Chi-Square Distributions with Microsoft Excel

###Chi-Square Distributions with Microsoft Excel### Advertisements

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

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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 changeable chi-square follows the chi-square probability distribution with n degrees of free time (df ), where n is a obvious integer equal to N-1. The degrees of free time parameter determines the shape of the distribution. With more degrees of freedom, the skew is less.

Chidist

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 trust 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 product and weigh a sample of 18 units to find a sample variance of 0.36, you may want to make a 90% trust interval assessment 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 free time and divide this product by each of the values returned from the Chiinv function to find the lower and upper limits of the trust interval. You can take the square root of these values to make interval estimates of the citizen accepted deviation.

Chitest

The chi-square test is used to test independence of two variables. You can use the chi-square test to decide either there is a valuable inequity in the middle of observed and staggering frequencies. For example, if you want to find out either soft drink preference differs in the middle of male and female drinkers, you can make a null hypothesis that soft drink preference is independent of the gender of the drinker, and create a worksheet range, or table, of staggering 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 always 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 method uses the following syntax:

=Chitest (actual range, staggering range)

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

The method 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% trust level.

Chi-Square Distributions with Microsoft Excel