# Null hypothesis

## The null hypothesis states that there is no difference or association

With hypothesis testing, the null hypothesis states that there is no difference or association between variables of interest. In the classical sense of hypothesis testing, researchers are not trying to prove that their research hypothesis true, they are trying to prove if the null hypothesis is true or untrue.

This is the reason for interpreting statistical findings as either "do not reject" the null hypothesis, meaning that there is no difference or association, or "reject" the null hypothesis, meaning that there is a difference or association. The focus is on proving the null hypothesis as correct, where there is not a statistically significant effect, or proving that the null hypothesis is incorrect, where there is a statistically significant effect.

When statistical significance is NOT achieved in the context of hypothesis testing (p > .05), then researchers "reject" the null hypothesis. This means that researchers have NOT found a significant difference/association/effect, and therefore do not reject the idea that there is NO difference/association/effect. Even though statistical significance was not achieved, there IS STILL EVIDENCE! The evidence that is yielded is that there is no difference/association/effect. This is still solid evidence generated by the study.

This is the reason for interpreting statistical findings as either "do not reject" the null hypothesis, meaning that there is no difference or association, or "reject" the null hypothesis, meaning that there is a difference or association. The focus is on proving the null hypothesis as correct, where there is not a statistically significant effect, or proving that the null hypothesis is incorrect, where there is a statistically significant effect.

When statistical significance is NOT achieved in the context of hypothesis testing (p > .05), then researchers "reject" the null hypothesis. This means that researchers have NOT found a significant difference/association/effect, and therefore do not reject the idea that there is NO difference/association/effect. Even though statistical significance was not achieved, there IS STILL EVIDENCE! The evidence that is yielded is that there is no difference/association/effect. This is still solid evidence generated by the study.

### Null hypothesis and between-subjects research design

The null hypothesis is stated in different fashions according to the number of groups being compared in between-subjects research designs.

For between-subjects designs with one group, the null hypothesis states that there is no difference between the expected proportion (categorical outcome), median (ordinal outcome), or mean (continuous outcome) and the observed proportion, median, or mean.

For between-subjects designs with two groups, the null hypothesis states that there is no difference between the proportions (categorical outcome), medians (ordinal outcome), or means (continuous outcome) of the two groups.

For between-subjects designs with three or more groups, the null hypothesis states that there is no difference between the proportions (categorical outcome), medians (ordinal outcome), or means (continuous outcome) of the three or more groups.

For between-subjects designs with one group, the null hypothesis states that there is no difference between the expected proportion (categorical outcome), median (ordinal outcome), or mean (continuous outcome) and the observed proportion, median, or mean.

For between-subjects designs with two groups, the null hypothesis states that there is no difference between the proportions (categorical outcome), medians (ordinal outcome), or means (continuous outcome) of the two groups.

For between-subjects designs with three or more groups, the null hypothesis states that there is no difference between the proportions (categorical outcome), medians (ordinal outcome), or means (continuous outcome) of the three or more groups.

### Null hypothesis and within-subjects research design

For within-subjects research designs, the null hypothesis is stated in a fashion that reflects the number of observations of an outcome that are being analyzed.

For within-subjects designs with two groups, the null hypothesis states that there is no difference between the "pre" and "post" observations of proportions (categorical outcome), medians (ordinal outcome), or means (continuous outcome).

For within-subjects designs with three groups, the null hypothesis states that there is no difference between the "pre," "post," and "maintenance" observations of proportions (categorical outcome), medians (ordinal outcome), or means (continuous outcome).

For within-subjects designs with two groups, the null hypothesis states that there is no difference between the "pre" and "post" observations of proportions (categorical outcome), medians (ordinal outcome), or means (continuous outcome).

For within-subjects designs with three groups, the null hypothesis states that there is no difference between the "pre," "post," and "maintenance" observations of proportions (categorical outcome), medians (ordinal outcome), or means (continuous outcome).

### Null hypothesis and correlation design

When writing the null hypothesis for a correlation design, it states that there is no association between the two variables that you are correlating. The expected correlation for the null hypothesis is equal to zero, "0."

### Null hypothesis and multivariate design

Though oftentimes not stated at all, the null hypothesis for a multivariate design using some form of regression is that the slope is zero, "0." If there is no relationship between variables in a regression model, the slope will equal zero.

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