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Assignment 3+4 - Applied Statistics: hand in your own (!) work on SAT, May 9
(Exercises 2 and 7 of the exercises L5: Two samples)
An educationalist developed a new method for teaching grade 5
pupils reading skills. To find out whether there is any difference
in reading skills when using the old method or his new method
he compared the test results of two classes, one using the new
and one using the old method. Here are the results:
Reading skills testscores
New method
Old method
24
61 56 42 46 37
43
44 59 43 10 42
58
67 52 55 17 55
71
49 62 26 60 28
43
53 54 62 53 48
49
43 57 37 42 54
46
57 33 33 19 20
41
85
Part 1: computation by hand (/calculator)
a.
Compute sample mean and sample standard deviation for both groups of pupils, using the
statistical functions on your calculator
b.
Compute a 99%-confidence interval for the difference in expected test scores. (Do not assume
that the variances are equal)
c.
Test at 1% level whether there is a difference in test results. Use a parametric test and write
down all (8) steps of the testing procedure.
d.
Explain why the results of b. and c. are equivalent with respect to the equality of expectations.
e.
Test whether the variances can be assumed equal, using the F-test at 5%-level. Report the
hypotheses, the value of the test statistic, the critical value(s) and your conclusion.
f.
Conduct a non parametric test at 1% level to show whether there is a difference in test results.
Part 2: Graphing and computations, using SPSS:
Enter the data in a SPSS data file, using two variables: method (1= new, 2 = old) and testscore
Descriptive statistics: go to Analyse ->Descriptives -> Explore: choose testscore as dependent
variable and method as factor. Click on the statistics –button to choose descriptives and confidence
level 90%. Check the mean and standard deviation, as computed at a.
g.
Report the 5-number summary and the computed confidence for both data sets.
Boxplots: go to Graphs -> boxplot -> simple and choose testscore as variable and method as category.
h.
Comment the box plots: 1. are there striking differences in centre or in variation, 2. are the
graphs (strongly) asymmetric an 3. are there outliers?
Checking the normality using the histogram: Graphs -> Histogram and choose testscore as variable,
method in the Columns (or Rows) and select “Display normal curve”.
i.
Taking the small sample sizes in consideration, would you say that the histograms show nonnormal shapes?
Testing the null hypothesis of normality versus the alternative of non-normal distributions for both
data sets: in the menu “Nonparametric tests” you can find the Kolmogorov-Smirnov test. If you
choose testscore as variable and select “normal” this test checks whether all 44 values can be assumed
normal. To test this for both groups, first go to : Data -> Split File and select “Organize output by
groups and choose method as grouping variable (and, after splitting the data, conduct the K-S test)
j.
Report the p-values of the K-S test for both groups: what is your conclusion?
k.
Independent of the outcome of j, we will conduct, using SPSS (first reset the split file
operation!):
A. Levene’s test on equality of variances.
B. a two independent samples t-test , depending on the outcome of Levene’s test.
C. Wilcoxon’s rank sum test as an non parametric alternative for the t-test at B.
Report for each of these tests 1. the observed value, 2. the p-value and 3. the conclusion.