To compare the population mean of X across more than two independent groups
Note:
The test variable X must be scale level and normally distributed in all groups
The groups must be independent
H0: All the groups have the same population mean of X.
H1: At least some of the groups have different population mean of X.
There is no one-tailed test for ANOVA.
You want to know if respondents of different income levels have the same answer in X.
H0: The population mean of X is the same across all income groups.
H1: The population mean of X is not the same across all income groups.
Analyze -> Compare Means -> One-Way ANOVA -> Select the dependent variables into the dependent list -> Select the grouping variable as Factor -> Click Post Hoc test and select the tests to use -> Click Options to check Descriptives and Homogeneity of variance test
In the Test of Homogeneity of Variances table, check the Sig. (p-value) of the "Based on Mean" row. A small enough p-value rejects the null hypothesis of the Test of Homogeneity of Variances, indicating that the populations do not have equal variances. In that case, you should go back to the ANOVA options and select Welch, and use the resulting table for conclusion.
Hypotheses for the Homogeneity test (Levene’s Test for Equality of Variances):
H0: All the groups have equal population variance. -> Use the ANOVA table for conclusions.
H1: At least some of the groups have different population variance. -> Use the Robust Tests of Equality of Means table for conclusions.
If the null hypothesis is rejected, i.e., if some of the means are not equal to the others, then the post hoc tests do the pairwise comparison between the samples, and show which two samples have different means. The homogeneity of variance test shows which of post hoc test results we should use. (See below for how to choose a post hoc test under different situations.)
Note: One-way ANOVA is not applicable if there are more than one grouping variables to be used in the comparison at the same time. In that case, you can use Analyze -> General Linear Model -> Univariate. Select the dependent variable and then put the grouping variables into Fixed Factors. Also select the Post Hoc tests and the Plots while necessary. There will be one pair of hypotheses for each grouping variable, and other pairs of hypotheses for the interaction effects. You need to interpret these separately.
Analyses -> ANOVA -> One-Way ANOVA -> Select the dependent variables into the Dependent Variables box -> Select the grouping variable
Under Variances, select Fisher’s when variances are equal, or Welch’s when variances are unequal. (The equality of variance can be tested by using Homogeneity test under Assumption Checks.)
Optionally, under Additional Statistics, select the descriptive statistics or confidence intervals to be shown. Also do the assumption checks if necessary.
Select the appropriate post-hoc tests. (See below for how to choose a post hoc test under different situations.)
Hypotheses for the Homogeneity test (Levene’s Test for Equality of Variances):
H0: All the groups have equal population variance. -> Use Fisher’s ANOVA.
H1: At least some of the groups have different population variance. -> Use Welch’s ANOVA.
Note: One-way ANOVA is not applicable if there are more than one grouping variables to be used in the comparison at the same time. In that case, you can use Analyses -> ANOVA -> ANOVA. Select the dependent variable and then put the grouping variables into Fixed Factors. Also select the Post Hoc tests and the Plots while necessary. There will be one pair of hypotheses for each grouping variable, and other pairs of hypotheses for the interaction effects. You need to interpret these separately.
To select the post-hoc test, first you need to determine if the groups have equal or unequal variables. SPSS provides a number of post-hoc tests to choose from in each case, while Jamovi only provide one in each case. Usually, it would suffice to use the two tests provided by Jamovi, i.e.,
If equal variance is assumed: Use Tukey
If equal variance is not assumed: Use Games-Howell
If however you want to compare your results with literature, then please follow whatever post-hoc test they use. In that case, you may need to use SPSS or R because Jamovi does not provide these tests.
For details of and differences between the different post-hoc tests, please consult your statistics textbook.
If p is not <0.05 (or other significant levels), we take H0 as true, i.e., the population mean of X is the same across all groups.
If p<0.05 (or other significant levels), we take H1 as true, i.e., the population mean of X is not the same across all groups.
Name of the test being used (One-way ANOVA)
The test variable and the grouping variable (or the groups concerned)
The F statistic
The p-value
If p<0.05, then also report the post-hoc test:
The name of the post-hoc test being used
The results of the post-hoc test, showing which groups are different from the others
Your conclusion of the test
Elaboration of the result in your research context