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Republic of the Philippines
CAVITE STATE UNIVERSITY
Don Severino de las Alas Campus
Indang, Cavite
(046) 4150-010 / (046) 4150-13 loc 253
www.cvsu.edu.ph
OFFICE OF THE GRADUATE SCHOOL AND OPEN LEARNING COLLEGE
LEARNING ACTIVITY
SPEARMAN’S RANK ORDER CORRELATION
Name:___________________________
Section:_____________________
Score: _________
Contact Number: ___________
Objectives: At the end of this exercise, the student is expected to:
1. know when and how to estimate the Spearman’s correlation coefficient;
2. interpret the estimated correlation coefficient.
Part I. Problem Solving
1. The marks obtained by twelve students in Math and Physics are given below:
MATH
PHYSICS
1 2 3 4 5 6 7 8 9 10 11 12
75 89 84 95 79 87 88 91 84 81 92 78
85 94 87 94 86 88 85 96 86 84 92 83
Assume that the variables are not
correlation coefficient.
normal, Compute and interpret the
You may use this example as your guide.
Dr. Cristina Hobbs, a Medical Curriculum Specialist, wants to determine if the score of
nursing students in a Creativity Test is correlated to their score in Board Examination
for Nursing. She randomly selected seven (7) graduates of nursing program from
different university. The result is given below:
Student
Creativity
1
2
3
4
5
6
7
97
94
90
89
87
85
83
Score in the
Board Exam
95
90
85
93
84
80
96
Is the score of students in a Creativity Test correlated to their performance in the Board
Exam?
Make a simple table like this one:
Student
Creativity
Score (y)
(x)
1
97
95
2
94
90
3
90
85
4
89
93
5
87
84
6
85
80
7
83
96
Rx (Rank
of x)
7
6
5
4
3
2
1
Ry (Rank
of y)
6
4
3
5
2
1
7
D = Rx Ry
1
2
2
-1
1
1
-6
D2
1
4
4
1
1
1
36
ΣD2 = 48
SOLUTION:
where:
N = number of observations = 7
rs = 0.14
Interpretation:
The obtained rs value is 0.14 hence, we can say that there is a very weak correlation
between the score of students in creativity test and their performance in the Board
Exam.
Part II. Problem Formulation
Using the data that you have as a teacher, create a realistic problem situation that will
require study of the relationship between two variables using non-parametric correlation
analysis. Use SPSS Package to facilitate the analysis( Please provide
screenshots/picture/raw outputs as proof)
Expected output:
1. Background of the problem including specific objective(s).
2. Estimation of the coefficient.
3. Interpretation of the obtained correlation coefficient in the context of the
problem.
4. Test of hypothesis on the significance of the correlation coefficient.
PREPARED BY:
ANALYN A. MOJICA
Associate Professor
January 9, 2021
Republic of the Philippines
CAVITE STATE UNIVERSITY
Don Severino de las Alas Campus
Indang, Cavite
(046) 4150-010 / (046) 4150-13 loc 253
www.cvsu.edu.ph
OFFICE OF THE GRADUATE SCHOOL AND OPEN LEARNING COLLEGE
Name: __________________________
Program: ________________________
Date: ______________
Learning Activity 3
DISCRETE PROBABILITY DISTRIBUTIONS
OBJECTIVES:
At the end of this exercise the student must be able:
1. to determine the different discrete probability functions.
2. to construct the distribution of a random variable.
METHODS:
1.
For each of the following, determine whether it can serve as the probability distribution of
some random variable:
a. f(x) = 1/10 for x = 1, 2, 3, … , 10;
b. f(x) = 1/8
for x = 0, 1, 2, …, 8;
c. f(x) =
for x = 1, 2, 3, 4, 5;
d. f(x) =
for x = 0, 1, 2, 3.
2. From a group of 24 students, 15 are boys and 9 are girls. Let X equal the number of boys in
a sample of five students selected at random and without replacement from the group. Find
the following probabilities:
a. P(X = 2)
b. P(X≤ 2)
3. Say there are 3 principals in a school of 50 teachers. A sample of size 10 is taken at
random and without replacement. Let X denote the number of principals in the sample.
Find the probability that the sample contains:
a. exactly 1 principal.
b. at most 1 principal.
4. On a ten-question multiple-choice test there are five possible answers, of which one is
correct (C) and four are incorrect (I). If a student guesses randomly and independently,
find the probability of:
a. being correct on two questions.
b. getting at least 1 correct answers.
c. getting between 4 and 8 correct answers inclusive.
5. Let p equal the proportion of all college and university students who would say yes to the
question, “Would you drink from the same glass as your friend if you suspected that this
friend was an AIDS virus carrier?” Assume that p=0.10. Let X equal the number of students
out of a random sample of size n=9 who would say yes to this question.
a. How is X distributed
b. Find P(X= 2)
c. Find P(X ≥ 2)
Note: To be submitted of November 28, 2020
Republic of the Philippines
CAVITE STATE UNIVERSITY
Don Severino de las Alas Campus
Indang, Cavite
(046) 4150-010 / (046) 4150-13 loc 253
www.cvsu.edu.ph
OFFICE OF THE GRADUATE SCHOOL AND OPEN LEARNING COLLEGE
Name: __________________________
Program: ________________________
Date: ______________
Score:____________
Learning Activity
COMPARISON OF 2 OR MORE POPULATIONS (NONPARAMETRIC)
OBJECTIVES: At the end of the exercise, the student must be able to:
1. implement Signed Rank test, Wilcoxon Signed Rank test and Mann-Whitney U test for
the analysis of 2 populations;
2. implement Kruskal Wallis H test for the analysis of k populations; and
3. formulate a realistic problem situation for comparing k populations.
MATERIALS:
Calculator, Class Record, Stat Software
PART 1: PROBLEM SOLVING
Directions:
1.
For each problem, follow the steps in Hypothesis Testing.
2.
Use SPSS or Excel.
3.
Copy paste Outputs.
1. The following are the weights (in pounds) before and after, of 16 persons who stayed on
a certain weight-reducing diet for 2 weeks:
Before
After
169.0
159.9
188.6
181.3
222.1
209.0
160.1
162.3
187.5
183.5
202.5
197.6
167.8
171.4
214.3
202.1
143.8
145.1
198.2
185.5
166.9
142.9
160.5
198.7
149.7
181.6
158.6
145.4
159.5
190.6
149.0
183.1
Use the large sample Signed Rank test at 0.05 level of significance to test whether the
weight-reducing diet is effective.
2.
The weights of five people before they stopped smoking and 5 weeks after they stopped
smoking, in kilograms, are as follows:
1
66
71
Before
After
INDIVIDUAL
3
69
68
2
80
82
4
52
56
5
75
73
Use the Wilcoxon signed-rank test to test the hypothesis, at the 0.05 level of
significance, that giving up smoking has no effect on a person’s weight against the
alternative that one’s weight increases if he quits smoking.
3. An experiment measures the intelligence quotients (IQs) of adult male students of tall,
And short stature. The results are given below. Assuming that the data are not
normally distributed, determine at the 0.01 significance level whether there is any
difference in the IQ scores relative to the height differences using Mann Whitney U Test.
Tall
Short
110
95
105
103
118
115
112
107
90
3. A teacher wishes to test three different teaching methods: I, II, and III. To do this, three
groups of five students are chosen at random, and each group is taught by a different
method. The same examination is then given to all students, and the grades obtained
are shown below. Assuming that assumption of normality is not satisfied, determine
whether there is a difference between the teaching methods at 0.05 level of significance
using Kruskal Wallis H Test.
Method I
75
62
71
58
73
Method II
81
85
68
92
90
Method III
73
PART II: Problem Formulation
79
60
75
81
Using the any data you have, construct a problem situation that would require the
comparison of k independent samples that can be analyzed by Kruskal Wallis Analysis of
Variance.
Guidelines:
1. Provide sufficient background of the problem.
2. State the necessary assumptions needed to perform the test.
3. Perform test of hypothesis at = 5 % to answer the objective of the study.
PREPARED BY:
ANALYN A. MOJICA
ASSO. PROF.
January 9, 2021
Republic of the Philippines
CAVITE STATE UNIVERSITY
Don Severino de las Alas Campus
Indang, Cavite
(046) 4150-010 / (046) 4150-13 loc 253
www.cvsu.edu.ph
OFFICE OF THE GRADUATE SCHOOL AND OPEN LEARNING COLLEGE
LEARNING ACTIVITY
PEARSON PRODUCT MOMENT CORRELATION
Name:___________________________
Section:_____________________
Score: ___________________
Contact Number: ___________
Objectives: At the end of this exercise, the student is expected to:
1. know when and how to estimate the Pearson’s correlation coefficient;
2. interpret the estimated correlation coefficient; and
3. perform test of hypothesis on the Pearson correlation coefficient.
Part I. Problem Solving
1. Princess wants to determine if there is a significant linear relationship between the
expenditures (Y) of UPLB students in a month measured in pesos are related to their age in
years (X). A random sample of 10 UPLB students was obtained and the following data were
gathered:
Student
1
2
3
4
5
6
7
8
9
10
Age
18
17
16
18
19
20
19
21
22
17
Expenditure 5000 5200 5300 4800 4900 4500 5000 4600 4500 5300
a. Compute and interpret the correlation coefficient between the expenditures (Y) and age (X) of
UPLB students. Assume that variables are bivariate normal.
SSx = _________________________
SSy = _________________________
SPxy = ________________________
r = ___________________________
Interpretation: ___________________________________________________________
_______________________________________________________________________.
b. Is there evidence to conclude that as the UPLB students get older, they become thriftier? Use
a 0.05 level of significance.
Ho: _______________________________________________________________________
Ha: _______________________________________________________________________
Test Statistic: _______________________________________________________________
Decision Rule: Reject Ho if _____________________________, otherwise fail to reject Ho.
Computations:
Decision: __________________________________________________________________
Conclusion: ________________________________________________________________
__________________________________________________________________________.
Part II. Problem Formulation
Using the data that you have as a teacher, create a realistic problem situation that will require study of
the relationship between two variables (at least interval in scale) using parametric correlation analysis.
Use SPSS Package to facilitate the analysis ( PLEASE provide screenshots, picture or raw outputs as
proof).
Expected output:
1.
2.
3.
4.
Background of the problem including specific objective(s).
Estimation of the Pearson Product Moment Correlation Coefficient.
Interpretation of the obtained correlation coefficient in the context of the problem.
Test of hypothesis on the significance of the correlation coefficient.
For manual computation, you may use this example as your guide.
1. It is believed that there is a linear relationship between an infant’s length and weight at birth. A
pediatrician obtained the following measurements on the length and weight of newly born infants
in a certain district hospital.
Infant
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Length (cm) Weight (kg)
57.5
2.75
52.8
2.15
61.3
4.41
67.0
5.52
53.5
3.21
62.7
4.32
56.2
2.31
68.5
4.30
69.2
3.71
68.7
4.40
67.1
4.89
56.7
2.50
58.3
2.38
51.0
2.14
59.9
3.72
Assume that the variables are bivariate normal.
1. Compute and interpret the correlation coefficient.
2. Is there evidence to say that the length and weight of newly born infants are positively linearly
related? Test at = 0.05.
1. Computations:
X
Y
1
57.5
2.75
X*X
3306.25
Y*Y
7.5625
X*Y
158.125
2
52.8
2.15
2787.84
4.6225
113.520
3
61.3
4.41
3757.69
19.4481
270.333
4
67
5.52
4489.00
30.4704
369.840
5
53.5
3.21
2862.25
10.3041
171.735
6
62.7
4.32
3931.29
18.6624
270.864
7
56.2
2.31
3158.44
5.3361
129.822
8
68.5
4.3
4692.25
18.4900
294.550
9
69.2
3.71
4788.64
13.7641
256.732
10
68.7
4.4
4719.69
19.3600
302.280
11
67.1
4.89
4502.41
23.9121
328.119
12
56.7
2.5
3214.89
6.2500
141.750
13
58.3
2.38
3398.89
5.6644
138.754
14
51
2.14
2601.00
4.5796
109.140
15
59.9
Totals 910.4
3.72
3588.01
13.8384
222.828
52.71 55798.54 202.2647 3278.392
(910.4)2
SS x = 55798.54 −
= 543.3293333 [1 pt]
15
(52.71) 2
SS y = 202.2647 −
= 17.04176 [1 pt]
15
(910.4)*(52.71)
SPxy = 3278.392 −
= 79.2464 [1 pt]
15
79.2464
r=
= 0.823551464 [2 pts]
543.3293333*17.04176
Interpretation: There is a very strong positive linear
relationship between length and weight of newly born
infants.
2. Test of hypothesis
Ho: There is no linear relationship between length and weight of newly born infants.
( = 0)
Ha: There is a positive linear relationship between length and weight of newly born
infants. ( > 0)
Test Procedure: t-test at = 0.05.
Decision Rule: Reject Ho if |tc| > t(n-2), otherwise fail to reject HO.
Computation:
t(n-2) = t0.05(15-2) = t0.05(13) = 1.771
tc =
0.823551464* 15 − 2
1 − (0.823551464) 2
= 5.2347
Decision: Since 5.2347 > ttab, we reject Ho.
Conclusion: At = 0.05, we have evidence to say that there is a positive linear
relationship
between
length
and
weight
of
newly
born
infants.
PREPARED BY:
ANALYN A. MOJICA
Associate Professor
January 9, 2021
Republic of the Philippines
CAVITE STATE UNIVERSITY
Don Severino de las Alas Campus
Indang, Cavite
(046) 4150-010 / (046) 4150-13 loc 253
www.cvsu.edu.ph
OFFICE OF THE GRADUATE SCHOOL AND OPEN LEARNING COLLEGE
Name: __________________________
Program: ________________________
Date: ______________
Score: _____________
Learning Activity
COMPARISON OF TWO OR MORE POPULATIONS (PARAMETRIC)
OBJECTIVES: At the end of the exercise, the student must be able to:
1. implement t-test for the analysis of 2 populations;
2. implement ANOVA for the analysis of k populations; and
3. formulate a realistic problem situation for the ONE-WAY ANOVA.
MATERIALS:
Calculator, Class Record, Stat Software
PART I: Computation
Direction: For each problem, show your complete solution and follow the steps in Hypothesis
Testing. Verify your answer using SPSS or Excel (Copy paste SPSS or Excel Outputs after
each manual computation)
1.
A Psychology professor, teaching at large university, wants to know whether there is
a difference between the IQs of male and female students in attendance. She randomly
and independently selects 20 female students and 20 male students and has them take
the IQ test. The resulting IQ data are as follows:
Female
130
117
124
120
125
109
100
118
127
130
126
Male
106
114
134
120
107
131
133
134
122
111
109
118
131
104
130
116
122
115
129
117
101
144
122
124
116
120
119
114
110
What conclusion can be drawn out of the given data? Test your hypothesis using 0.01
level of significance. Use t-test for two independent samples, assuming unequal
population variances.
2. As part of the study to determine the effects of a feeding program on weight gain, 12
healthy students were weighed at the beginning of the said program. They were
reweighed after three months. Do the results suggest evidence of weight gain? Use ttest for dependent/related samples with alpha
.
Subject
Initial
Weight
(lb)
3-Month
Weight (lb)
3.
1
120
2
141
3
130
4
162
5
150
6
148
7
135
8
140
9
129
10
120
11
140
12
130
123
143
140
162
145
150
140
143
130
118
141
132
A school district supervisor wishes to compare four programs for training teachers to
perform a certain manual task. Twenty new teachers are randomly assigned to the
training programs, with 5 in each program. At the end of the training period, a test is
conducted to see how quickly teachers can perform the task. The number of times the
task is performed per minute is recorded for each trainee, with the following results:
Program 1: 9, 12, 14, 11, 13
Program 2: 10, 6, 9, 9, 10
Program 3: 12, 14, 11, 13, 11
Program 4: 9, 8, 11, 7, 8
(a) Construct the ANOVA table
(b) Using α = .05, determine whether the treatments differ in their effectiveness.
For ANOVA, use this example as your guide.
The following data represent the scores of a random sample of students in each section during
the first long examination:
Section
Samples
A
87
45
75
65
82
B
78
56
66
49
56
45
C
53
76
59
73
43
32
62
Is there a significant difference between the performances of students in the three sections?
Use 0.01 level of significance.
Solution:
1. Ho : There is no significant difference between means
Ha : At least one mean is significantly different
2. Specify the level of significance and the sample sizes
3. Test Statistics : F-test (One-way ANOVA)
4. Critical Region : Reject Ho if
Fc > Ftab at 0.05 level of significance
5. Computations: Construct an ANOVA Table
Section
ΣX
ΣX2
354
26168
350
21138
398
24112
Samples
A
87 45 75 65
82
B
78 56 66 49
56
45
C
53 76 59 73
43
32
62
ΣX2 = 71418
GT = 354+350+398 = 1102
SST = 71418 - (11022/18) = 3951.11
SSB = [(3542/5) + (3502/6)+ (3982/7)] - (11022/18) = 642.12
SSW = SST – SSB =3951.11 – 642.12 = 3308.99
MSB = SSB/df = 642.12 / 2 = 321.06
MSW = SSW/df = 3308.99 / 15 = 220.60
Fc = MSB/MSW = 321.06/220.60 = 1.455
ANOVA TABLE
F tab
df
Sum of
Square
Mean
Square
Fcomp
0.05
0.01
Between(TREATMENT)
2
642.12
321.06
1.455
3.68
6.36
Within(ERROR)
15
3308.99
220.60
Total
17
3951.11
Source of Variation
6. Decision :
Since Fc < Ftab at 0.05 level of significance, therefore accept Ho and
conclude that there is no significant differences between the mean scores of three sections.
Note: Use F table for the critical value of F, (Ftab)
Part II. Problem Formulation
Construct a problem situation that would require the comparison of k independent samples
that can be analyzed by ONE-WAY ANOVA (parametric).
Guidelines:
1. Provide sufficient background of the problem.
2. State the necessary assumptions needed to perform the test.
3. Perform test of hypothesis at = 5 % to answer the objective of the study.
PREPARED BY:
ANALYN A. MOJICA
ASSO. PROF.
January 9, 2021
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