Is it any point in doing a test for homoscedasticity when the dependent variable is a scale variable and we have one independent as a dichotomous variable? The scatterplot in SPSS is just two lines. What can I interpret from it?
This is regarding testing the assumptions for linear regression. We know that homoscedasticity is related to normality, but dichotomous variables are not considered normally distributed.
Thanks
For an independent-samples t test (or one-way ANOVA) with a dichotomous independent (predictor) variable ("factor") the question here would be whether the dependent variable is normally distributed with equal variances in the two populations that are defined by your dichotomous independent variable. In regression, the question would be whether the errors (residuals) are normally distributed with equal variances in the two populations that are defined by your dichotomous variable.
So, in summary, the issues of normality and homoscedasticity (equal variances) are not about the distribution of the dichotomous independent variable; these issues concern the distribution of the dependent variable in your two groups/two populations.
Christian Geiser thank you.
So in regards to homoscedasticity, what test can be used to see whether the errors are normally distributed with equal variance?
Hello Dilpreet Singh. Please report n, mean and SD for your two groups. Thank you.
You're welcome, Dilpreet Singh. But what I meant was please write another post in which you tell readers of this discussion the mean, n, and SD for each of your groups. Thank you.
Dilpreet Singh , there is not a test to show that the errors are normally distributed with equal variance. The tests are only designed to detect if there are sufficient differences from these to reject them. Try quantile-quantile plots.
For the bivariate case (one dichotomous predictor, one continuous DV), you could examine the Levene test, Bartlett test, or Browne-Forsythe test of equality of variances.
With sample sizes that differ by that much (25 vs 81), I would just use a t-test that does not assume equal (population) variances. You mentioned SPSS earlier. In the output for an unpaired t-test on these data, the line labeled Equal variances not assumed (or something like that) will show you Satterthwaite's t-test. As the label says, it does not assume (or require) homogeneous population variances.
If you have the needed extension command installed, you can also get the result using the summary data, as follows:
SPSSINC SUMMARY TTEST
N1=25 MEAN1=3.64 SD1=2.984 LABEL1="Group 0"
N2=81 MEAN2=7.85 SD2=2.455 LABEL2="Group 1" CI=95.
Just note that the table showing 95% CIs is a bit confusing--or at least I found it confusing when I first saw it. The top section (labeled Asymptotic) uses a critical z-value when computing the CIs. The lower section (labeled Exact) uses a critical t-value, which is the usual approach!
Christian Geiser but is Levene's test appropriate to test the assumption for homoscedasticity for linear regression, or is it just t-tests?
Christian Geiser and Bruce Weaver
My professor told me today that homoscedasticity is not relevant because there's a low probability of random measurement error for one dichotomous variable, what's your opinion on that?
Thanks
The issue of homoscedasticity is separate from the question of measurement error. When your group variances are different and your group sample sizes vary greatly also, the results of your regular t test may be compromised. In that case, I would follow @Bruce Weaver's suggestion and pick the "equal variances not assumed" robust version of the test.
With random coefficient models and a dichotomous predictor variable you have a single overall model that differs in the fixed part (effectively two means) and differs in the random part (two variances). This approach models heteroscedasticity directly and the estimated standard errors of the fixed part take account of this. It is also possible to have a set of means and variances associated with a polychotomous predictor. You can also condition on other categorical and continuous variables and further nested and non-nested structures.
This paper discusses this conceptually
Article Modelling Complexity: Analysing Between-Individual and Betwe...
and this manual gives practical applications.
Book Developing multilevel models for analysing contextuality, he...
I would argue that the modelling approach is much more flexible than just testing for heteroscedasticity.
I just noticed that one of Dilpreet Singh's questions has not been explicitly addressed. Dilpreet asked, "is Levene's test appropriate to test the assumption for homoscedasticity for linear regression, or is it just t-tests?"
The linear regression model in question has one dichotomous explanatory variable. In that case, it is equivalent to the pooled variances version of the unpaired t-test. Here is an example that demonstrates the equivalence. Copy the code, paste it into a syntax window, execute it, and then study the output. HTH.
* Unpaired t-test example from this web page:
* https://stats.oarc.ucla.edu/spss/output/t-test/
* Download the data file from a link near the top of the page.
GET FILE='C:\bw\SPSS\data\UCLA\hsb2.sav'.
t-test groups=female(0 1) /variables=write.
* Now estimate a simple linear regression model
* with X = female and Y = write.
REGRESSION
/STATISTICS COEFF OUTS CI(95) R ANOVA
/DEPENDENT write
/METHOD=ENTER female.
* The constant = the mean when female=0, i.e., the mean for males.
* The coefficient for female shows the change in Y-prime when
* variable female increases from 0 to 1. I.e., it shows the
* change in the mean write score when we move from looking at
* males to looking at females. In other words, it shows the
* Female-Male mean difference.
* Notice that the coefficient for Female and the t-value have
* the same magnitude as the mean difference and t-value from
* the t-test command we ran earlier, but with the opposite signs.
* To make t-test show the same sign, we can reverse the
* order in which we list the group values.
t-test groups=female(1 0) /variables=write.
* Now the signs match what we see in the REGRESSION output.
If you have only one dichotomous variable in your regression model, then the test for homoscedasticity is not necessary.
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