## 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: (Click On Image and See a larger Version)

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

Excel Master Series Blog Directory

Statistical Topics and Articles In Each Topic

• Histograms in Excel
• Bar Chart in Excel
• Combinations & Permutations in Excel
• Normal Distribution in Excel
• t-Distribution in Excel
• Binomial Distribution in Excel
• z-Tests in Excel
• t-Tests in Excel
• Hypothesis Tests of Proportion in Excel
• Chi-Square Independence Tests in Excel
• Chi-Square Goodness-Of-Fit Tests in Excel
• F Tests in Excel
• Correlation in Excel
• Pearson Correlation in Excel
• Spearman Correlation in Excel
• Confidence Intervals in Excel
• Simple Linear Regression in Excel
• Multiple Linear Regression in Excel
• Logistic Regression in Excel
• Single-Factor ANOVA in Excel
• Two-Factor ANOVA With Replication in Excel
• Two-Factor ANOVA Without Replication in Excel
• Randomized Block Design ANOVA in Excel
• Repeated-Measures ANOVA in Excel
• ANCOVA in Excel
• Normality Testing in Excel
• Nonparametric Testing in Excel
• Post Hoc Testing in Excel
• Creating Interactive Graphs of Statistical Distributions in Excel
• Solving Problems With Other Distributions in Excel
• Optimization With Excel Solver
• Chi-Square Population Variance Test in Excel
• Analyzing Data With Pivot Tables and Pivot Charts
• SEO Functions in Excel
• Time Series Analysis in Excel
• VLOOKUP
• Simplifying Useful Excel Functions

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