Problem set #8 Fall 2023
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BIOL 4500 – Introduction to Biological Research Name_________________________
Problem Set # 8
(1) An experiment was conducted to evaluate the effectiveness of a treatment for tapeworm in the stomachs of sheep. A random sample of 60 worm-infected sheep of approximately the same age and health was randomly divided into two groups. Thirty of the sheep were injected with an experimental drug and the remaining 30 were left untreated. After a 6-month period, the sheep were slaughtered and the following worm counts from their small intestines were recorded. Animals infected with a heavy parasite load will often have a lower weight than individuals with a low parasite load or animals free of parasites. Therefore, to further assess the effectiveness of the experimental drug in reducing parasite load, a subset of the
sheep given the experimental drug were weighed (in pounds) both before and after the experiment. Analyze the data using the appropriate statistical techniques in SPSS and answer the questions.
Drug-treated sheep: 78, 75, 68, 92, 55, 74, 65, 80, 98, 52, 67, 55, 49, 66, 75, 90, 89, 73, 61, 76, 81, 89, 82, 70, 68, 74, 85, 97, 95, 78
Untreated sheep: 71, 70, 66, 85, 60, 72, 57, 75, 92, 56, 63, 52, 48, 67, 70, 88, 80, 65, 60, 74, 76, 78, 78, 62, 73, 73, 75, 88, 94, 75
Initial weight of sheep: 30.20, 40.90, 50.10, 60.30, 70.10, 30.80, 80.10, 70.30, 50.90, 80.90
Final weight of sheep: 30.70, 40.20, 50.40, 50.80, 80.80, 30.40, 40.70, 50.30, 60.80, 70.20
(a) What are the means, standard deviations, standard errors, and variance for the data sets? (2 pts.)
Descriptive Statistics
N
Minimu
m
Maximu
m
Mean
Std.
Deviation
Varianc
e
Statistic
Statistic
Statistic
Statistic
Std.
Error
Statistic
Statistic
Drugtreated
30
49.00
98.00
75.2333
2.42624
13.28905
176.599
Untreated
30
48.00
94.00
71.4333
2.08590
11.42497
130.530
Valid N (listwise)
30
Descriptive Statistics
N
Minimu
m
Maximu
m
Mean
Std.
Deviation
Varianc
e
Statistic
Statistic
Statistic
Statistic
Std.
Error
Statistic
Statistic
Initialweight
10
30.20
80.90
56.4600
5.97216
18.88563
356.667
Finalweight
10
30.40
80.80
50.5300
5.17535
16.36589
267.842
Valid N (listwise)
10
(b) Calculate a 95% Confidence Interval for each mean. (1 pt.)
One-Sample Test
Test Value = 0
t
df
Significance
Mean
Difference
95% Confidence Interva
the Difference
One-Sided
p
Two-Sided
p
Lower
Upper
Initialweigh
t
9.454
9
<.001
<.001
56.46000
42.9500
69.9
Finalweigh
t
9.764
9
<.001
<.001
50.53000
38.8225
62.2
Drugtreate
d
31.008
29
<.001
<.001
75.23333
70.2711
80.1
Untreated
34.246
29
<.001
<.001
71.43333
67.1672
75.6
(c) State your null (H
0
) and alternative hypothesis (H
a
) for each test you intend to conduct. (2 pts.)
Null: There is no difference between the drug treated and the untreated sheep Alternative: There is a greater change between the Drug treated and the untreated sheep
(d) Are these tests one-tailed or two-tailed? Why? (2 pts.)
One-tailed (e) Are the data normally distributed? What evidence do you have of this? Which test (parametric or non-parametric) is most appropriate in each case? (2 pts.)
Tests of Normality
Kolmogorov-Smirnov
a
Shapiro-Wilk
Statistic
df
Sig.
Statistic
df
Sig.
Drugtreated
.133
10
.200
*
.968
10
.872
Untreated
.146
10
.200
*
.941
10
.562
Initialweight
.165
10
.200
*
.923
10
.385
Finalweight
.193
10
.200
*
.939
10
.539
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction
(f) For the parasite load comparison, does each group have equal variance? How did you test this? What do these results mean for the tests that you will be using? (2 pts.)
Independent Sam
Levene's Test for Equality of
Variances
F
Sig.
t
df
On
Drugtreated
Equal variances assumed
.436
.512
1.163
57
Equal variances not assumed
1.165
56.451
Independent Samples Effect Sizes
Standardizer
a
Point
Estimate
95% Confidence
Interval
Lower
Upper
Drugtreated
Cohen's d
12.50020
.303
-.212
.815
Hedges' correction
12.66774
.299
-.209
.804
Glass's delta
11.62690
.326
-.195
.840
a. The denominator used in estimating the effect sizes. Cohen's d uses the pooled standard deviation. Hedges' correction uses the pooled standard deviation, plus a correction factor. Glass's delta uses the sample standard deviation of the control (i.e., the second) group.
-
We can see that there more than a .0005 probability so we fail to reject our null hypothesis. (g) For each test you conducted, state the calculated test statistic, degrees of freedom, and
its associated p-value. Interpret your p-value statistically and biologically. (6 pts.)
-
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