An introduction to statistical significance

If a result is statistically significant, that means it’s unlikely to be explained solely by chance or random factors. In other words, a statistically significant result has a very low chance of occurring if there were no true effect in a research study.

The p value, or probability value, tells you the statistical significance of a finding. In most studies, a p value of 0.05 or less is considered statistically significant, but this threshold can also be set higher or lower.

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Effect size in statistics

Effect size tells you how meaningful the relationship between variables or the difference between groups is. It indicates the practical significance of a research outcome.

A large effect size means that a research finding has practical significance, while a small effect size indicates limited practical applications.

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How to write an APA results section

The results section of a quantitative research paper is where you summarize your data and report the findings of any relevant statistical analyses.

The APA manual provides rigorous guidelines for what to report in quantitative research papers in the fields of psychology, education, and other social sciences.

Use these standards to answer your research questions and report your data analyses in a complete and transparent way.

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Standard error in statistics

The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean. It tells you how much the sample mean would vary if you were to repeat a study using new samples from within a single population.

The standard error of the mean (SE or SEM) is the most commonly reported type of standard error. But you can also find the standard error for other statistics, like medians or proportions. The standard error is a common measure of sampling error—the difference between a population parameter and a sample statistic.

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Parameter vs statistic: what’s the difference?

A parameter is a number describing a whole population (e.g., population mean), while a statistic is a number describing a sample (e.g., sample mean).

The goal of quantitative research is to understand characteristics of populations by finding parameters. In practice, it’s often too difficult, time-consuming or unfeasible to collect data from every member of a population. Instead, data is collected from samples.

With inferential statistics, we can use sample statistics to make educated guesses about population parameters.

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The standard normal distribution

The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.

Any normal distribution can be standardized by converting its values into z-scores. Z-scores tell you how many standard deviations from the mean each value lies.

The standard normal distribution has a mean of 0 and a standard deviation of 1.

Converting a normal distribution into a z-distribution allows you to calculate the probability of certain values occurring and to compare different data sets.

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Understanding normal distributions

In a normal distribution, data is symmetrically distributed with no skew. When plotted on a graph, the data follows a bell shape, with most values clustering around a central region and tapering off as they go further away from the center.

Normal distributions are also called Gaussian distributions or bell curves because of their shape.

Bar chart showing a normal distribution of SAT scores

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How to find the median

The median is the value that’s exactly in the middle of a data set when it is ordered. It’s a measure of central tendency that separates the lowest 50% from the highest 50% of values.

The steps for finding the median differ depending on whether you have an odd or an even number of data points. If there are two numbers in the middle of a data set, their mean is the median.

The median is usually used with quantitative data (where the values are numerical), but you can sometimes also find the median for an ordinal data set (where the values are ranked categories).

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How to find the mode

The mode or modal value of a data set is the most frequently occurring value. It’s a measure of central tendency that tells you the most popular choice or most common characteristic of your sample.

When reporting descriptive statistics, measures of central tendency help you find the middle or the average of your data set. The three most common measures of central tendency are the mode, median, and mean.

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