[讨论]Levenes Test

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How should one apply Levene's Test when testing the difference in means between two groups for a large number of variables.

The data consists of replies from two groups of respondents (n=66 and n=21, respectively). All respondents have answered a large number of questions (a battery of 40 similar questions, most of them on a 7-step Likert scale). Now I want to examine whether the two groups are significantly different in their replies.

To do this, I have used the 'Independent-Samples T-test'. For each of the 15 variables SPSS gives me one significance for 'Equal variances assumed' and another significance for 'Equal variances not assumed'. Had I done this test for a single variable only, it would have been straight forward: I would simply have used Levene's Test to determine which of the two assumptions to go with. However, since I have 40 variables to test I am not sure what the correct procedure would be:

a) Should I apply Levene's test independently for each variable and thus use the 'Equal variances assumed' value for some variables and the 'Equal variances not assumed' for others? (The questions are all of the same type, so there is no a priori reason why variances should be equal for some questions but not for others.)

b) Or should I draw the conclusion that since equal variances can not be assumed for SOME of the variables, I should not assume it for ANY of the variables, and thus consistently use the 'Equal variances not assumed' values for all variables?

I am grateful for any guidance you can suggest.

Göran Lindqvist PhD candidate Stockholm School of Economics

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关键词：Levenes levene Even Leve test 讨论 test Levenes

Marta,

I'm curious - are you saying that t-tests are inappropriate for all Likert-based data, or just in the case where n's are dramatically different, as in Goran's study?

TIA,

Fred

Hi Göran, Perhaps this is not the answer you ere expecting to get, but... I would NOT use t-tests (either with equal or unequal variances) with a 7 step Likert scale, but Mann-Whitney's U (distributions roughly equal) or median tests (distributions different). With a sample size of 21 for one group, I don't think you can apply central limit theorem and consider them aproximately normal. That's my opinion.

There are a wide variety of opinions on this. There was a lot of work in the 60's and early 70's showing that likert items are not severely discrepant from interval level. There is some rationale for this being enhanced by including numbers as part of the anchoring. 7 point response scales being less likely to be severely discrepant than 5 point response scales. However, Likert type items are customarily designed to be part of a Likert scale. The summated scale scores are not severely discrepant from interval level. My reservation would be about using a single item as if it were a scale. If you are using them as repeated measures of a few constructs (i.e., as parts of summative scales), I would suggest using scale scores. This is especially so if the items are part of a previously developed scale, but should be considered if you designed the scale ad hoc.. Wrt the question of degrees of freedom for error (based on sample size), the old rule of thumb is for n1 + n2 -2 ge 30. You might consider whether you would be committing the fallacy of precision to report p's to more than 2 places after the decimal point. If the items are all stand-alone, depending where you are publishing, I would suggest that you do the t-tests using the separate variance estimate for consistency. The resulting probabilities should not be very different from separate vs pooled analyses when the DV passes the Levene's test anyway. I would then run the non-parametric test. In a footnote, I would summarize which variables led to differences in the meaning of the conclusions. For some audiences you might simply report something like "all differences were statistically significant at least at .05. This was also true using the non parametric xxx test." Boxplots would be one good way to visualize the results. Art Art@DrKendall.org Social Research Consultants

Hi Fred In my opinion, t-tests are not appropriate for Likert data, unless sample sizes are really big. It's not the difference in n's (this is bad when lack of HOV is found, even for continuous data), it's just the fact that Likert data are ORDINAL, not quantitative. The median is a good central tendency statistic for them, not the mean. Regards Marta

Not only that....one should consider the bounded nature of Likert data.You may want to check out using the Score interval for hypothesis testing. It actually works better than the Wald when sample sizes are small. Check out * A score method of constructing asymmetric confidence intervals for the mean of a rating scale item. Psychol Methods. 2003 Jun;8(2):149-63. * Improving Content Validation Studies Using an Asymmetric Confidence Interval for the Mean of Expert Ratings Randall D. Penfield, Jeffrey M. Miller. Applied Measurement in Education, 2004, Vol. 17, No. 4, Pages 359-370 There is also a forthcoming article in Behavior, Research, Instruments, Methods, & Computers that includes SAS and SPSS code. *Miller, J. M., & Penfield, R. D. Using the score method to construct asymmetric confidence intervals: An SAS program for content validation in scale development *How's that for plugging research in which I've been involved.

Hope it helps! Jeff

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