The Single-factor analysis of variance is a hypothesis test that evaluates the statistical significance of the mean differences among two or more sets of scores obtained from a single-factor multiple group design. Also known as one-way ANOVA.

In psychology, the one-way single-factor analysis of variance (ANOVA) is a statistical test used to compare the means of two or more groups on a single variable. This test is used to determine whether there are significant differences between the groups.

Here's an example to illustrate how the one-way single-factor ANOVA works:

Suppose a researcher wants to compare the levels of anxiety in three different groups of participants: Group A, Group B, and Group C. Each group contains 20 participants. The researcher administers an anxiety questionnaire to all participants and obtains scores ranging from 0-100. The researcher wants to determine whether there are any significant differences in anxiety levels between the groups.

To analyze the data using a one-way single-factor ANOVA, the researcher would follow these steps:

1. Calculate the mean anxiety score for each group.
2. Calculate the overall mean anxiety score across all three groups.
3. Calculate the sum of squares between groups (SSB), which represents the variability between the group means.
4. Calculate the sum of squares within groups (SSW), which represents the variability within each group.
5. Calculate the total sum of squares (SST), which represents the total variability in anxiety scores across all participants.
6. Calculate the degrees of freedom (df) for each source of variability.
7. Calculate the F-ratio by dividing the SSB by the SSW.
8. Determine the p-value associated with the F-ratio using a statistical table or software.
9. If the p-value is less than the predetermined alpha level (usually 0.05), reject the null hypothesis and conclude that there are significant differences in anxiety levels between the groups.

For example, if the researcher finds an F-ratio of 4.34 with a p-value of 0.02, they would conclude that there are significant differences in anxiety levels between the three groups.

Overall, the one-way single-factor ANOVA is a useful tool in psychology research for comparing means across multiple groups.

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