# One Sample Tests

- 8.5.1. Normality Tests
- 8.5.2. One Median

## 8.5.1. Normality Tests

The normality test tool provides for four tests of normality.

- Anderson Darling Test
- Cramér-von Mises Test
- Lilliefors (Kolmogorov-Smirnov) Test
- Shapiro-Francia Test

The data range is specified via the “Input Range:” entry (see Figure 8-76). The given range or list of ranges can be grouped into separate data sets by columns, rows, or areas. The tool performs a separate test for each data set.

On the test tab one specifies which of the four tests to perform, the significance level for the test and whether to include a normal probability plot of the data (see Figure 8-77).

Suppose you want to perform a Lilliefors (Kolmogorov-Smirnov) Test for Normality on the data given in Figure 8-78.

- Enter A1:A50 (or Sheet1!$A$1:$A$50) in the “Input Range:” entry by typing this directly into the entry or clicking in the entry field and then selecting the range on the sheet.
- Select the “ option since the first row contains a label (see ”Figure 8-79).
- On the test tab of the dialog (see Figure 8-80) select the Lilliefors (Kolmogorov-Smirnov) Test.
- Specify an appropriate significance level Alpha, say 0.05.
- Select the “ option to include a normal probability plot in the output. ”
- Specify the output options as described above.
- Press the OK button.

The output of this normality test is shown in Figure 8-81. Note that the graph appears initially on top of the output data and needs to be moved to make the data visible.

## 8.5.2. One Median

The One Median test tool provides two non-parametric tests that test the null hypothesis that the sample comes from a population with a given median:

- Sign Test
- Wilcoxon Signed Rank Test

Selecting the appropriate submenu item opens the dialog with the respective test preselected.

- 8.5.2.1. Sign Test
- 8.5.2.2. Wilcoxon Signed Rank Test

### 8.5.2.1. Sign Test

This section describes the one sample sign test to test the null hypothesis that the sample comes from a population with the given median. The tool to perform a sign test to test the null hypothesis that two paired samples come from populations with the same median is in section Section 8.6.2.1 ― Sign Test.

The Sign Test tool performs a one-sample sign test whether the sample comes from a population with a given median.

The sample data range is specified via the “Input Range:” entry (see Figure 8-82). The given range or list of ranges can be grouped into separate data sets by columns, rows, or areas. The tool performs a separate test for each data set.

On the “Test”tab of the dialog (see Figure 8-83) the predicted median as well as the significance level are specified.

Suppose you want to perform a Sign Test on the data given in Figure 8-82 to determine whether the sample comes from a population of mean 3.

- Enter A1:A19 (or Sheet1!$A$1:$A$19) in the “Input Range:” entry by typing this directly into the entry or clicking in the entry field and then selecting the range on the sheet.
- Select the “ option since the first row contains a label. (see ”Figure 8-82).
- On the “ tab of the dialog (see ”Figure 8-83) select the Sign Test.
- Specify an appropriate significance level Alpha, say 0.05.
- Select thepecify the median of the null hypothesis (3) in the “ entry. ”
- Specify the output options as described above.
- Press the OK button.

The output of this sign test is shown in Figure 8-84.

### 8.5.2.2. Wilcoxon Signed Rank Test

This section describes the one sample Wilcoxon signed rank test to test the null hypothesis that the sample comes from a population with the given median. The tool to perform a Wilcoxon signed rank test to test the null hypothesis that two paired samples come from populations with the same median is in section Section 8.6.2.2 ― Wilcoxon Signed Rank Test.

The Wilcoxon Signed Rank TTest tool performs a one-sample sign test whether the sample comes from a population with a given median.

The sample data range is specified via the “Input Range:” entry (see Figure 8-82). The given range or list of ranges can be grouped into separate data sets by columns, rows, or areas. The tool performs a separate test for each data set.

On the “Test”tab of the dialog (see Figure 8-83) the predicted median as well as the significance level are specified.

The p-values given by this tool are determined using a normal approximation. This approximation is only valid if the sample size is at least 12.

Suppose you want to perform a Wilcoxon Signed Rank Test on the data given in Figure 8-82 to determine whether the sample comes from a population of mean 3.

- Enter A1:A19 (or Sheet1!$A$1:$A$19) in the “Input Range:” entry by typing this directly into the entry or clicking in the entry field and then selecting the range on the sheet.
- Select the “ option since the first row contains a label. (see ”Figure 8-82).
- On the “ tab of the dialog (see ”Figure 8-83) select the Wilcoxon Signed Rank Test.
- Specify an appropriate significance level Alpha, say 0.05.
- Select thepecify the median of the null hypothesis (3) in the “ entry. ”
- Specify the output options as described above.
- Press the OK button.

The output of this sign test is shown in Figure 8-85.