How to test Statistical Significance by T-test?

A t-test is a statistical test that helps to determine if there is a significant difference between the means of two sets of data.  In MS Excel, we can easily test statistical significance by using the function TTEST. Let's first understand the parameters of this function.

Ttest function syntax

=TTEST(array1, array2, tails, type)

Array1 (Required): Range for dataset 1

Array2 (Required): Range for dataset 2

Tails (Required): This determines if it is a one-tail T-test or two tail T-test.

• 1: One tail T-test
• 2: Two tail T test

Type (required): Type of t-test

• 1: Paired T-test, i.e. if the two data sets are related to each other
• 2: Unpaired T-test, the two samples have equal variance
• 3: Unpaired T-test , the two samples have unequal variance

Ttest formula example

Example:

1. Consider the following dataset for T-test.

2. Select the two –datasets in array 1 and array 2.

3. On an Empty Cell, write the formula to perform 1-tail Paired T test

One-tailed probability obtained

4. Similarly, perform a two–tailed paired T test

Two-tailed probability obtained

Based on the obtained value you can accept or reject the null hypothesis. If the T-test gives the probability less than 0.05, then reject the null hypothesis. This means there is less than 5% probability that the null hypothesis is true.

Here, in both cases, p-value> 0.05. So, we accept the null hypothesis.

Performing a t-test using the "Data Analysis"

In Microsoft Excel, you can also perform a t-test using the "Data Analysis" tool. Here are the steps to perform such a t-test in Excel:

1. Prepare your data: Organize your data into two columns, one for each group that you want to compare. Make sure that the data is clean and free of errors.
2. Open the Data Analysis Tool: Click on the "Data" tab in the ribbon menu and then click on "Data Analysis" in the "Analysis" section. If the "Data Analysis" tool is not visible, you may need to install it. To do so, go to "File" > "Options" > "Add-ins" > "Excel Add-ins" and then select "Analysis ToolPack".
3. Select the "t-Test: Two-Sample Assuming Equal Variances" option: In the "Data Analysis" dialog box, select "t-Test: Two-Sample Assuming Equal Variances" and then click on the "OK" button.
4. Enter the input range: In the "t-Test: Two-Sample Assuming Equal Variances" dialog box, enter the input range for the two columns of data. Make sure to select the correct range, including the labels if they exist.
5. Select the output options: In the same dialog box, select the output options that you want, such as the location of the output, whether to display descriptive statistics, and whether to display the pooled variance.
6. Click on the "OK" button: Excel will now perform the t-test and display the results.

The results of the t-test will include the t-statistic, the degrees of freedom, the p-value, and the confidence interval. The t-statistic and the p-value are used to determine whether the difference between the means is statistically significant. A small p-value (less than 0.05) indicates that the difference between the means is statistically significant, while a large p-value (greater than 0.05) indicates that the difference between the means is not statistically significant.

It is important to note that a t-test assumes that the two sets of data are normally distributed and have equal variances. Before performing a t-test, you may want to check these assumptions using a histogram or a normality test.

Errors

• #NUM! – If the arguments for tail or type are not correct. Tail argument must be 1 or 2. Type argument must be 1,2 or 3.
• #N/A! – The datasets are of different length
• #VALUE – The tail-argument or the type argument are non-numeric
```Further reading:
How to run f test in Excel```