Using SPSS to compute binomial distribution pmf and cdf values


Below are instructions for obtaining pmf and cdf values for a binomial (5, 0.4) distribution. Specifically, if Y is a binomial (5, 0.4) random variable, the instructions below can be used to obtain the values of P(Y = y) and P(Y <= y) for y = 0, 1, 2, 3, 4, 5.
  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 values 0 through 5 into the first 6 rows 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 y. 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 pmfy. Next, in the Functions box, scroll down and find PDF.BINOM(q,n,p). Highlight (click on it to make it blue) PDF.BINOM(q,n,p). At this point, the "up arrow" next to Functions should become "active." Click on the arrow, and PDF.BINOM(?,?,?) should appear in the Numeric Expression box, with the first ? highlighted blue.
  5. Highlight y 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 y.
  6. Click in the Numeric Expression box to make it "active" and use the keys on your computer keyboard (including the right arrow key on your keyboard) to move the cursor and then replace the next ? with 5. Then replace the last ? with 0.4.
  7. Now click OK at near the bottom of the Compute Variable window. This should cause the numbers .08, .26, .35, .23, .08, .01 to appear in a column (the 2nd column) of the Data Editor window, with the column named pmfy. These values are the desired pmf values --- the values of P(Y=y) corresponding to the values of y given in the first column.
  8. An annoying thing is that the probabilities have 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 pmfy 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 probabilities in the 2nd column have been expressed with 4 digits after the decimal.
  9. To obtain the desired cdf values, once again click on Transform and select Compute. Enter cdfy into the Target Variable box. Next, click in the Numeric Expression box to make it active, and use your computer keyboard to change P to C, to make it read CDF.BINOM(y,5,0.4). Upon clicking OK, the desired cdf values appear in a column labeled cdfy (annoyingly with only 2 digits showing after the decimal, and so again one might want to change things to make the values appear with 4 or more digits after the decimal). These are the values of P(Y<=y) corresponding to the values of y given in the first column.