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One-sample median test

One-sample median tests compare an observed median to a hypothesized value in a given population

The one-sample median test is used to test a hypothesized median value against an observed median value in a representative sample. The hypothesized median value for a one-sample median test is stipulated in an a priori fashion.

For instance, let's say researchers believe that the college-age students will rate the look of a new social networking site at as a "4" on a 5-point Likert scale. Researchers collect a representative sample from a Psychology 101 class and find a median value of "1."  This difference of ratings between what researchers expected (Median = 4) and the observed value (Median = 1) may be statistically significant according to a one-sample median test.

The most important part of the one-sample median test is to state the hypothesis for the expected median value in an a priori fashion.

The steps for conducting a one-sample median test in SPSS

1. The data is entered in a between-subjects fashion and is specified as a scale variable in the Variable View.

2. Click Analyze.

3. Drag the cursor over the Nonparametric Tests drop-down menu.

4. Click One Sample.

5. Click on the Settings tab.

6. Under the Customize tests marker, click on the Compare median to hypothesized (Wilcoxon Signed-rank test) box to select it.

7. In the Hypothesized median: box, type in the a priori hypothesized median value.

8. Click on the Run button. 

The steps for interpreting the SPSS output for one-sample median test

1. In the Hypothesis Test Summary table, look under the Sig. column. This is the p-value that will be interpreted.

If the p-value is LESS THAN .05, then the observed median was significantly different than the hypothesized median.

If the p-value is MORE THAN .05, then the observed median was NOT significantly different than the hypothesized median. 

Click on the Download Database and Download Data Dictionary buttons for a configured database and data dictionary for a one-sample median test. 
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