from the mean, while a low standard deviation indicates that values are clustered close to the mean.
In a thesis or dissertation, the discussion is an in-depth exploration of the results, going into detail about the meaning of your findings and citing relevant sources to put them in context.
The results chapter or section simply and objectively reports what you found, without speculating on why you found these results. The discussion interprets the meaning of the results, puts them in context, and explains why they matter.
Results are usually written in the past tense, because they are describing the outcome of completed actions.
The results chapter of a thesis or dissertation presents your research results concisely and objectively.
In quantitative research, for each question or hypothesis, state:
In qualitative research, for each question or theme, describe:
Don’t interpret or speculate in the results chapter.
No. Because the range formula subtracts the lowest number from the highest number, the range is always zero or a positive number.
There are three types of cluster sampling: single-stage, double-stage and multi-stage clustering. In all three types, you first divide the population into clusters, then randomly select clusters for use in your sample.
Variability tells you how far apart points lie from each other and from the center of a distribution or a data set.
Variability is also referred to as spread, scatter or dispersion.
The vast majority of essays written at university are some sort of argumentative essay. Almost all academic writing involves building up an argument, though other types of essay might be assigned in composition classes.
Essays can present arguments about all kinds of different topics. For example:
At high school and in composition classes at university, you’ll often be told to write a specific type of essay, but you might also just be given prompts.
Look for keywords in these prompts that suggest a certain approach: The word “explain” suggests you should write an expository essay, while the word “describe” implies a descriptive essay. An argumentative essay might be prompted with the word “assess” or “argue.”
For example, temperature in Celsius or Fahrenheit is at an interval scale because zero is not the lowest possible temperature. In the Kelvin scale, a ratio scale, zero represents a total lack of thermal energy.
In rhetorical analysis, a claim is something the author wants the audience to believe. A support is the evidence or appeal they use to convince the reader to believe the claim. A warrant is the (often implicit) assumption that links the support with the claim.
Logos appeals to the audience’s reason, building up logical arguments. Ethos appeals to the speaker’s status or authority, making the audience more likely to trust them. Pathos appeals to the emotions, trying to make the audience feel angry or sympathetic, for example.
Collectively, these three appeals are sometimes called the rhetorical triangle. They are central to rhetorical analysis, though a piece of rhetoric might not necessarily use all of them.
The goal of a rhetorical analysis is to explain the effect a piece of writing or oratory has on its audience, how successful it is, and the devices and appeals it uses to achieve its goals.
Unlike a standard argumentative essay, it’s less about taking a position on the arguments presented, and more about exploring how they are constructed.
A critical value is the value of the test statistic which defines the upper and lower bounds of a confidence interval, or which defines the threshold of statistical significance in a statistical test. It describes how far from the mean of the distribution you have to go to cover a certain amount of the total variation in the data (i.e. 90%, 95%, 99%).
If you are constructing a 95% confidence interval and are using a threshold of statistical significance of p = 0.05, then your critical value will be identical in both cases.
The t-distribution gives more probability to observations in the tails of the distribution than the standard normal distribution (a.k.a. the z-distribution).
In this way, the t-distribution is more conservative than the standard normal distribution: to reach the same level of confidence or statistical significance, you will need to include a wider range of the data.
A t-score (a.k.a. a t-value) is equivalent to the number of standard deviations away from the mean of the t-distribution.
The t-distribution is a way of describing a set of observations where most observations fall close to the mean, and the rest of the observations make up the tails on either side. It is a type of normal distribution used for smaller sample sizes, where the variance in the data is unknown.
The t-distribution forms a bell curve when plotted on a graph. It can be described mathematically using the mean and the standard deviation.
If properly implemented, simple random sampling is usually the best sampling method for ensuring both internal and external validity. However, it can sometimes be impractical and expensive to implement, depending on the size of the population to be studied,
If you have a list of every member of the population and the ability to reach whichever members are selected, you can use simple random sampling.
If you have to hand in your essay outline, you may be given specific guidelines stating whether you have to use full sentences. If you’re not sure, ask your supervisor.
When writing an essay outline for yourself, the choice is yours. Some students find it helpful to write out their ideas in full sentences, while others prefer to summarize them in short phrases.
You will sometimes be asked to hand in an essay outline before you start writing your essay. Your supervisor wants to see that you have a clear idea of your structure so that writing will go smoothly.
Even when you do not have to hand it in, writing an essay outline is an important part of the writing process. It’s a good idea to write one (as informally as you like) to clarify your structure for yourself whenever you are working on an essay.
Ordinal data has two characteristics:
However, unlike with interval data, the distances between the categories are uneven or unknown.
To automatically insert a table of contents in Microsoft Word, follow these steps:
Make sure to update your table of contents if you move text or change headings. To update, simply right click and select Update Field.
All level one and two headings should be included in your table of contents. That means the titles of your chapters and the main sections within them.
The contents should also include all appendices and the lists of tables and figures, if applicable, as well as your reference list.
Nominal data is data that can be labelled or classified into mutually exclusive categories within a variable. These categories cannot be ordered in a meaningful way.
For example, for the nominal variable of preferred mode of transportation, you may have the categories of car, bus, train, tram or bicycle.
If your confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.
If your confidence interval for a correlation or regression includes zero, that means that if you run your experiment again there is a good chance of finding no correlation in your data.
In both of these cases, you will also find a high p-value when you run your statistical test, meaning that your results could have occurred under the null hypothesis of no relationship between variables or no difference between groups.
Any normal distribution can be converted into the standard normal distribution by turning the individual values into z-scores. In a z-distribution, z-scores tell you how many standard deviations away from the mean each value lies.
These scores are used in statistical tests to show how far from the mean of the predicted distribution your statistical estimate is. If your test produces a z-score of 2.5, this means that your estimate is 2.5 standard deviations from the predicted mean.
The predicted mean and distribution of your estimate are generated by the null hypothesis of the statistical test you are using. The more standard deviations away from the predicted mean your estimate is, the less likely it is that the estimate could have occurred under the null hypothesis.
To calculate the confidence interval, you need to know:
Then you can plug these components into the confidence interval formula that corresponds to your data. The formula depends on the type of estimate (e.g. a mean or a proportion) and on the distribution of your data.
The confidence level is the percentage of times you expect to get close to the same estimate if you run your experiment again or resample the population in the same way.
The confidence interval is the actual upper and lower bounds of the estimate you expect to find at a given level of confidence.
For example, if you are estimating a 95% confidence interval around the mean proportion of female babies born every year based on a random sample of babies, you might find an upper bound of 0.56 and a lower bound of 0.48. These are the upper and lower bounds of the confidence interval. The confidence level is 95%.
This means that 95% of the time, you can expect your estimate to fall between 0.56 and 0.48.
In a thesis or dissertation, the acknowledgements should usually be no longer than one page. There is no minimum length.
In the acknowledgements of your thesis or dissertation, you should first thank those who helped you academically or professionally, such as your supervisor, funders, and other academics.
Then you can include personal thanks to friends, family members, or anyone else who supported you during the process.
It’s also possible to combine both methods, for example by writing a full paragraph on each of your topics and then a final paragraph contrasting the two according to a specific metric.
Your subjects might be very different or quite similar, but it’s important that there be meaningful grounds for comparison. You can probably describe many differences between a cat and a bicycle, but there isn’t really any connection between them to justify the comparison.
Comparing and contrasting is also a useful approach in all kinds of academic writing: You might compare different studies in a literature review, weigh up different arguments in an argumentative essay, or consider different theoretical approaches in a theoretical framework.
Narrative and descriptive essays both allow you to write more personally and creatively than other kinds of essays, and similar writing skills can apply to both.
If you’re not given a specific prompt for your descriptive essay, think about places and objects you know well, that you can think of interesting ways to describe, or that have strong personal significance for you.
The best kind of object for a descriptive essay is one specific enough that you can describe its particular features in detail—don’t choose something too vague or general.
For data from skewed distributions, the median is better than the mean because it isn’t influenced by extremely large values.
The measures of central tendency you can use depends on the level of measurement of your data.
Measures of central tendency help you find the middle, or the average, of a data set.
The 3 most common measures of central tendency are the mean, median and mode.
If you’re not given much guidance on what your narrative essay should be about, consider the context and scope of the assignment. What kind of story is relevant, interesting, and possible to tell within the word count?
The best kind of story for a narrative essay is one you can use to reflect on a particular theme or lesson, or that takes a surprising turn somewhere along the way.
Don’t worry too much if your topic seems unoriginal. The point of a narrative essay is how you tell the story and the point you make with it, not the subject of the story itself.
Narrative essays are usually assigned as writing exercises at high school or in university composition classes. They may also form part of a university application.
When you are prompted to tell a story about your own life or experiences, a narrative essay is usually the right response.
The majority of the essays written at university are some sort of argumentative essay. Unless otherwise specified, you can assume that the goal of any essay you’re asked to write is argumentative: To convince the reader of your position using evidence and reasoning.
In composition classes you might be given assignments that specifically test your ability to write an argumentative essay. Look out for prompts including instructions like “argue,” “assess,” or “discuss” to see if this is the goal.
All essays written at a university level need to properly cite their sources (with the exception of exams or in-class exercises).
Citations should appear in your essay wherever you quote or paraphrase information from a source. These citations usually correspond to entries in a bibliography or reference list at the end of your essay.
Some variables have fixed levels. For example, gender and ethnicity are always nominal level data because they cannot be ranked.
However, for other variables, you can choose the level of measurement. For example, income is a variable that can be recorded on an ordinal or a ratio scale:
If you have a choice, the ratio level is always preferable because you can analyze data in more ways. The higher the level of measurement, the more precise your data is.
Levels of measurement tell you how precisely variables are recorded. There are 4 levels of measurement, which can be ranked from low to high:
No. The p-value only tells you how likely the data you have observed is to have occurred under the null hypothesis.
If the p-value is below your threshold of significance (typically p < 0.05), then you can reject the null hypothesis, but this does not necessarily mean that your alternative hypothesis is true.
The alpha value, or the threshold for statistical significance, is arbitrary – which value you use depends on your field of study.
In most cases, researchers use an alpha of 0.05, which means that there is a less than 5% chance that the data being tested could have occurred under the null hypothesis.
P-values are calculated from the null distribution of the test statistic. They tell you how often a test statistic is expected to occur under the null hypothesis of the statistical test, based on where it falls in the null distribution.
If the test statistic is far from the mean of the null distribution, then the p-value will be small, showing that the test statistic is not likely to have occurred under the null hypothesis.
The test statistic you use will be determined by the statistical test.
You can choose the right statistical test by looking at what type of data you have collected and what type of relationship you want to test.
The test statistic will change based on the number of observations in your data, how variable your observations are, and how strong the underlying patterns in the data are.
For example, if one data set has higher variability while another has lower variability, the first data set will produce a test statistic closer to the null hypothesis, even if the true correlation between two variables is the same in either data set.
An argumentative essay tends to be a longer essay involving independent research, and aims to make an original argument about a topic. Its thesis statement makes a contentious claim that must be supported in an objective, evidence-based way.
An expository essay also aims to be objective, but it doesn’t have to make an original argument. Rather, it aims to explain something (e.g., a process or idea) in a clear, concise way. Expository essays are often shorter assignments and rely less on research.
An expository essay is a common assignment in high-school and university composition classes. It might be assigned as coursework, in class, or as part of an exam.
Sometimes you might not be told explicitly to write an expository essay. Look out for prompts containing keywords like “explain” and “define.” An expository essay is usually the right response to these prompts.
An expository essay is a broad form that varies in length according to the scope of the assignment.
Expository essays are often assigned as a writing exercise or as part of an exam, in which case a five-paragraph essay of around 800 words may be appropriate.
You’ll usually be given guidelines regarding length; if you’re not sure, ask.
Blinding is important to reduce bias and ensure a study’s internal validity.
If participants know whether they are in a control or treatment group, they may adjust their behavior in ways that affect the outcome that researchers are trying to measure. If the people administering the treatment are aware of group assignment, they may treat participants differently and thus directly or indirectly influence the final results.
The 3 main types of descriptive statistics concern the frequency distribution, central tendency, and variability of a dataset.
Without a control group, you can’t know whether it was the treatment or some other variable that caused the outcome of the experiment. By including a control group, you can eliminate the possible impact of all other variables.
An experimental group, also known as a treatment group, receives the treatment whose effect researchers wish to study, whereas a control group does not. They should be identical in all other ways.
Individual Likert-type questions are generally considered ordinal data, because the items have clear rank order, but don’t have an even distribution.
Overall Likert scale scores are sometimes treated as interval data. These scores are considered to have directionality and even spacing between them.
The type of data determines what statistical tests you should use to analyze your data.
A Likert scale is a rating scale that quantitatively assesses opinions, attitudes, or behaviors. It is made up of 4 or more questions that measure a single attitude or trait when response scores are combined.
To use a Likert scale in a survey, you present participants with Likert-type questions or statements, and a continuum of items, usually with 5 or 7 possible responses, to capture their degree of agreement.
In scientific research, concepts are the abstract ideas or phenomena that are being studied (e.g., educational achievement). Variables are properties or characteristics of the concept (e.g., performance at school), while indicators are ways of measuring or quantifying variables (e.g., yearly grade reports).
The process of turning abstract concepts into measurable variables and indicators is called operationalization.
There are various approaches to qualitative data analysis, but they all share five steps in common:
There are five common approaches to qualitative research:
Operationalization means turning abstract conceptual ideas into measurable observations.
For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioral avoidance of crowded places, or physical anxiety symptoms in social situations.
When conducting research, collecting original data has significant advantages:
However, there are also some drawbacks: data collection can be time-consuming, labor-intensive and expensive. In some cases, it’s more efficient to use secondary data that has already been collected by someone else, but the data might be less reliable.
Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organizations.
There are several methods you can use to decrease the impact of confounding variables on your research: restriction, matching, statistical control and randomization.
In restriction, you restrict your sample by only including certain subjects that have the same values of potential confounding variables.
In matching, you match each of the subjects in your treatment group with a counterpart in the comparison group. The matched subjects have the same values on any potential confounding variables, and only differ in the independent variable.
In statistical control, you include potential confounders as variables in your regression.
In randomization, you randomly assign the treatment (or independent variable) in your study to a sufficiently large number of subjects, which allows you to control for all potential confounding variables.
A confounding variable is closely related to both the independent and dependent variables in a study. An independent variable represents the suppose cause, while the dependent variable is the supposed effect. A confounding variable is a third variable that influences both the independent and dependent variables.
Failing to account for confounding variables can cause you to wrongly estimate the relationship between your independent and dependent variables.
Yes, but including more than one of either type requires multiple research questions.
For example, if you are interested in the effect of a diet on health, you can use multiple measures of health: blood sugar, blood pressure, weight, pulse, and many more. Each of these is its own dependent variable with its own research question.
You could also choose to look at the effect of exercise levels as well as diet, or even the additional effect of the two combined. Each of these is a separate independent variable.
No. The value of a dependent variable depends on an independent variable, so a variable cannot be both independent and dependent at the same time. It must be either the cause or the effect, not both!
You want to find out how blood sugar levels are affected by drinking diet soda and regular soda, so you conduct an experiment.
Determining cause and effect is one of the most important parts of scientific research. It’s essential to know which is the cause – the independent variable – and which is the effect – the dependent variable.
In non-probability sampling, the sample is selected based on non-random criteria, and not every member of the population has a chance of being included.
Common non-probability sampling methods include convenience sampling, voluntary response sampling, purposive sampling, snowball sampling, and quota sampling.
Some common types of sampling bias include self-selection, non-response, undercoverage, survivorship, pre-screening or advertising, and healthy user bias.
Sampling bias is a threat to external validity – it limits the generalizability of your findings to a broader group of people.
A sampling error is the difference between a population parameter and a sample statistic.
A statistic refers to measures about the sample, while a parameter refers to measures about the population.
Samples are used to make inferences about populations. Samples are easier to collect data from because they are practical, cost-effective, convenient and manageable.
There are seven threats to external validity: selection bias, history, experimenter effect, Hawthorne effect, testing effect, aptitude-treatment and situation effect.
The two types of external validity are population validity (whether you can generalize to other groups of people) and ecological validity (whether you can generalize to other situations and settings).
The external validity of a study is the extent to which you can generalize your findings to different groups of people, situations, and measures.
Cross-sectional studies are less expensive and time-consuming than many other types of study. They can provide useful insights into a population’s characteristics and identify correlations for further research.
Sometimes only cross-sectional data is available for analysis; other times your research question may only require a cross-sectional study to answer it.
Longitudinal studies can last anywhere from weeks to decades, although they tend to be at least a year long.
Longitudinal studies are better to establish the correct sequence of events, identify changes over time, and provide insight into cause-and-effect relationships, but they also tend to be more expensive and time-consuming than other types of studies.
Longitudinal studies and cross-sectional studies are two different types of research design. In a cross-sectional study you collect data from a population at a specific point in time; in a longitudinal study you repeatedly collect data from the same sample over an extended period of time.
|Longitudinal study||Cross-sectional study|
|Repeated observations||Observations at a single point in time|
|Observes the same group multiple times||Observes different groups (a “cross-section”) in the population|
|Follows changes in participants over time||Provides snapshot of society at a given point|
There are eight threats to internal validity: history, maturation, instrumentation, testing, selection bias, regression to the mean, social interaction and attrition.
Internal validity is the extent to which you can be confident that a cause-and-effect relationship established in a study cannot be explained by other factors.
If you’ve gone over the word limit set for your assignment, shorten your sentences and cut repetition and redundancy during the editing process. If you use a lot of long quotes, consider shortening them to just the essentials.
If you need to remove a lot of words, you may have to cut certain passages. Remember that everything in the text should be there to support your argument; look for any information that’s not essential to your point and remove it.
Revising, proofreading, and editing are different stages of the writing process.
In statistics, model selection is a process researchers use to compare the relative value of different statistical models and determine which one is the best fit for the observed data.
The Akaike information criterion is one of the most common methods of model selection. AIC weights the ability of the model to predict the observed data against the number of parameters the model requires to reach that level of precision.
AIC model selection can help researchers find a model that explains the observed variation in their data while avoiding overfitting.
In statistics, a model is the collection of one or more independent variables and their predicted interactions that researchers use to try to explain variation in their dependent variable.
The Akaike information criterion is calculated from the maximum log-likelihood of the model and the number of parameters (K) used to reach that likelihood. The AIC function is 2K – 2(log-likelihood).
Lower AIC values indicate a better-fit model, and a model with a delta-AIC (the difference between the two AIC values being compared) of more than -2 is considered significantly better than the model it is being compared to.
The Akaike information criterion is a mathematical test used to evaluate how well a model fits the data it is meant to describe. It penalizes models which use more independent variables (parameters) as a way to avoid over-fitting.
AIC is most often used to compare the relative goodness-of-fit among different models under consideration and to then choose the model that best fits the data.
If you adapt or reproduce a table or figure from another source, you should include that source in your APA reference list. You should also acknowledge the original source in the note or caption for the table or figure.
Tables and figures you created yourself, based on your own data, are not included in the reference list.
APA doesn’t require you to include a list of tables or a list of figures. However, it is advisable to do so if your text is long enough to feature a table of contents and it includes a lot of tables and/or figures.
A list of tables and list of figures appear (in that order) after your table of contents, and are presented in a similar way.
In an APA style paper, use a table or figure when it’s a clearer way to present important data than describing it in your main text. This is often the case when you need to communicate a large amount of information.
Before including a table or figure in your text, always reflect on whether it’s useful to your readers’ understanding:
If the data you need to present only contains a few relevant numbers, try summarizing it in the text. If describing the data makes your text overly long and difficult to read, a table or figure may be the best option.
Some examples of factorial ANOVAs include:
In ANOVA, the null hypothesis is that there is no difference among group means. If any group differs significantly from the overall group mean, then the ANOVA will report a statistically significant result.
Significant differences among group means are calculated using the F statistic, which is the ratio of the mean sum of squares (the variance explained by the independent variable) to the mean square error (the variance left over).
If the F statistic is higher than the critical value (the value of F that corresponds with your alpha value, usually 0.05), then the difference among groups is deemed statistically significant.
The only difference between one-way and two-way ANOVA is the number of independent variables. A one-way ANOVA has one independent variable, while a two-way ANOVA has two.
All ANOVAs are designed to test for differences among three or more groups. If you are only testing for a difference between two groups, use a t-test instead.
Multiple linear regression is a regression model that estimates the relationship between a quantitative dependent variable and two or more independent variables using a straight line.
Linear regression most often uses mean-square error (MSE) to calculate the error of the model. MSE is calculated by:
Linear regression fits a line to the data by finding the regression coefficient that results in the smallest MSE.
Simple linear regression is a regression model that estimates the relationship between one independent variable and one dependent variable using a straight line. Both variables should be quantitative.
For example, the relationship between temperature and the expansion of mercury in a thermometer can be modeled using a straight line: as temperature increases, the mercury expands. This linear relationship is so certain that we can use mercury thermometers to measure temperature.
A regression model is a statistical model that estimates the relationship between one dependent variable and one or more independent variables using a line (or a plane in the case of two or more independent variables).
A regression model can be used when the dependent variable is quantitative, except in the case of logistic regression, where the dependent variable is binary.
There are several reasons to conduct a literature review at the beginning of a research project:
Writing the literature review shows your reader how your work relates to existing research and what new insights it will contribute.
The sections in your graduate school resume depend on two things: your experience, and the focus of the program you’re applying to.
Always start with your education. If you have more than one degree, list the most recent one first.
The title and order of the other sections depend on what you want to emphasize. You might include things like:
The resume should aim for a balance between two things: giving a snapshot of what you’ve done with your life so far, and showing that you’re a good candidate for graduate study.
A resume is typically shorter than a CV, giving only the most relevant professional and educational highlights.
An academic CV should give full details of your education and career, including lists of publications and presentations, certifications, memberships, grants, and research projects. Because it is more comprehensive, it’s acceptable for an academic CV to be many pages long.
Note that, outside of the US, resume and CV are often used interchangeably.
No, don’t include your high school courses and grades. The education section should only detail your college education.
If you want to discuss aspects of high school in your graduate school application, you can include this in your personal statement.
A resume for a graduate school application is typically no more than 1–2 pages long.
Note, however, that if you are asked to submit a CV (curriculum vitae), you should give comprehensive details of all your academic experience. An academic CV can be much longer than a normal resume.
Always carefully check the instructions and adhere to any length requirements for each application.
A t-test should not be used to measure differences among more than two groups, because the error structure for a t-test will underestimate the actual error when many groups are being compared.
A one-sample t-test is used to compare a single population to a standard value (for example, to determine whether the average lifespan of a specific town is different from the country average).
A paired t-test is used to compare a single population before and after some experimental intervention or at two different points in time (for example, measuring student performance on a test before and after being taught the material).
A t-test measures the difference in group means divided by the pooled standard error of the two group means.
In this way, it calculates a number (the t-value) illustrating the magnitude of the difference between the two group means being compared, and estimates the likelihood that this difference exists purely by chance (p-value).
Your choice of t-test depends on whether you are studying one group or two groups, and whether you care about the direction of the difference in group means.
If you are studying one group, use a paired t-test to compare the group mean over time or after an intervention, or use a one-sample t-test to compare the group mean to a standard value. If you are studying two groups, use a two-sample t-test.
If you want to know only whether a difference exists, use a two-tailed test. If you want to know if one group mean is greater or less than the other, use a left-tailed or right-tailed one-tailed test.
If information about your source is not available, you can either leave it out of the MLA citation or replace it with something else, depending on the type of information.
A standard MLA Works Cited entry is structured as follows:
Only relevant information is included in the reference.
Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test. Significance is usually denoted by a p-value, or probability value.
Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. The most common threshold is p < 0.05, which means that the data is likely to occur less than 5% of the time under the null hypothesis.
When the p-value falls below the chosen alpha value, then we say the result of the test is statistically significant.
A test statistic is a number calculated by a statistical test. It describes how far your observed data is from the null hypothesis of no relationship between variables or no difference among sample groups.
The test statistic tells you how different two or more groups are from the overall population mean, or how different a linear slope is from the slope predicted by a null hypothesis. Different test statistics are used in different statistical tests.
Statistical tests commonly assume that:
If your data does not meet these assumptions you might still be able to use a nonparametric statistical test, which have fewer requirements but also make weaker inferences.
There are some circumstances where you might need to mention other sources in an abstract: for example, if your research responds directly to another study or focuses on the work of a single theorist. In general, though, don’t include citations unless absolutely necessary.
Abstracts are often indexed along with keywords on academic databases, so they make your work more easily findable. Since the abstract is the first thing any reader sees, it’s important that it clearly and accurately summarizes the contents of your paper.
The title of an article is not italicized in MLA style, but placed in quotation marks. This applies to articles from journals, newspapers, websites, or any other publication. Use italics for the title of the source where the article was published. For example:
Use the same formatting in the Works Cited entry and when referring to the article in the text itself.
The format is the same in the Works Cited list and in the text itself. However, when you mention the book title in the text, you don’t have to include the subtitle.
The title of a part of a book – such as a chapter, short story or poem in a collection – is not italicized, but instead placed in quotation marks.
The DOI is usually clearly visible when you open a journal article on an academic database. It is often listed near the publication date, and includes “doi.org” or “DOI:”. If the database has a “cite this article” button, this should also produce a citation with the DOI included.
If you can’t find the DOI, you can search on Crossref using information like the author, the article title, and the journal name.
Journal articles and ebooks can often be found on multiple different websites and databases. The URL of the page where an article is hosted can be changed or removed over time, but a DOI is linked to the specific document and never changes.
A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.
In your research design, it’s important to identify potential confounding variables and plan how you will reduce their impact.
Discrete and continuous variables are two types of quantitative variables:
Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).
Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).
In an experiment, you manipulate the independent variable and measure the outcome in the dependent variable. For example, in an experiment about the effect of nutrients on crop growth:
Defining your variables, and deciding how you will manipulate and measure them, is an important part of experimental design.
MLA recommends using 12 point Times New Roman since it’s easy to read and installed on every computer. Other standard fonts such as Arial or Georgia are also acceptable. If in doubt, check with your supervisor which font you should be using.
Experimental design means planning a set of procedures to investigate a relationship between variables. To design a controlled experiment, you need:
When designing the experiment, you decide:
Experimental design is essential to the internal and external validity of your experiment.
External validity is the extent to which your results can be generalized to other contexts.
The validity of your experiment depends on your experimental design.
In APA Style, all sources that are not retrievable for the reader are cited as personal communications. In other words, if your source is private or inaccessible to the audience of your paper, it’s a personal communication.
Common examples include conversations, emails, messages, letters, and unrecorded interviews or performances.
When you quote or paraphrase a specific passage from a source, you need to indicate the location of the passage in your in-text citation. If there are no page numbers (e.g. when citing a website), you can instead use section headings, paragraph numbers, or a combination of the two:
(Caulfield, 2019, “Linking” section, para. 1).
Section headings can be shortened if necessary. Kindle location numbers should not be used in ebook citations, as they are unreliable.
If you are referring to the source as a whole, it’s not necessary to include a page number or other marker.
However, if you are citing a website or online article that’s likely to change over time, it’s a good idea to include an access date. In this case, place the month, day, and year directly after the word “Retrieved”, and before the URL.
The best plagiarism checkers of 2019 are:
Each plagiarism checker in this list has been tested to assess how accurately it can detect similarities and to analyze what kind of databases (e.g. websites, scholarly articles, books) your document is compared with. Check out the test results.
The 7th edition APA Manual, published in October 2019, is the most current edition. However, the 6th edition, published in 2009, is still used by many universities and journals.
The American Psychological Association anticipates that most people will start using the 7th edition in the spring of 2020 or thereafter.
It’s best to ask your supervisor or check the website of the journal you want to publish in to see which APA guidelines you should follow.
If you’re citing from an edition other than the first (e.g. a 2nd edition or revised edition), the edition is abbreviated in parentheses after the book’s title (e.g. 2nd ed. or rev. ed.).
The 6th edition of the APA manual requires you to include the publisher’s location when you cite from a print book. The city and state should be included for US-based publishers, the city and country for publishers anywhere else.
If you are following the 7th edition, just write the name of the publisher – no location information is required.
If an article has no DOI, and you accessed it through a database or in print, just omit the DOI.
If an article has no DOI, and you accessed it through a website other than a database (for example, the journal’s own website), include a URL linking to the article.
The old guidelines were to present DOIs by writing “doi:” followed by the numerical string. For example:
If you’re following the 6th edition, this format is still accepted, as long as it’s used consistently.
Reliability and validity are both about how well a method measures something:
If you are doing experimental research, you also have to consider the internal and external validity of your experiment.
A sample is a subset of individuals from a larger population. Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students.
In statistics, sampling allows you to test a hypothesis about the characteristics of a population.
In a scientific paper, the methodology always comes after the introduction and before the results, discussion and conclusion. The same basic structure also applies to a thesis, dissertation, or research proposal.
Methodology refers to the overarching strategy and rationale of your research project. It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.
In shorter scientific papers, where the aim is to report the findings of a specific study, you might simply describe what you did in a methods section.
In a longer or more complex research project, such as a thesis or dissertation, you will probably include a methodology section, where you explain your approach to answering the research questions and cite relevant sources to support your choice of methods.
If you’re applying to multiple graduate school programs, you should tailor your personal statement to each application.
Some applications provide a prompt or question. In this case, you might have to write a new personal statement from scratch: the most important task is to respond to what you have been asked.
If there’s no prompt or guidelines, you can re-use the same idea for your personal statement – but change the details wherever relevant, making sure to emphasize why you’re applying to this specific program.
If the application also includes other essays, such as a statement of purpose, you might have to revise your personal statement to avoid repeating the same information.
The typical length of a personal statement for graduate school applications is between 500 and 1,000 words.
Different programs have different requirements, so always check if there’s a minimum or maximum length and stick to the guidelines. If there is no recommended word count, aim for no more than 1-2 pages.
A statement of purpose is usually more formal, focusing on your academic or professional goals. It shouldn’t include anything that isn’t directly relevant to the application.
A personal statement can often be more creative. It might tell a story that isn’t directly related to the application, but that shows something about your personality, values, and motivations.
However, both types of document have the same overall goal: to demonstrate your potential as a graduate student and show why you’re a great match for the program.
Chicago format doesn’t require you to use any specific font, as long as you choose something readable. A good standard choice is 12 pt Times New Roman.
Both present the exact same information – the only difference is the placement of the year in source citations:
There are also other types of bibliography that work as stand-alone texts, such as an annotated bibliography.
Turabian style is a version of Chicago style designed specifically for students and researchers. It follows most Chicago conventions, but also adds extra guidelines for formatting research papers, theses and dissertations.
More information can be found in A Manual for Writers of Research Papers, Theses, and Dissertations by Kate L. Turabian, now in its ninth edition.
In notes and bibliography style, you use Chicago style footnotes to cite sources; a bibliography is optional but recommended. If you don’t include one, be sure to use a full note for the first citation of each source.
When a source has four or more authors, your in-text citation or footnote should give only the first author’s name followed by “et al.” (Latin for “and others”). This makes your citations more concise.
In your bibliography or reference list, when a source has more than 10 authors, list the first seven followed by “et al.”
Page numbers should be included in your Chicago in-text citations when:
When you’re referring to the overall argument or general content of a source, it’s unnecessary to include page numbers.
To create a correctly formatted block quote in Microsoft Word, follow these steps:
If line numbers or page numbers are included in the original source, add these to the citation.
In the list of Works Cited, start with the poet’s name and the poem’s title in quotation marks. The rest of the citation depends on where the poem was published.
Only use line numbers in an MLA in-text citation if the lines are numbered in the original source. If so, write “lines” in the first citation of the poem, and only the numbers in subsequent citations.
If the quote includes line breaks, mark these using a forward slash with a space on either side. Use two slashes to indicate a stanza break.
If the quote is longer than three lines, set them off from the main text as an MLA block quote. Reproduce the line breaks, punctuation and formatting of the original.
When citing an entire website or online article in APA Style, the in-text citation consists of the author’s last name and year of publication. For example: (Worland & Williams, 2015).
Note that the author can also be an organization. For example: (American Psychological Association, 2019).
Since web pages don’t have page numbers, you don’t include a locator in the in-text citation.
Sources with 3–5 authors are written in full the first time and shortened from the second citation onwards. Sources with 6+ authors are always shortened, even the first time.
Whether you’re publishing a blog, submitting a research paper, or even just writing an important email, there are a few techniques you can use to make sure it’s error-free:
If you want to be confident that an important text is error-free, it might be worth choosing a professional proofreading service instead.
Editing and proofreading are different steps in the process of revising a text.
Editing comes first, and can involve major changes to content, structure and language. The first stages of editing are often done by authors themselves, while a professional editor makes the final improvements to grammar and style (for example, by improving sentence structure and word choice).
Proofreading is the final stage of checking a text before it is published or shared. It focuses on correcting minor errors and inconsistencies (for example, in punctuation and capitalization). Proofreaders often also check for formatting issues, especially in print publishing.
The cost of proofreading depends on the type and length of text, the turnaround time, and the level of services required. Most proofreading companies charge per word or page, while freelancers sometimes charge an hourly rate.
For proofreading alone, which involves only basic corrections of typos and formatting mistakes, you might pay as little as $0.01 per word, but in many cases, your text will also require some level of editing, which costs slightly more.
It’s often possible to purchase combined proofreading and editing services and calculate the price in advance based on your requirements.
There are many different routes to becoming a professional proofreader or editor. The necessary qualifications depend on the field – to be an academic or scientific proofreader, for example, you will need at least a university degree in a relevant subject.
For most proofreading jobs, experience and demonstrated skills are more important than specific qualifications. Often your skills will be tested as part of the application process.
To learn practical proofreading skills, you can choose to take a course with a professional organization such as the Society for Editors and Proofreaders. Alternatively, you can apply to companies that offer specialized on-the-job training programmes, such as the Scribbr Academy.
Articles in newspapers and magazines can be primary or secondary depending on the focus of your research.
In historical studies, old articles are used as primary sources that give direct evidence about the time period. In social and communication studies, articles are used as primary sources to analyze language and social relations (for example, by conducting content analysis or discourse analysis).
If you are not analyzing the article itself, but only using it for background information or facts about your topic, then the article is a secondary source.
A fictional movie is usually a primary source. A documentary can be either primary or secondary depending on the context.
If you are directly analyzing some aspect of the movie itself – for example, the cinematography, narrative techniques, or social context – the movie is a primary source.
If you use the movie for background information or analysis about your topic – for example, to learn about a historical event or a scientific discovery – the movie is a secondary source.
To determine if a source is primary or secondary, ask yourself:
Some types of source are nearly always primary: works of art and literature, raw statistical data, official documents and records, and personal communications (e.g. letters, interviews). If you use one of these in your research, it is probably a primary source.
Anything that summarizes, evaluates or interprets primary sources can be a secondary source. If a source gives you an overview of background information or presents another researcher’s ideas on your topic, it is probably a secondary source.
Common examples of primary sources include interview transcripts, photographs, novels, paintings, films, historical documents, and official statistics.
Anything you directly analyze or use as first-hand evidence can be a primary source, including qualitative or quantitative data that you collected yourself.
The easiest way to set up APA format in Word is to download Scribbr’s APA format Word template. This will make sure that:
In addition, you’ll have an easy-to-follow structure with examples and useful links to more information.
There are many guidelines and exceptions when citing sources in APA format. The easiest and most effective way of citing in APA format is by using Scribbr’s free APA Citation Generator. This is how it works:
APA is a publication manual widely used by professionals, researchers and students in the social and behavioural sciences, including fields like education, psychology, and business.
Be sure to check the guidelines of your university or the journal you want to be published in before applying APA format.
Page numbers should be right aligned in the header (top of the page). Don’t forget to set the font to Times New Roman, size 12.
If you’ve correctly cited all the sources you used, then you do not need to use a plagiarism checker before submitting your paper to your instructor. However, if you want to be sure that you didn’t forget to cite anything, then you can use a plagiarism checker yourself.
To help you, we compared popular plagiarism checkers to find out which one is best.
Although it sounds contradictory, you can indeed plagiarize yourself. This is called self-plagiarism. Self-plagiarism goes against the expectations of the reader that the paper you submitted is new.
You can plagiarize yourself by, for instance:
Although self-plagiarism is often unintentional, it can have serious consequences. Be sure to cite your previous work or discuss the decision to use your old paper with your professor.
Plagiarism is the act of using someone else’s work or ideas without crediting the original author and thereby pretending it’s your own.
Paraphrasing means rephrasing the original text in your own words.
When using someone else’s work, you can either quote or paraphrase it to prevent plagiarism. Paraphrase a text if you want to clarify or shorten the original text. Quote the text if you want to keep the exact wording and meaning of the original source.
Unfortunately, as a student, you cannot use Turnitin for free. Turnitin only makes its plagiarism prevention software available to universities and other institutions. If you’re a representative of a university you can contact the sales department of Turnitin.
For students, a good alternative to Turnitin is the Scribbr Plagiarism Checker. Prices depend on the size of your document and start at $18.95.
For this price, students receive a full report that highlights the similarities in the text, displays a plagiarism percentage, and includes a list of the sources found.
If you correctly cite the source you do not commit plagiarism. However, the word ‘correct’ is vital in this sentence. In order to avoid plagiarism you must adhere to the guidelines of your citation style (e.g. APA citation style or MLA citation style).
Plagiarism checker software can be used to check your text for plagiarism. This software compares your text with billions of webpages, books and articles.
The accuracy depends on the plagiarism checker you use. Scribbr is the most accurate plagiarism checker. Many free plagiarism checkers fail to detect all plagiarism or falsely flag text as plagiarism.
Take a look at this comparison of free and paid plagiarism checkers for students to find the most accurate plagiarism checker.
The accuracy is determined by two factors: the algorithm (which recognizes the plagiarism) and the size of the database (with which your document is compared).
Many free plagiarism checkers only check your paper against websites – not against books, journals or papers previously submitted by other students. Therefore, these plagiarism checkers are not very accurate, as they miss a lot of plagiarism.
Most plagiarism checkers are only able to detect “direct plagiarism”, or instances where the sentences are exactly the same as in the original source. However, a good plagiarism checker is also able to detect “patchwork plagiarism” (sentences where some words are changed or synonyms are used).
If you’re a student, then you might fail the course, be suspended or expelled, or be obligated to attend a workshop on plagiarism. It depends on whether it’s your first offense or whether you’ve done it before.
As an academic or professional, the consequences are more serious. Aside from the fact that plagiarizing seriously damages your reputation, you might also lose your research funding and/ or your job.
Plagiarizing is a serious offense, and knowing how to avoid plagiarism is therefore important. Read more about the consequences of plagiarism and use a plagiarism checker to detect plagiarism yourself.
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The Scribbr Plagiarism Checker is powered by elements of Turnitin’s Similarity Checker, namely the plagiarism detection software and the Internet Archive and Premium Scholarly Publications content databases.