# Indpendent t-test

The independent *t*- test is a test for a difference in central location (mean) between two independent samples.

The requirements of the test are:

- Two independent samples measured on a continuous scale.
- Samples are from a population with a normal distribution.

## Arranging the dataset

Data in existing Excel worksheets can be used and should be arranged in a List dataset layout or Table dataset layout. The dataset must contain a continuous scale variable and a nominal/ordinal scale variable containing two independent groups.

When entering new data we recommend using New Dataset to create a new **2 variables (1 categorical)** dataset ready for data entry.

**Using the test**** **

To start the test:

- Excel 2007:

Select any cell in the range containing the dataset to analyse, then click**Compare Groups**on the**Analyse-it**tab, then click**t****- test**. - If the dataset is arranged using the table layout:

Click**Variable - Group 1**and**Variable - Group 2**and select the groups to compare.If the dataset is arranged using the list layout:

Click**Variable**and select the dependent variable and click**Factor**and select the independent variable containing the two groups to compare. - Click
**Alternative hypothesis**and select the alternative hypothesis to test. - Tick
**Unequal variances**if the samples do not have the same variance and Welch's correction for unequal variance should be applied. - Enter
**Confidence interval**to calculate around the mean difference. The level should be entered as a percentage between 50 and 100, without the % sign. - Click
**OK**to run the test.

Excel 97, 2000, 2002 & 2003:

Select any cell in the range containing the dataset to analyse, then click **Analyse **on the **Analyse-it **toolbar, click **Compare Groups** then click **t****- test**.

X ≠ Y to test if the mean(X) is not equal to mean(Y). |

X > Y to test if the mean(X) is greater than mean (Y). |

X < Y to test if the mean(X) is less than mean (Y). |

The report shows the number of observations analysed, and, if applicable, how many missing values were excluded. Summary statistics for each sample are then shown.

The difference between the means and a confidence interval are shown to quantify the difference between the samples in terms that can be practically evaluated.

The t-statistic and hypothesis test are shown. The *p*-value is the probability of rejecting the null hypothesis, that the samples have the same mean, when it is in fact true. A significant p-value implies that the two samples have different means.

## Further reading & references

- Handbook of Parametric and Nonparametric Statistical Procedures (3rd edition)

David J. Sheskin, ISBN 1-58488-440-1 2003; 375.

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- Independent t-test
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- Kruskal-Wallis test
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- Test Difference in Proportion
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