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Probability Density Function | The F distribution is the ratio of two chi-square distributions with degrees of freedom and , respectively, where each chi-square has first been divided by its degrees of freedom. The formula for the probability density function of the F distribution is | ||||||||||||
Cumulative Distribution Function | The formula for the Cumulative distribution function of the F distribution is | ||||||||||||
Percent Point Function | The formula for the percent point function of the F distribution does not exist in a simple closed form. It is computed numerically.The following is the plot of the F percent point function with the same values of and as the pdf plots above. | ||||||||||||
Other Probability Functions | Since the F distribution is typically used to develop hypothesis tests and confidence intervals and rarely for modeling applications, we omit the formulas and plots for the hazard, cumulative hazard, survival, and inverse survival probability functions. | ||||||||||||
Common Statistics | The formulas below are for the case where the location parameter is zero and the scale parameter is one.
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Parameter Estimation | Since the F distribution is typically used to develop hypothesis tests and confidence intervals and rarely for modeling applications, we omit any discussion of parameter estimation. | ||||||||||||
Comments | The F distribution is used in many cases for the critical regions for hypothesis tests and in determining confidence intervals. Two common examples are the analysis of variance and the F test to determine if the variances of two populations are equal. | ||||||||||||
Software | Most general purpose statistical software programs support at least some of the probability functions for the F distribution |
Learning Objectives Create and interpret frequency polygons Create and interpret cumulative frequency polygons Create and interpret overlaid frequency polygons Frequency polygons are a graphical device for understanding the shapes of distributions. They serve the same purpose as histograms, but are especially helpful for comparing sets of data. Frequency polygons are also a good choice for displaying cumulative frequency distributions . To create a frequency polygon, start just as for histograms , by choosing a class interval. Then draw an X-axis representing the values of the scores in your data. Mark the middle of each class interval with a tick mark, and label it with the middle value represented by the class. Draw the Y-axis to indicate the frequency of each class. Place a point in the
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