It has been stated that income increases with the amount of education one receives. Recently I sampled some managers (technical, construction, sales, and manufacturing), compared their salaries to each other and asked the amount of education that had received. .At the 0.05 alpha determine if there is any variance among the three groups related to income when compared to the amount of education they received.
INCOME (In Thousands)
High School Diploma Undergrad Master’s or more
45 49 51
47 57 73
53 85 82
62 73 59
39 81 94
43 84 89
54 89 89
60 92 96
56 62 73
To determine if there is any variance among the three groups related to income when compared to the amount of education they received, you can use a one-way analysis of variance (ANOVA). ANOVA allows us to compare the means of more than two groups to determine if there is a statistically significant difference among them.
In this case, the three groups are categorized by the level of education received: High School Diploma, Undergrad, and Master's or more. The income data for each group is provided.
1. Calculate the means of income for each education group.
- For the High School Diploma group, the mean income is calculated by adding up the income values and then dividing by the number of data points (which is 9 in this case).
- Repeat the process for the Undergrad and Master's or more groups.
2. Calculate the sum of squares within groups (SSW).
- The SSW measures the variability or variation within each group.
- For each group, calculate the sum of the squared differences between each income value and its respective group mean.
- Sum up these squared differences for all groups.
3. Calculate the sum of squares between groups (SSB).
- The SSB measures the variability or variation between the groups.
- Calculate the squared differences between each group mean and the overall mean of all groups.
- Multiply these squared differences by the number of data points in each group.
- Sum up these squared differences for all groups.
4. Calculate the degrees of freedom (df) for both SSW and SSB.
- The df for SSW is equal to the total number of data points minus the number of groups.
- The df for SSB is equal to the number of groups minus 1.
5. Calculate the mean sum of squares within groups (MSW).
- Divide the SSW by its corresponding degrees of freedom.
6. Calculate the mean sum of squares between groups (MSB).
- Divide the SSB by its corresponding degrees of freedom.
7. Calculate the F-statistic.
- Divide the MSB by the MSW.
8. Determine the critical F-value.
- Look up the critical F-value for the specified alpha level (0.05) and the degrees of freedom for SSB and SSW. This can be done using an F-distribution table or an online calculator.
9. Compare the calculated F-statistic to the critical F-value.
- If the calculated F-statistic is greater than the critical F-value, then there is a statistically significant difference in income among the three education groups.
- If the calculated F-statistic is not greater than the critical F-value, then there is not enough evidence to conclude that there is a significant difference in income among the groups.
Following the steps above, you can perform the ANOVA analysis to determine if there is any variance among the three groups related to income when compared to the amount of education they received.