## Friday, May 30, 2014

### Two-Sample t-Test - All Excel Calculations

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

Excel Variance Tests: Levene’s, Brown-Forsythe, and F Test For 2-Sample Pooled t-Test in Excel 2010 and Excel 2013

Excel Normality Tests Kolmogorov-Smirnov, Anderson-Darling, and Shapiro Wilk Tests For Two-Sample Pooled t-Test

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

Mann-Whitney U Test in 12 Steps in Excel as 2-Sample Pooled t-Test Nonparametric Alternative in Excel 2010 and Excel 2013

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

# All Excel Calculations For the Two-Sample Pooled t- Test

This two-independent-sample, Pooled t-Test can be solved much quicker using the following Excel data analysis tool:

t-Test: Assuming Equal Variances

Before this test is employed, all required assumptions such as normality of data must be verified as was done.

The two-independent sample, pooled t-Test can be quickly solved in Excel using either the Data Analysis tool or the formula that are both specific for this test. The Excel tool can be found by clicking Data Analysis under the Data tab. The tool is titled t-Test:Two-Sample Assuming Equal Variances. The entire Data Analysis Toolpak is an add-in that ships with Excel but must first be activated by the user before it is available. This tool will be applied to the following data set using the same data as the preceding example in this section.

As mentioned, the data should be input with the sample having the largest mean being designated as the sample group. Doing so ensures that the Excel output will have the same signs for the t Value and Critical t Value. If the sample with the smallest mean is input is the first sample, the t Value will correctly be negative but the Critical t Value will be incorrectly listed by Excel as being positive.

Following are screen shots of how the data should be entered: (Click On Image To See a Larger Version)

The completed dialogue box for this tool is shown as follows: (Click On Image To See a Larger Version)

Clicking OK will produce the following result. This result agrees with the calculations that were performed in this section. (Click On Image To See a Larger Version)

The calculations to create the preceding output were performed as follows. The individual outputs are color-coded so it is straight-forward to match the calculations with the outputs of the tool. (Click On Image To See a Larger Version) (Click On Image To See a Larger Version) (Click On Image To See a Larger Version)

## Excel Statistical Function Shortcut

Another very quick way to perform this t-Test is to calculate the p value and compare it to Alpha (for a one-tailed test) or Alpha/2 for a two-tailed test.

The p Value of this two-independent-sample, Pooled t-Test can be very quickly using the following Excel statistical function:

=T.TEST(array 1,array2,1,2)

Before this test is employed, all required assumptions such as normality of data must be verified as was done.

The stand-alone Excel formula to perform a two-independent sample, pooled t-Test is shown as follows. If the resulting p Value is smaller than α for a one-tailed test or α/2 for a two-tailed test, the difference between the means of the samples is deemed to be statistically significant. This indicates that the two samples were likely drawn from different populations. (Click On Image To See a Larger Version)

The Null Hypothesis of the t-Test would not be rejected if the test were two-tailed because the p Value (0.042) is greater than Alpha/2 (0.025).The Null Hypothesis of the t-Test would be rejected if the test were one-tailed because the p Value (0.042) is less than Alpha/2 (0.025). A one-tailed test is less.

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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