Using SPSS to compute critical values (inverse cdf values)

Below are instructions for obtaining z0.025 and t7,0.025, which are also known as the inverse cdf values corresponding to the cdf value of 0.975. (The inverse cdf value corresponding to the cdf value of 0.975 is the value for which the cdf evaluated at that value is 0.975. For example, the inverse cdf value corresponding to 0.975 for the standard normal distribution is 1.9600, because the cdf of the standard normal distribution at 1.9600 is 0.975. (1.9600 is the value for which the probability mass in the standard normal distribution above it is 0.025, which of course means that the probability mass below it is 0.975.))

Similar critical values, for different levels, and different distributions, can be obtained in a similar manner using SPSS.
  1. Start SPSS. The Data Editor spreadsheet should appear in the background with a smaller window/box opened on top of it. Click the Type in data "button" and then click OK.
  2. Enter the value 0.975 into the first row of the first column on the Data Editor spreadsheet. To name the column, click on Variable View at the bottom of the Data Editor window, and then replace VAR00001 in the first row of the name column by prob (or you can use some other name, or simply just let the name stay as VAR00001). Finally, click of Data View at the bottom of the window to get back the original spreadsheet.
  3. Click on Transform on the main menu bar near the top of the window, pull down, and select Compute. This should cause a Compute Variable window to open.
  4. In the Target Variable box on the Compute Variable window, type crit. Next, in the Functions box, scroll down and find IDF.NORMAL(p,mean,stddev). Highlight (click on it to make it blue) IDF.NORMAL(p,mean,stddev). At this point, the "up arrow" next to Functions should become "active." Click on the arrow, and IDF.NORMAL(?,?,?) should appear in the Numeric Expression box, with the first ? highlighted blue.
  5. Highlight prob in the Type & Label box. Next, click on the "right arrow" between the Type & Label and Numeric Expression boxes, which should cause the previously highlighted ? to become prob. Then use your keyboard to change the last two ?s to 0 and 1 (since a standard normal distribution has mean 0 and standard deviation 1).
  6. Now click OK at near the bottom of the Compute Variable window. This should cause the number 1.96 to appear in a column (the 2nd column) of the Data Editor window, with the column named crit. This value is the desired z critical value (inverse cdf value).
  7. To obtain the desired t critical value (for the T distribution having 7 df), just change IDF.NORMAL(prob,0,1) to IDF.T(prob,7).
  8. An annoying thing is that the probability has been rounded to the nearest hundreth. To get more digits, click on Variable View at the bottom of the Data Editor window, and then click on the cell in the 2nd row (the crit row) of the Decimals column. (This cell should contain a 2.) Clicking the cell should make up and down arrows appear the the cell. Click the up arrow to change the 2 to a 3. Then click Data View at the bottom of the Data Editor window. Now you should see that the desired probability in the 2nd column have been expressed with 3 digits after the decimal, making it match the value of 2.365 given on p. 677 of S&W.