Posted by
Richard Ristow on
Mar 27, 2007; 12:19am
URL: http://spssx-discussion.165.s1.nabble.com/Levene-test-with-large-sample-tp1074661p1074662.html
At 06:03 PM 3/23/2007, Stephen Salbod wrote:
>Which t test do I want to report?
>
>I have two groups:
>
>Group1 n= 1,512 M=2.5668 SD1=.80339
>Group2 n= 273 M=2.3187 SD2=.96877
>
>Levene's Test for Equality of Variance F= 27.531, p<.0001.
>
>1) Equal Variances Assumed t(1783) = 4.542, p <.001.
>2) Equal Variances NOT Assumed t(342.79) = 3.991.
>
>Can Levene's result be ignored because of the large sample or is it
>recommended that I report t test #2?
As others have noted, the simplest answer is, the test says different
variances, you test assuming different variances. So far, so good,
especially as it doesn't change anything of note.
Now, you wrote,
>The large N has created a statistically significance difference out of
>a trivial difference
That's the more interesting thing going on here: N is large enough that
the old-school 'whether' test (i.e., for a significant difference)
needs to be replaced by 'how much' tests (i.e., confidence intervals).
Perhaps something like that should be done regarding Levene's test:
variances within a certain ratio of each other may be treated as equal,
even if 'significantly' different.
In any case, simply reporting the t-test isn't illuminating, for the
same reason. More like the following (based on generated data whose
population parameters match the estimates you posted):
a. Yes, the between-groups effect is strongly significant (p<.001)
b. However, that is not much of the observed variance (R^2=.011)
c. The best estimate of the difference between groups is
.242 (95% CI, .137 to .346). Whether that's of practical significance,
depends on the study.
SPSS 15 draft output, heavily edited to shorten lines:
UNIANOVA
OBSERVE BY GROUP
/METHOD = SSTYPE(3)
/INTERCEPT = INCLUDE
/PRINT = DESCRIPTIVE OPOWER PARAMETER HOMOGENEITY
/CRITERIA = ALPHA(.05)
/DESIGN = GROUP .
Univariate Analysis of Variance
|-----------------------------|---------------------------|
|Output Created |26-MAR-2007 18:27:30 |
|-----------------------------|---------------------------|
[Salbod]
Between-Subjects Factors [suppressed - see descriptives]
Descriptive Statistics
Dependent Variable: OBSERVE
|-----|------|--------------|----|
|GROUP|Mean |Std. Deviation|N |
|-----|------|--------------|----|
|1 |2.5724|.77670 |1512|
|2 |2.3308|.96286 |273 |
|-----|------|--------------|----|
|Total|2.5355|.81232 |1785|
|-----|------|--------------|----|
Levene's Test of Equality of Error Variances(a)
Dependent Variable: OBSERVE
|------|---|----|----|
|F |df1|df2 |Sig.|
|------|---|----|----|
|18.996|1 |1783|.000|
|------|---|----|----|
Tests the null hypothesis that the error variance of the
dependent variable is equal across groups.
a Design: Intercept+GROUP
Tests of Between-Subjects Effects
Dependent Variable: OBSERVE
|----------|-----------|----|--------|--------|----|--------|---------|
|Source |Type III |df |Mean |F |Sig.|Noncent.|Observed |
| |Sum of | |Square | | |Param. |Power(a) |
| |Squares | | | | | | |
|----------|-----------|----|--------|--------|----|--------|---------|
|Corrected |13.498(b) |1 |13.498 |20.682 |.000|20.682 |.995 |
|Model | | | | | | | |
|----------|-----------|----|--------|--------|----|--------|---------|
|Intercept |5559.515 |1 |5559.515|8518.133|.000|8518.133|1.000 |
|----------|-----------|----|--------|--------|----|--------|---------|
|GROUP |13.498 |1 |13.498 |20.682 |.000|20.682 |.995 |
|----------|-----------|----|--------|--------|----|--------|---------|
|Error |1163.707 |1783|.653 | | | | |
|----------|-----------|----|--------|--------|----|--------|---------|
|Total |12652.135 |1785| | | | | |
|----------|-----------|----|--------|--------|----|--------|---------|
|Corrected |1177.206 |1784| | | | | |
|Total | | | | | | | |
|----------|-----------|----|--------|--------|----|--------|---------|
a Computed using alpha = .05
b R Squared = .011 (Adjusted R Squared = .011)
Parameter Estimates
Dependent Variable: OBSERVE
|---------|-----------|------|-------|------|----------------|----------|---------|
|Parameter|B |Std. |t |Sig. |95%
Confidence |Noncent. |Observed |
| | |Error | | |Interval |Parameter
|Power(a) |
|
|-----------|------|-------|------|--------|-------|----------|---------|
| | | | | |Lower |Upper |
| |
| | | | | |Bound |Bound |
| |
|---------|-----------|------|-------|------|--------|-------|----------|---------|
|Intercept|2.331 |.049 |47.669
|.000 |2.235 |2.427 |47.669 |1.000 |
|---------|-----------|------|-------|------|--------|-------|----------|---------|
|[GROUP=1]|.242 |.053 |4.548 |.000 |.137 |.346 |4.548
|.995 |
|---------|-----------|------|-------|------|--------|-------|----------|---------|
|[GROUP=2]|0(b) |. |. |. |. |. |.
|. |
|---------|-----------|------|-------|------|--------|-------|----------|---------|
a Computed using alpha = .05
b This parameter is set to zero because it is redundant.
===================
APPENDIX: Test data
===================
Since this is randomly-generated data, a separate run will generally
yield somewhat different results. Yeah, I could have put in a SET SEED.
NEW FILE.
INPUT PROGRAM.
. NUMERIC SAMPLE (F3)
/GROUP (F2)
/OBSERVE (F5.2).
. LEAVE SAMPLE
GROUP.
* Characteristics of the generated sample ......... .
. COMPUTE #N1 = 1512 /* N, group 1 */.
. COMPUTE #MEAN1 = 2.5668 /* Mean, group 1 */.
. COMPUTE #SD1 = .80339 /* Std dev., group 1 */.
. COMPUTE #N2 = 273 /* N, group 2 */.
. COMPUTE #MEAN2 = 2.3187 /* Mean, group 2 */.
. COMPUTE #SD2 = .96877 /* Std dev., group 2 */.
. LOOP SAMPLE = 1 TO 1.
. COMPUTE GROUP = 1.
. LOOP #OBSNUM = 1 TO #N1.
. COMPUTE OBSERVE = RV.NORMAL(#MEAN1,#SD1).
. END CASE.
. END LOOP.
. COMPUTE GROUP = 2.
. LOOP #OBSNUM = 1 TO #N2.
. COMPUTE OBSERVE = RV.NORMAL(#MEAN2,#SD2).
. END CASE.
. END LOOP.
. END LOOP.
END FILE.
END INPUT PROGRAM.
DATASET NAME Salbod WINDOW=Front.