Null and Alternate Hypothesis

Okay Okay Okay....I have to admit that the Scott Peterson case is relatively easy....since I give you the Expected (behavior) frequency distribution. In reality, that is not going to be the case (most of the time in your academic research). If you come across a data table in a study and the researchers utlize the chi-square as their statistical tool, the researchers probably will not give you the % of expected frequency (fe). Especially if the researchers is determining the frequency of behavior for 2 different (unpaired) populations such as a boys frequency of behavior versus a girls frequency of behavior type of study.

The reader need to determine the expected frequency for both populations in order to understand how the researcher came to their conclusion. Such is the case for the use of the Chi-Square test with Yates Correction.

The Chi-square test with Yates Correction is applied to studies that have 2 variables (IV and DV), both with a dichotomous (2 categories) Nominal level of measurement for Unpaired units of analysis. Unpaired of course means 2 different populations such as Boys versus Girls. In these types of studies, we are interested in comparing the frequency of OBSERVED behavior. In order to do this....YOU need to determine the EXPECTED frequency of behavior. Let me show you how that is done

The following example deals with a situation of possible gender discrimination in employment which violates Title 7 of the 1964 Civil Rights Act. The case is called Little v. Master-Bilt Products, Inc., 506 F Supp 319 (1980) . I am not going to go into much detail about this case because it is long....plus it gets very intricate.

In a nut shell, the Master-Bilt Products Inc, a manufacturer of commercial refrigeration equipment in New Albany, Mississippi, is being accused of promoting men only. The plaintiffs argued that men were being promoted based solely on subjective assessments such as; appearance, attitude and "potential" for future development. The company lacked any type of formal personnel procedures and an objective system of employee evaluations.

The researchers present the following table which illustrates the OBSERVED frequency of men and women by pay category in 1979. This is a 2 x 2 cross tabulation. Each Cell contains the OBSERVED frequency of the number of employees for the higher and lower pay grades. You will notice that there is NO EXPECTED frequency of behavior distribution given:

Observed Employment Status of Men and Women at Master-Bilt Products Inc in 1979
PAY CATEGORY MALE FEMALE TOTAL
G-4, G-5 & Supervisor 57 2 59
G-3 125 34 159
TOTAL 182 36 N = 218

In this case, the IV (Nominal level of measurement) is Gender with dichotomous categories (Male and female). The DV is a nominal level of measurement with dichotomous categories (higher pay scale and lower pay scale).

This is how you determine EXPECTED frequency in order to apply the Chi-Square with Yates correction:

Step 1: Find the levels of EXPECTED Frequency (Fe = Frequency Expected)
PAY CATEGORY MALE FEMALE TOTAL
G-4, G-5 & Supervisor (59/218) x 182 = Fe = 49.26 (59/218) x 36 =
Fe = 9.74 59
G-3 (159/218) x 182 =
Fe = 132.74 (159/218) x 36 =
Fe = 26.26 159
TOTAL 182 36 N = 218

Step 2: Set up your Chi-square table
PAY CATEGORY MALE
Observed Male Expected FEMALE
Observed Female Expected TOTAL
G-4, G-5 & Supervisor 57 49.26 2 9.74 59
G-3 125 132.74 34 26.26 159
TOTAL 182 182 36 36 N = 218

Step 3: You now can follow the traditional chi-square format. However the Chi-square formula is adjusted slightly to correct a bias in our Frequency calculations. The adjustment is in the numerator (subtract .5). This is the Yates' Correction (Giventer, 1989):

x2 = (/fo - fe/ - .5)2 ÷ fe (denominator)

CELL (fo - fe) - .5 (/fo - fe/ - .5)2 Divide by fe Chi-square
1 (57-49.26) - .5 = 7.24 52.42 52.42/49.26 = 1.06
2 (2-9.72) - .5 = 7.24 52.42 52.42/9.74 = 5.38
3 (125 - 132.74) - .5 = 7.24 52.42 52.42/132.74 = .39
4 (34 - 26.26) - .5 = 7.24 52.42 52.42/26.26 = 2
TOTAL 8.83

Step 4: Find your Chi-square Critical at the 95% level of confidence (.05 in book)

At 95% level of confidence our Chi-square critical is:
DF = (number of rows -1) x (number of columns - 1)
DF = (2-1) x (2-1)
DF = 1

Go to the Chi-square table in Eresource. At 95% level of confidence (or .05) at 1 degree of freedom our Chi-square critical is 3.84

Step 5:
Compare the Chi-square calculated to the Chi-square critical. A significant relationship occurs if our Chi-square calculated is greater than the Chi-square critical. As you can see, the Chi-square calculated of 8.83 is greater than the Chi-square critical of 3.84. This means that the distribution of the populations is not equal. The distributions of pay are significantly different between males and females.

How would you set up the H1 and Ha for this problem?