I need a little help understanding my statistics. I ran the regular ANOVA for three groups of unequal n and got a P value of .415, which is way higher than the alpha .05 and meant that I would not reject Ho and conclude that there is not a significant difference in the means of the three groups. Then, I got worried about type II error, ran a modified Levene ANOVA, and got a P value of .046. Should I use the Levene's?
Hello Seth. I've never heard the term modified Levene ANOVA before. I wonder if you meant you decided (on the basis of Levene's test for equality of variances) that you could not assume homogeneity of variance, and therefore decided to use a method that does not assume/require homogeneity of variance--e.g., the Brown-Forsyth method, or Welch's method (both available as options for the ONEWAY command in SPSS).
If you post basic descriptive stats (n, mean, SD) for each group, readers will be able to estimate the model themselves and perhaps have a better understanding of what's going on. And if you indicate which software you are using, respondents may be able to give more precise help.
HTH.
Perhaps this can be of help
Article StaTips Part I: Choosing statistical test when dealing with ...
Hello Seth. I've never heard the term modified Levene ANOVA before. I wonder if you meant you decided (on the basis of Levene's test for equality of variances) that you could not assume homogeneity of variance, and therefore decided to use a method that does not assume/require homogeneity of variance--e.g., the Brown-Forsyth method, or Welch's method (both available as options for the ONEWAY command in SPSS).
If you post basic descriptive stats (n, mean, SD) for each group, readers will be able to estimate the model themselves and perhaps have a better understanding of what's going on. And if you indicate which software you are using, respondents may be able to give more precise help.
HTH.
1. "Type II error" is a red herring here. The time to think about that
is *before you collect any data*. You input your planned sample sizes
and wished-for difference into a power analysis and see if you have
the power you want. (Typically, this analysis would assume that a
regular ANOVA is appropriate; if it turns out that it is not, you will
probably want larger sample sizes than an ANOVA would.)
2. Before you do *any* testing, *always* look at your data. In this
case, something like side-by-side boxplots are ideal. Look at these in
terms of the assumptions you are making about your data: in the case
of one-way ANOVA, are the distributions of values within each group
approximately normal? Are the spreads (heights of boxes on boxplot)
approximately the same for each group? Are there any outliers? Use
this to determine whether you are justified in doing a regular ANOVA,
whether you need a transformation first, or whether you need something
like Mood's Median test (comparing medians rather than means). Then
pick a test, do it, and abide by the results.
3. Choosing to do another test because you didn't like the P-value
from the first one is called "P-value hacking", and is bad
science. This is because the P-value you see from the second and
subsequent tests is wrong: it doesn't reflect the process you carried
out.
4. I too have not heard of "modified Levene ANOVA". Are you sure
you're not running Levene's test, which is a (reputable) test that the
groups all have the same variance?
The Levene test* is a test of homogeneity of variance (strictly a testing strategy as there are various ways to formulate the test). If the Levene test in your computer output it statistically significant you have detected a differences in the variances of the groups.
Bruce's suggestion to report mean n and SD by group should help.
* The Levene test is in fact a form of modified ANOVA in which the absolute deviations from the group average (usually mean or median) are analysed rather than the raw scores.
@ Thom, good point about how Levene's test is computed! Perhaps that is what Seth meant.
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Modeling
- Analyses of Variance
- ANOVA