A researcher has collected statistics pretest scores for students representing 3 different age groups
18-30 31-45 45 and up
3 5 10
7 10 2
9 9 8
6 8 8
4 6 5
Do hypothesis test using ANOVA to find if significant difference. Use alpha .05. All hypothesis steps and find degrees of freedom and critical values, calulate test statistic and effect size and write results in apa style.
Use Scheffe posttest if appropriate.
If you really want an expert to help you, be sure to follow directions and type your subject in the School Subject box. Any other words, including obscure abbreviations, are likely to delay responses from a teacher who knows that subject well.
thank you
To conduct an ANOVA hypothesis test, you need to follow these steps:
Step 1: State the hypotheses:
H0 (Null Hypothesis): There is no significant difference in pretest scores among the three age groups.
H1 (Alternative Hypothesis): There is a significant difference in pretest scores among the three age groups.
Step 2: Set the significance level (alpha). In this case, it is given as 0.05.
Step 3: Calculate the degrees of freedom:
Between groups: df_between = k - 1 (where k is the number of groups, in this case, it is 3)
Within groups: df_within = N - k (where N is the total number of observations, in this case, it is 15)
Step 4: Calculate the F-test statistic using the ANOVA formula:
F = (SS_between / df_between) / (SS_within / df_within)
Where SS_between is the sum of squares between groups, and SS_within is the sum of squares within groups.
Step 5: Find the critical value:
To find the critical value for an F-test with df1 = df_between and df2 = df_within, you can use a critical value table or an online calculator. For alpha = 0.05, the critical value is approximately 3.89.
Step 6: Compare the calculated F-value with the critical value:
If the calculated F-value is greater than the critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
Step 7: Calculate the effect size:
Eta-squared (η²) is commonly used as an effect size measure for ANOVA. It can be calculated as:
η² = SS_between / (SS_between + SS_within)
Step 8: Write the results in APA style:
After conducting the ANOVA analysis, the results showed a significant difference in pretest scores among the three age groups, F(df_between, df_within) = calculated F-value, p < 0.05, η² = effect size.
Step 9: Post hoc test (Scheffe posttest):
If there is a significant difference among the groups according to the ANOVA result, you can conduct post hoc tests to determine which specific group(s) differ from each other. In this case, Scheffe post hoc test can be used to compare all pairs of the means.
Please note that the specific calculations and interpretations of the data are not provided in the question. To perform the ANOVA test and calculate the statistics accurately, you will need to have the raw data values.