Question

Exercises $20.46-20.58$ require the use of a computer and software. Use a $5 \%$ significance level unless specified otherwise. The manager of a personnel company is in the process of examining her company's advertising programs. Currently, the company advertises in each of the three local newspapers for a wide variety of positions, including computer programmers, secretaries and receptionists. The manager has decided that only one newspaper will be used if it can be determined that there are differences in the number of inquiries generated by each newspaper. The following experiment was performed. For 1 week ( 6 days), six different jobs were advertised in each of the three newspapers. The number of inquiries for the positions was recorded for each newspaper. The results are shown in the table below. (TABLE CAN'T COPY) a What techniques should be considered to apply in reaching a decision? What are the required conditions? How do we determine whether the conditions are satisfied? b Assuming that the data are not normally distributed, can we conclude at the $5 \%$ significance level that differences exist between the newspapers' abilities to attract potential employees? 

   Exercises $20.46-20.58$ require the use of a computer and software. Use a $5 \%$ significance level unless specified otherwise.
The manager of a personnel company is in the process of examining her company's advertising programs. Currently, the company advertises in each of the three local newspapers for a wide variety of positions, including computer programmers, secretaries and receptionists. The manager has decided that only one newspaper will be used if it can be determined that there are differences in the number of inquiries generated by each newspaper. The following experiment was performed. For 1 week ( 6 days), six different jobs were advertised in each of the three newspapers. The number of inquiries for the positions was recorded for each newspaper. The results are shown in the table below.
(TABLE CAN'T COPY)
a What techniques should be considered to apply in reaching a decision? What are the required conditions? How do we determine whether the conditions are satisfied?
b Assuming that the data are not normally distributed, can we conclude at the $5 \%$ significance level that differences exist between the newspapers' abilities to attract potential employees?
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Statistics for Management and Economics + XLSTAT Bind-in
Statistics for Management and Economics + XLSTAT Bind-in
Gerald Keller 8th Edition
Chapter 20, Problem 52 ↓

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Given the scenario, the appropriate statistical test to determine if there are differences in the number of inquiries among the three newspapers is the Kruskal-Wallis test. This test is a non-parametric alternative to the one-way ANOVA and is used when the data do  Show more…

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Exercises $20.46-20.58$ require the use of a computer and software. Use a $5 \%$ significance level unless specified otherwise. The manager of a personnel company is in the process of examining her company's advertising programs. Currently, the company advertises in each of the three local newspapers for a wide variety of positions, including computer programmers, secretaries and receptionists. The manager has decided that only one newspaper will be used if it can be determined that there are differences in the number of inquiries generated by each newspaper. The following experiment was performed. For 1 week ( 6 days), six different jobs were advertised in each of the three newspapers. The number of inquiries for the positions was recorded for each newspaper. The results are shown in the table below. (TABLE CAN'T COPY) a What techniques should be considered to apply in reaching a decision? What are the required conditions? How do we determine whether the conditions are satisfied? b Assuming that the data are not normally distributed, can we conclude at the $5 \%$ significance level that differences exist between the newspapers' abilities to attract potential employees?
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Key Concepts

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Analysis of Variance (ANOVA)
ANOVA is a statistical method used to compare the means of three or more groups to determine if at least one group mean is statistically significantly different from the others. When employing ANOVA, it is essential to check underlying assumptions including the normality of the data, homogeneity of variances (equal variances across groups), and the independence of observations. These conditions ensure that the F-test used in ANOVA yields valid results.
Assumptions Checking
Before applying techniques like ANOVA or its nonparametric alternatives, it is crucial to verify the required conditions. This involves testing for normality (using methods such as the Shapiro-Wilk test) and assessing the equality of variances (using tests like Levene’s test). Independence of observations should be ensured by proper experimental design. If the data deviate substantially from normality or homoscedasticity, this impacts the reliability of standard parametric methods and may necessitate alternative approaches.
Nonparametric Alternatives (Kruskal-Wallis Test)
When the assumption of normality is violated, the Kruskal-Wallis test serves as a nonparametric equivalent of one-way ANOVA. It is used to determine whether there are statistically significant differences between the medians of three or more independent groups. This test does not assume a normal distribution and is based on ranking the data, making it robust to outliers and violations of the normality assumption.
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