Saturday, May 31, 2014

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

This is one of the following six articles on 1-Sample t-Tests in Excel

1-Sample t-Test in 4 Steps in Excel 2010 and Excel 2013

Excel Normality Testing For the 1-Sample t-Test in Excel 2010 and Excel 2013

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

1-Sample t-Test Power With G*Power Utility

Wilcoxon Signed-Rank Test in 8 Steps As a 1-Sample t-Test Alternative in Excel 2010 and Excel 2013

Sign Test As a 1-Sample t-Test Alternative in Excel 2010 and Excel 2013

 

Effect Size of a One-

Sample t-Test in Excel

Effect size for a one-sample t-Test is a method of expressing the difference between the sample mean, x_bar, 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 one-sample t-Test calculated by the following formula:

effect size, t test, t-test, excel, excel 2010, excel 2013, statistics
(Click On Image and See a larger Version)

since SE = (Sample mean) / SQRT(Sample Size) = s/SQRT(n)

effect size, t test, t-test, excel, excel 2010, excel 2013, statistics
(Click On Image and See a larger Version)

The t Value specifies the number of Standard Errors that the sample mean, 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 (H0: x_bar = Constant) has been rejected.

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

effect size, t test, t-test, excel, excel 2010, excel 2013, statistics
(Click On Image and 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:

effect size, t test, t-test, excel, excel 2010, excel 2013, statistics
(Click On Image and See a larger Version)

The d measured here is Cohen’s d for a one-sample 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 one-sample 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 one-sample 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 – Constant| / s = |200,000 – 186,000| / 29,736.68 = 0.471

An effect size of d = 0.471 is considered to be a small effect.

 

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1 comment:

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