On-line statistics

Null and Alternative Hypotheses

For the z-test, t-tests, Mann-Whitney U, Wilcoxon matched pairs and one-way ANOVA for two samples the H_O would be:

H_O: there are no differences between the means of the samples () (median₁ =median₂ for non-parametric)

Or:

H_O: there is no difference between brain sizes of male and female university students

The H_A would be:

H_A: there is a difference between the means of the two samples () (median₁?median₂)

Or:

H_A: the brain sizes of male and female university students differ

Where you have more than two samples in an ANOVA, Kruskal-Wallis or multiple comparison test the hypotheses should read something like this:

H_O: there are no differences between the means of the samples ()(median1=median2=median3.)

H_A: there is a difference between the means of the two samples ()(median1≠median2≠median3..)

For two-way ANOVA the hypotheses must be something like this:

H_O1: There are no significant differences between the effects of the hormones on the growth of the animals

H_A1: There are significant differences between the effects of the hormones on the growth of the animals

 

H_O2: There are no significant differences between the weights of male and female animals

H_A2: There are significant differences between the weights of male and female animals

 

H_O3: There is no significant interaction between the effects of hormones and sex

H_A3: There is a significant interaction between the effects of hormone and sex

Spearman's rank, Pearson's product moment and linear regression tests compare the slope of the line with zero (zero being no correlation). Therefore the hypotheses are as follows:

H_O: There is no significant difference between the slope of the line and zero ()

Or

H_O: there is no correlation between the samples

 

H_A: There is a significant difference between the slope of the line and zero ()

Or

H_A: There is a correlation (relationship) between the two samples

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