2. A researcher wants to find out how students feel about a proposal to ban smoking on campus. She selected THREE groups of “students who currently smoke”, “students who formerly smoke”, and “students who never smoke”. Also, she selects a sample of 5 students from each group and conduct an ANOVA test. The researcher obtained the following results:
SST=70
SSW=30
• Write the ANOVA formula.
• Set up the HO and H1
• Calculate ANOVA (F) and conclude whether accept or reject HO.
(Hint; you must calculate and obtain the other components of ANOVA from the given information)
To answer this question, we will first need to understand the ANOVA formula and the null and alternative hypotheses (HO and H1). Then we can calculate the ANOVA F-value and draw a conclusion based on that.
1. ANOVA formula:
The ANOVA formula is as follows:
F = (SSB / dfB) / (SSW / dfW)
where:
- SSB is the sum of squares between groups
- dfB is the degrees of freedom between groups
- SSW is the sum of squares within groups
- dfW is the degrees of freedom within groups
2. Null and Alternative Hypotheses (HO and H1):
The null hypothesis (HO) states that there is no significant difference in the mean feelings towards the proposal to ban smoking on campus between the three groups of students (students who currently smoke, students who formerly smoke, and students who never smoke). The alternative hypothesis (H1) states that there is a significant difference in the mean feelings between at least two of the groups.
3. Calculation of ANOVA F-value and Conclusion:
Given the information provided, we have:
SST = 70 (total sum of squares)
SSW = 30 (sum of squares within groups)
To calculate the sum of squares between groups (SSB), we can use the formula:
SSB = SST - SSW
SSB = 70 - 30
SSB = 40
The degrees of freedom between groups (dfB) is equal to the number of groups minus 1. Since there are three groups (students who currently smoke, students who formerly smoke, and students who never smoke), dfB = 3 - 1 = 2.
The degrees of freedom within groups (dfW) is equal to the total number of observations (5 students per group) minus the number of groups. Since we have 3 groups and 5 students in each group, dfW = (3 * 5) - 3 = 12.
Now we can calculate the ANOVA F-value using the formula:
F = (SSB / dfB) / (SSW / dfW)
F = (40 / 2) / (30 / 12)
F = 20 / 2.5
F = 8
To conclude whether we accept or reject the null hypothesis (HO), we need to compare the calculated F-value (8) with the critical F-value at a given significance level. If the calculated F-value is greater than the critical F-value, we reject the null hypothesis. If it is less than or equal to the critical F-value, we accept the null hypothesis.
Unfortunately, the critical F-value at a given significance level is not provided in the question. You would need to consult a critical F-value table or use statistical software to determine the critical F-value based on your chosen significance level (e.g., 0.05). Once you have the critical F-value, you can compare it to the calculated F-value (8) to draw the final conclusion.
In summary, to complete the ANOVA and draw a conclusion, you would need to calculate the other components of ANOVA (SSB, dfB, dfW), determine the critical F-value based on your chosen significance level, and then compare the calculated F-value with the critical F-value.