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# Using CDF NORMAL and IDF NORMAL

last edited by 8 years, 9 months ago

CDF.NORMAL and IDF.NORMAL are commands which determine a quantity or probability based on a normal model. CDF stands for Cumulative Distribution Function, and the CDF.NORMAL command evaluates the probability of a value occurring to the left of a given quantity within a normal distribution. IDF stands for Inverse Distribution Function. Given a probability, the IDF.NORMAL command determines what value corresponds to that left-tailed probability.

CDF.NORMAL is useful when determining the probability of a value falling to the left of a given quantity. For example, Sokal and Hunter collected data on the wing lengths of 100 houseflies and found a sample mean of 45.5 mm with a standard deviation of 3.92 mm. The CDF.NORMAL command could be used to determine what percent of these house flies have a wing length of 38 mm or shorter. The answer of .027 means that 2.7% of house flies in the sample had a wing length under 38 mm. This result can then be used to make predictions about the entire population. Note that the CDF.NORMAL command includes the probability of values falling anywhere to the left of the given quantity. When presented graphically, this includes all data under the normal curve to the left of the given quantity. In order to determine the probability of a value falling to the right of the quantity, such as the percent of house flies with a wing length over 38 mm, subtract CDF.NORMAL from 1. In the case of the house fly example, 1- .027 is .972, which means that the model predicts 97.2% of house flies have a wing length over 38 mm.

IDF.NORMAL is useful when determining what value corresponds to that left-tailed probability. For example, the command could be used to determine the wing length of the shortest 30% of fruit flies in a sample. Using Sokal and Hunter's sample mean of 45.5 mm and standard deviation of 3.92 mm, the IDF.NORMAL answer of 43.44 means that the model predicts the shortest 30% of house flies have a wing length of 43.44 mm or less.

The CDF.NORMAL command is presented in the form CDF.Normal(?,?,?), where the first question mark represents the given quantity. The second question mark represents the mean, and the third, the standard deviation. IDF.NORMAL requires a given probability instead of a given quantity. The command is presented as IDF.Normal(?,?,?), where the first question mark represents given probability. Note that this probability should always be in decimal form. The second question mark represents mean, and the third, standard deviation.

Below is a picture of the "Compute Variable" box completed in order to determine the percentage of house flies with a wing length under 38 mm, based on Sokal and Hunter's sample mean of 45.5 mm and standard deviation of 3.92 mm. The "Target Variable" box in the upper lefthand corner contains the column name under which the output will appear. This label will have no effect on the output, but including a representative title may help prevent confusion. The "Function Group" box on the righthand side has "CDF and Noncentral CDF" selected, with "Cdf.Normal" selected in the "Functions and Special Variables" box below. The command is in the "Numeric Expression" field, with 38 as the given quantity, 45.5 as the mean, and 3.92 as the standard deviation. Below is a picture of the data editor window, where an approximation of the CDF.NORMAL output has appeared under the target variable name. The VAR00001 value is whatever was typed to activate the page, but has no impact on the output. The exact probability can be seen in the box above the column headings. In this case, .03 means that the model predicts about 3% of house flies have a wing length of 38 mm or less. Below is a picture of the "Compute Variable" box completed in order to determine the wing length for the shortest 30% of house flies. The "Target Variable" box in the upper lefthand corner contains the column name under which the output will appear. This label will have no effect on the output, but a representative title may prevent confusion later. The "Function Group" box on the righthand side has "Inverse DF" selected, with "Idf.Normal" selected in the "Functions and Special Variables" box below. The command is in the "Numeric Expression" field, with .3 as the given probability, 45.5 as the mean, and 3.920 as the standard deviation. Below is a picture of the data editor window, where an approximation of the IDF.NORMAL output has appeared under the target variable name. The exact quantity can be seen in the box above the column headings. The VAR00001 value is whatever was typed to activate the page, but has no impact on the output. In this case, 43.44 means that the model predicts that the shortest 30% of house flies have a wing length of 43.44 mm or less. # How to Use CDF.NORMAL in SPSS

• Open a new SPSS Data Editor page.
• Type something in the first cell to activate the page, then click outside of the cell.
• Go to the "Transform" menu and select "Compute Variable".
• Put a label of your choosing in the "Target Variable" space at in the upper lefthand corner of the "Compute Variable" box (this will label your column but does nothing more.)
• On the righthand side of the "Compute Variable" box, find the "Function Group" box and click "CDF & Noncentral CDF".
• In the "Functions and Special Variables" box, find "Cdf.Normal" and double click.
• The command will appear in the  "Numeric Expression" box as CDF.NORMAL(?,?,?).
• Replace the first question mark with the given quantity.
• Replace the second question mark with the mean.
• Replace the third question mark with the standard deviation.
• To determine the probability of data falling to the right of the given quantity, type 1- in front of the command.
• The percentage will be displayed in decimal form in the column with the target variable name.

# How to Use IDF.NORMAL in SPSS

• Open a new SPSS Data Editor page.
• Type something into the first cell to activate the page, then click outside of the cell.
• Go to the "Transform" menu and select "Compute Variable".
• Put a label of your choosing in the "Target Variable" space at in the upper lefthand corner of the "Compute Variable" box (this will label your column but does nothing more.)
• On the righthand side of the "Compute Variable" box, find the "Function Group" box and click "Inverse DF".
• In the "Functions and Special Variables" box, find "IDF.Normal" and double click.
• The command will appear in the  "Numeric Expression" box as IDF.NORMAL(?,?,?).
• Replace the first question mark with the given probability in decimal form.
• Replace the second question mark with the mean.
• Replace the third question mark with the standard deviation.
• To evaluate the probability for a two-tailed area, type 2* in front of the command.
• The quantity will be displayed in decimal form in the column with the target variable name.

The video below shows the steps taken to use the CDF.NORMAL command:

The video below shows the steps taken to use the IDF.NORMAL command: