I am aware that we should use the t-test for comparing means when the sample size is small and when we do not know the SD of the population and that , the z-test is to be used for comparing means when we have a large sample size and the SD of the population is known.
Now, my sample size is - 400. I don't know the population SD (and I simply cannot understand how is it ever possible to know the population SD, please forgive me for my ignorance and lack of knowledge).
What I do know is, that after data collection I can conduct the Kolmogorov-Smirnov test and the Shapiro-Wilk test(on SPSS) to determine if my sample is a normally distributed one.
I can even check for homogeneity of variance.
But, I will still never know the population SD.
If the sample is a normally distributed one, should I proceed with the z-test? (in spite of not knowing the population SD) or do I just stick to the t-test?
Any help from Professors and fellow researchers will be greatly appreciated!
You can use t-test.
Don't use K-S, S-W, or other tests to check for normality or equality of variance. Instead, plot the histograms or quantile-quantile plots. (Read this on why: http://blog.fellstat.com/?p=61 )
If the variances are not equal in the groups, use Welch's t-test. Some people say to use Welch's t-test routinely whether the variances are equal or not.
You can use t-test.
Don't use K-S, S-W, or other tests to check for normality or equality of variance. Instead, plot the histograms or quantile-quantile plots. (Read this on why: http://blog.fellstat.com/?p=61 )
If the variances are not equal in the groups, use Welch's t-test. Some people say to use Welch's t-test routinely whether the variances are equal or not.
Salvatore S. Mangiafico - Thank you so much Sir for your valuable insight!
There also are more powerful non-parametric methods that compare entire distributions, rather than a single value (e.g., median, mean) between two or more samples. This method requires no distributional assumptions:
- https://odajournal.com/2015/12/02/unioda-vs-t-test-low-brain-uptake-of-l-11c5-hydroxytryptophan-in-major-depression/
- https://odajournal.com/2014/03/27/unioda-vs-students-t-test-comparing-two-migraine-treatments-2/
And this non-parametric method is easily extended to designs involving more than two groups:
- https://odajournal.com/2013/11/19/oda-range-test-vs-one-way-analysis-of-variance-comparing-strength-of-alternative-line-connections/
Here is a brief review of this non-parametric method:
- https://odajournal.com/2017/04/18/what-is-optimal-data-analysis/
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