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In this lesson, we have explored some of the similarities and differences between two statistical methods: z-tests and t-tests . Z-tests are statistical calculations that can be used to compare population means to a sample's. T-tests are calculations used to test a hypothesis, but they are most useful when we need to determine if there is a statistically significant difference between two independent sample groups. Generally, z-tests are used when we have large sample sizes (* n* > 30), whereas t-tests are most helpful with a smaller sample size (* n* < 30). Both methods assume a normal distribution of the data, but the z-tests are most useful when the standard deviation is known.

Hello Charles,

Thank you very much for your reply!

1) For experiment 1, both data sets that failed the normality test (p= and p=) are not symmetric, according to the box plot. Therefore, a nonparametric test should be used for the analysis, right?

2) For experiment 2, there are two experimental groups. I only have three values for each group. The data for group A are: , , (normality test P<). The data for group B are: , , (normality test P=). The results from t-test (p=) and Mann-Whitney Rank sum test (p=) are very different.

Thank you!

Mauchly’s test for sphericity can be run in the majority of statistical software, where it tends to be the default test for sphericity. Mauchly’s test is ideal for mid-size samples. It may fail to detect sphericity in small samples and it may over-detect in large samples.

If the test returns a small p-value (p ≤.05), this is an indication that your data has violated the assumption. The following picture of SPSS output for ANOVA shows that the significance “sig” attached to Mauchly’s is .274. This means that the assumption has not been violated for this set of data.

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Mauchly’s test for sphericity can be run in the majority of statistical software, where it tends to be the default test for sphericity. Mauchly’s test is ideal for mid-size samples. It may fail to detect sphericity in small samples and it may over-detect in large samples.

If the test returns a small p-value (p ≤.05), this is an indication that your data has violated the assumption. The following picture of SPSS output for ANOVA shows that the significance “sig” attached to Mauchly’s is .274. This means that the assumption has not been violated for this set of data.