Question

Dr. X would like to examine the relative effectiveness of two teaching methods for improving college students’ statistical skills. A control group in which students received no training is also included in the study. A sample of 30 college students is randomly selected from the subject pool. These individuals are then randomly assigned to one of the three teaching methods. The dependent variable is a measure of statistical skills after one semester.

control	method a	method b
8	20	9
7	17	8
6	12	8
8	16	6
5	18	7
6	19	10
9	17	6
7	16	8
6	18	7
6	17	8

1. Specify a research hypothesis (2 pts)

2. Specify a null hypothesis (2 pts )

3. Create the dataset according to the observations above and read it into R. In your original dataset, the categorical variable may contain a set of values. Relabel the categorical variable with corresponding labels (see descriptions above) by forming a new variable. To demonstrate your work, show the R scripts, the variable names, and the first 3 rows of your data. (10 pts)

4. Calculate the means and standard deviations of each group. Answer this question with R. To show your work, copy and paste the R-script and output below. (5 pts)

5. Compute the F-statistic and effect size with R. To show your work, copy and paste the R-script and output below. (5 pts)

6. Based on the calculation of F, make a decision whether reject or do not reject the null hypothesis. (2 pts)

7. Based on the calculation of F, perform post-hoc analyses with R if necessary. Briefly summarize your findings. (5 pts)8. Report your findings in APA format. (5 pts).

Answer 1

1)

2)

3)

skills <-c(8,7,6,8,5,6,9,7,6,6,   20,17,12,16,18,19,17,16,18,17, 9,8,8,6,7,10,6,8,7,8)

group<-c(rep("contrl",10),rep("A",10),rep("B",10))

4)

mean (skills[1:10])
[1] 6.8
> sd (skills[1:10])
[1] 1.229273

> mean (skills[11:20])
[1] 17

> sd (skills[11:20])
[1] 2.160247

> mean (skills[21:30])
[1] 7.7
> sd (skills[21:30])
[1] 1.251666

5)

a1<-aov(skills ~group)
summary(a1)

summary(a1)
            Df Sum Sq Mean Sq F value   Pr(>F)  
group        2 637.8   318.9   123.5 2.58e-14 ***
Residuals   27   69.7     2.6                   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

F = 123.5

6)

we reject the null hypothesis as p-value = 0.0000 < 0.05

7)

TukeyHSD(a1)
Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = skills ~ group)

$group
          diff        lwr        upr     p adj
B-A       -9.3 -11.081555 -7.5184451 0.0000000
contrl-A -10.2 -11.981555 -8.4184451 0.0000000
contrl-B -0.9 -2.681555 0.8815549 0.4335632

(B& A) and (Control & A) are significantly different

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