This is one of the following eight articles on 2-Independent-Sample Pooled t-Tests in Excel

2-Independent-Sample Pooled t-Test in 4 Steps in Excel 2010 and Excel 2013

Two-Independent-Sample Pooled t-Test - All Excel Calculations

2-Sample Pooled t-Test – Effect Size in Excel 2010 and Excel 2013

2-Sample Pooled t-Test Power With G*Power Utility

2- Sample Pooled t-Test = Single-Factor ANOVA With 2 Sample Groups

# Effect Size of a Two-

Sample Pooled 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 two-independent-sample, pooled t-Test is a method of expressing the distance between the difference between sample mean, x_bar** _{1}**-x_bar

**, and the Constant in a standardized form that does not depend on the sample size.**

_{2}Remember that the Test Statistic (the t Value) for a two-independent-sample t-Test calculated by the following formula:

*(Click On Image To See a Larger Version)*

which equals

** **

*(Click On Image To See a Larger Version)*

since

*(Click On Image To See a Larger Version)*

*(Click On Image To See a Larger Version)*

Since degrees of freedom for a two-independent-sample, pooled t-Test equals the following:

df = n_{1} + n_{2} – 2

*(Click On Image To See a Larger Version)*

The t Value specifies the number of Standard Errors that the differences between sample means, x_bar** _{1}**-x_bar

**, 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 (H**

_{2}_{0}: x_bar

**-x_bar**

_{1}**= Constant = 0) has been rejected.**

_{2}The t Value for a two-independent-sample, pooled is calculated as follows:

** ***(Click On Image To See a Larger Version)*

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

*(Click On Image To See a Larger Version)*

s_{pooled} pools the sample standard deviations based upon the proportion of combined samples that each of the sample sizes n_{1} and n_{2} represent and not the absolute values of n_{1} and n_{2}. s_{pooled} is therefore not directly dependent on sample sizes n_{1} and n_{2}.

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:

*(Click On Image To See a Larger Version)*

The d measured here is Cohen’s d for a two-independent-sample, pooled 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 two-independent-sample, pooled 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 two-independent-sample, pooled 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** _{1}** - x_bar

**– Constant| / s**

_{2}_{pooled}= |43.56 – 33.53 – 0| / 16.09 = 0.623

An Effect Size of d = 0.623 is considered to be a medium effect.

**Excel Master Series Blog Directory**

Statistical Topics and Articles In Each Topic

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- Test Power of a 2-Independent Sample Unpooled t-Test With G-Power Utility

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