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.
The most common scenarios (and what to do) are:
A standard MLA Works Cited entry is structured as follows:
Only relevant information is included in the reference.
The research methods you use depend on the type of data you need to answer your research question.
Statistical significance occurs when an observed pattern in the data is unlikely to have happened by chance (i.e. it falls outside of the range of values predicted by the null hypothesis).
Significance is usually denoted by a probability value (p-value). When this falls below a certain alpha value, then we say the result of the test is statistically significant. The alpha value is often set at 0.05 – that is, when there is a less than 5% probability that the result could have happened by chance.
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.
For example, in an experiment about the effect of salt addition on plant health, confounding variables could include pot size and soil type, which might affect plant health as much as or more than salt addition. These variables need to be held constant to allow you to measure the true effect of the variable you are interested in.
In your experimental design, it’s important to identify potential confounding variables and plan how you will control for them.
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).
Independent variables are the variables you manipulate in an experiment, and dependent variables are variables which represent the outcome of the experiment.
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.
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.
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.
Statistical sampling allows you to test a hypothesis about the characteristics of a population. There are various sampling methods you can use to ensure that your sample is representative of the population as a whole.
Quantitative methods allow you to test a hypothesis by systematically collecting and analyzing data. Common methods include experiments, observations recorded as numbers, and surveys with closed-ended questions.
Qualitative methods allow you to explore ideas and experiences in depth. Common methods include interviews with open-ended questions, observations described in words, and literature reviews that explore concepts and theories.
Qualitative methods tend to be more flexible, while quantitative methods are more reproducible.
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.
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.