0

The data contains two groups and the intended comparison will be completed via independent t-test. Options that I have considered is using the entire sample's mean or one of the group means. However, I am concerned about inflating the differences between the groups. Which method is most ideal and why?

Anya
  • 1
  • 1
    Could you clarify how you propose to use the "entire sample's mean" in your t-test? To what independent set of data would that mean be compared? – whuber Jul 31 '13 at 17:44
  • 1
    To add to @whuber, $t$-tests do not need (or want) normalization of the data. – Frank Harrell Jul 31 '13 at 18:22
  • are you comparing means or variances? If you are scaling and you don't do it right then you can mess up the comparison. – EngrStudent Aug 01 '13 at 01:55

1 Answers1

1

General points

As already stated, by @FrankHarrell t-tests do not require you to convert the raw scores to z-scores.

If you adjust scores in both groups by a constant mean and standard deviation, your t-test and p-value will be unchanged. As long as the standard deviation is greater than zero, this is true whether the means and sds come from group 1, group 2, the overall group means, or some form of reference normative sample.

Thus, the only reason why you might convert to z-scores is that if you or your audience found such a scaling easier to interpret than the raw scores.

Adjusting for age

Thinking more broadly, some researchers in developmental contexts use age-specific test norms. These are typically external to the sample. In such cases, researchers often convert raw scores into some form of age-referenced normative score (e.g., percentile, IQ, z-score, t-score, etc.). If this applies to you, then it makes sense to use these norms to rescale data.

In other cases, researchers use the age data to statistically control for age. ANCOVA with age as a covariate, group as the IV, and test score as the DV is a tradition method for doing this. However, there are many other approaches to controlling for a covariate.

Jeromy Anglim
  • 44,984