Tuesday, May 27, 2014

Paired t-Test – Effect Size in Excel 2010, and Excel 2013

This is one of the following seven articles on Paired (2-Sample Dependent) t-Tests in Excel

Paired t-Test in 4 Steps in Excel 2010 and Excel 2013

Excel Normality Testing of Paired t-Test Data

Paired t-Test Excel Calculations, Formulas, and Tools

Paired t-Test – Effect Size in Excel 2010, and Excel 2013

Paired t-Test – Test Power With G-Power Utility

Wilcoxon Signed-Rank Test in 8 Steps As a Paired t-Test Alternative

Sign Test in Excel As A Paired t-Test Alternative

 

Effect Size of a Paired

t-Test in Excel

Effect size in a t-Test is a convention of expressing how large the difference between two groups is without taking into account the sample size and whether that difference is significant.

Effect size of Hypotheses Tests of Mean is usually expressed in measures of Cohen’s d. Cohen’s d is a standardized way of quantifying the size of the difference between the two groups. This standardization of the size of the difference (the effect size) enables classification of that difference in relative terms of “large,” “medium,” and “small.”

A large effect would be a difference between two groups that is easily noticeable with the measuring equipment available. A small effect would be a difference between two groups that is not easily noticed.

Effect size for a paired (two-dependent-sample) t-Test is a method of expressing the difference between the sample mean, x_bardiff, and the Constant in a standardized form that does not depend on the sample size.

Remember that the Test Statistic (the t Value) for a paired t-Test calculated by the following formula:

paired t-test, t-test, effect size, excel, excel 2010, excel 2013, statistics,paired t test,cohens d,cohen's d
(Click on Image To See a Larger Version)

since

paired t-test, t-test, effect size, excel, excel 2010, excel 2013, statistics,paired t test,cohens d,cohen's d
(Click on Image To See a Larger Version)

then

paired t-test, t-test, effect size, excel, excel 2010, excel 2013, statistics,paired t test,cohens d,cohen's d
(Click on Image To See a Larger Version)

The t Value specifies the number of Standard Errors that the sample mean, x_bardiff, is from the Constant. The t Value is dependent upon the sample size, n. The t Value determines whether the test has achieved statistical significance and is dependent upon sample size. Achieving statistical significance means that the Null Hypothesis (H0: x_bar = Constant) has been rejected.

The Effect Size, d, for a paired-sample t-Test is a very similar measure that does not depend on sample size and has the following formula:

paired t-test, t-test, effect size, excel, excel 2010, excel 2013, statistics,paired t test,cohens d,cohen's d(Click on Image To See a Larger Version)

A test’s Effect Size can be quite large even though the test does not achieve statistical significance due to small sample size.

If the t Value has already been calculated, the Effect Size can be quickly calculated by the following formula:

paired t-test, t-test, effect size, excel, excel 2010, excel 2013, statistics,paired t test,cohens d,cohen's d
(Click on Image To See a Larger Version)

The d measured here is Cohen’s d for a paired t-Test. The Effect Size is a standardized measure of size of the difference that the t-Test is attempting to detect. The Effect Size for a paired t-Test is a measure of that difference in terms of the number of sample standard deviations. Note that sample size has no effect on Effect Size. Effect size values for the paired t-Test are generalized into the following size categories:

d = 0.2 up to 0.5 = small Effect Size

d = 0.05 up to 0.8 = medium Effect Size

d = 0.8 and above = large Effect Size

In this example, the Effect Size is calculated as follows:

d = |x_bar diff – Constant| / sdiff = |–3.35- 0| / 6.40 = 0.523

An effect size of d = 0.523 is considered to be a medium effect.

 

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