Chi-Square Distributions with Microsoft Excel

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The chi-square distribution is commonly used to make inferences about a citizen variance.

If a citizen follows the general distribution, you can draw a sample of size N from this distribution and form the sum of the squared standardized scores (chi-square). This random variable chi-square follows the chi-square probability distribution with n degrees of leisure (df ), where n is a sure integer equal to N-1. The degrees of leisure parameter determines the shape of the distribution. With more degrees of freedom, the skew is less.

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Chidist

Chi-Square Distributions with Microsoft Excel

The Chidist function returns the area in the upper tail of the chi-square distribution. You use the Chidist function the same way you would use a chi-square distribution table. The Chidist function uses the following syntax:

=Chidist (x, df)

For example, if you pull a random sample of 16 from a citizen and want to find the probability of a sample chi-square value (x) 25 or larger, you would enter:

=Chidist (25,15)

The function returns the value 0.049943, meaning that a value of 25 or more should in the long run occur about five times in a hundred.

Chiinv

You can use the Chiinv function to create confidence interval estimates of a citizen variance. That is, you use the Chidist function if you know x and want to find the probability, and you use the Chiinv function if you have a probability and want to find x. For example, if you're creating a goods and weigh a sample of 18 units to find a sample variance of 0.36, you may want to create a 90% confidence interval estimation of the citizen variance for the product. With a sample size of 18, you have 17 degrees of freedom.

To find the upper limit, enter:

=Chiinv (0.95,17)

To find the lower limit, enter:

=Chiinv (0.05,17)

These formulas return the values 8.67175 and 27.5871. Multiply the sample variance of 0.36 by the degrees of leisure and divide this goods by each of the values returned from the Chiinv function to find the lower and upper limits of the confidence interval. You can take the quadrilateral root of these values to create interval estimates of the citizen acceptable deviation.

Chitest

The chi-square test is used to test independence of two variables. You can use the chi-square test to decree whether there is a significant incompatibility between observed and unbelievable frequencies. For example, if you want to find out whether soft drink preference differs between male and female drinkers, you can create a null hypothesis that soft drink preference is independent of the gender of the drinker, and create a worksheet range, or table, of unbelievable results based on a sample of 93 male drinkers and 85 female drinkers. You can then create a table of the results of the actual study findings.

Tip: You can use the Microsoft Excel Fisher's test function instead of the chi-square test for analyzing contingency tables with two rows and two columns. Fisher's test all the time returns the exact P value, whereas the chi-square test returns only an approximate p value. Undoubtedly avoid the chi-square test when the numbers in the contingency table are very small (in the particular digits).

The Chitest recipe uses the following syntax:

=Chitest (actual range, unbelievable range)

where actual range is the data in the actual sample results table and unbelievable range is the data from the unbelievable results table.

The recipe returns the p-value. You reject the null hypothesis if this value is less than your level of importance alpha. So if your level of importance is .05, you would reject it, but not if your level of importance is .025 or .01. The test for independence is a one-tailed test, so a level of importance of .05 corresponds with a 95% confidence level.

Chi-Square Distributions with Microsoft Excel