Using SPSS to compute normal distribution cdf values & other probabilities


Below are instructions for obtaining P(Z <= 1) = Φ(1) and P(-1 < Z <= 1), where Z is a standard normal random variable. (Scroll down to see how to deal with other normal distributions.)
  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 1 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 z (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 prob. Next, in the Functions box, scroll down and find CDFNORM(zvalue). Highlight (click on it to make it blue) CDFNORM(zvalue). At this point, the "up arrow" next to Functions should become "active." Click on the arrow, and CDFNORM(?) should appear in the Numeric Expression box, with the ? highlighted blue.
  5. Highlight z 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 z.
  6. Now click OK at near the bottom of the Compute Variable window. This should cause the number .84 to appear in a column (the 2nd column) of the Data Editor window, with the column named prob. This value is the desired probability --- the value of P(Z<=1).
  7. 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 prob 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 twice to change the 2 to a 4. 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 4 digits after the decimal.
  8. To obtain P(-1 < Z <= 1), we can subtract P(Z <= -1) from P(Z <= 1). To do this, once again click on Transform and select Compute. You should find that CDFNORM(z) is still in the Numeric Expression box. Click in the box right after CDFNORM(z) and use your keyboard to type a minus sign right after CDFNORM(z). Then once again highlight CDFNORM(zvalue) in the Functions box and click the up arrow to put CDFNORM(?) after the minus sign. Use your keyboard to change the ? to -1, and then click OK. When you agree to change the existing variable (SPSS will query you about this), the value of prob should become 0.6827, which is the desired probability (rounded to 4 decimal places).
To obtain P(X <= 1), where X is a normally distributed random variable having mean 2 and standard deviation 0.5, you can follow steps 1 through 7 above, only selecting CDF.NORMAL(q,mean,stddev) instead of CDFNORM(zvalue), and also using your keyboard to change the last two question marks to 2 and 0.5 (the desired values for the mean and standard deviation) before clicking OK. (Note: When you use the up arrow, CDF.NORMAL(q,mean,stddev) becomes CDF.NORMAL(?,?,?) in the Numeric Expression box.) The value of prob that you obtain should be .0228.