Verbal IQ Scores? Example in this section used ?performance? IQ scores from Data Set 5 in Appendix B for two-way analysis of variance with the factors of sex (male, female) and measured blood lead level (low, medium, high). If we use the verbal? IQ scores with those same factors, we get the accompanying results. Use the displayed results and use a 0.05 significance level. What do you conclude? Example
Solution 7 BSC Step 1: From the given information the data are verbal IQ scores based on the sex and the blood lead level. The data is divided into two factors namely, the sex and blood lead level. If the given sample data is used to infer about the verbal IQ scores based on sex and the blood lead level, the following conditions should met. (i) For each cell, the sample values appear to be from an approximately normally distributed population. (ii) It is assumed that, the population variances are same, as the standard deviations of the three samples are not significantly different. (iii) Based on the careful design of the study, the given samples are treated as simple random samples. (iv) The samples are independent to each other, as the subjects are not matched in any way. (v) The three samples are drawn from the populations which are categorized according to sex and blood lead level. (vi) All of the cells have the same number of sample values. Thus the assumptions are reasonable and the conditions are satisfied. Hence, in this case two way analysis of variance is used. Step 2: In two way analysis of variance,to test the interaction level between the sex and blood lead level. Null hypothesis (H ): T he null hypothesis states that there is no interaction between 0 the sex and blood lead level on verbal IQ scores. Step 3: From the given minitab display there are two categories of sex and three categories of blood lead level. The test statistic for testing the above null hypothesis can be defined as: mean square (interaction) F = mean square(error) 160.633 = 152.933 = 1.05. The value of the test statistic is 1.05. From the output the p-value is 0.365 with degrees of freedom 2 and 24. Comparing the P-value with the significance level 0.05. Here the p-value is greater than the significance level 0.05. So the null hypothesis can not be rejected. Step 4: Here we conclude that there is no interaction effect between the sex and blood lead level on verbal IQ scores. Step 5: Now to test the effect of the sex on verbal IQ scores the following null hypothesis is used. Null hypothesis (H )::0 The null hypothesis states that, there is no effect of the sex on verbal IQ scores. The test statistic for testing the above null hypothesis can be defined as: F = mean square (sex) mean square(error) = 700.833 152.933 = 4.58 The value of the test statistic is 4.58.