Question

please show all 6 steps with calculations

Assignment #IS: Within Subjects ANOVA Instructions: For each research scenario, please complete the source table and conduct a hypothesis test at α-.05 significance level using a within-subjects ANOVA to determine if one condition is different from the others. Please be sure to show your work when performing mathematical operations. Please round all source table calculations to two decimal places Scenario 1. Dr. Smith has developed a new way to administer a GRE prep workshop to psychology and psychological science majors at her university. She wants to know if the effectiveness of her new program is different from the effectiveness of her old one, so she compares the average GRE practice test performance of her junior students from last year to se same students' average GRE performance on this year's practice test. To keep things simple, Dr. Smith adds each student's GRE quantitative and GRE verbal scores to get a single composite GRE score in each year. Dr. Smith has data for 7 students. Year/Person A Year 080 297543 2170 310 800 and Mean- 304 300 290 | 300 310 | 310 | 320 320 32 285 295 305 305 310 310 315 G MS Source Between-conditions Within-conditions df Subjects Error Total Step 1. Describe the populations, distribution, and assumptions. For this step, please only test the assumption on homogeneity of variances Year 1 Condition s2 Year 2 Condition s2 Step 2. State the null and research hypotheses. Step 3. Determine the characteristcs of the comparison distribution. Step 4. Determine the critical values. Step 5. Calculate the test statistic. Assignment #15: Within-Subjects ANOVA Step 6. Make a decision and report your findings in APA format. Calculate the effect size for this ANOVA using the following equation: size in RSStotal-SS subjects

Answer 1

(1)

2 2 = sample variance xi ith element of the sample x = mean of the sample n = sample size

So,

S² (Year 1) = 90.47

S² (Year 2) = 133.34

(2)

H₀: U₁ = U₂ (Null)

H_a: Not all the means are equal (Alternate)

U is the mean of the independent groups...

(3)

Here a One Factor Anova will be performed to do the analysis...

The characteristics of the comparison distribution are the values of mean and standard deviation that we will use in our test statistic...

Mean = 297.14 (Year 1), 310 (Year 2)

SD = 9.51 (Year 1), 11.55 (Year 2)

(4), (5)

ANOVA Single Factor 0.05 Groups Column 1 Column 2 Count Sum Mean Variance 2080 297.1428571 90.47619048 2170 310 133.3333333 MS 1 578.5714286 5.170212766 0.042146982 4.747225347 Source of Variation SS Between Groups 578.5714286 Within Groups1342.857143 Total df P-value F critical 12 111.9047619 13 1921.428571

F Critical = 4.75

F = 5.17 (Refer the output above)

(6)

R2 = SS_between/(SS_total - SS_subjects) = 578.57/1921.43 = 0.3011 (SS_sub is not considered in this regard)

End of the Solution...