A presentation about statistics

1. 1/25/2023 2:04 PM 1
* T-test (independent and paired samples)
* One – way analysis of variance (between groups
and repeated measures ANOVA)
*Two – way between groups ANOVA

2. METHODS OF EDUCATIONAL RESEARCH
ASSUMPTIONS
• Level of measurement
• Random sampling
• Independence of observations
• Normal distribution
• Homogeneity of variance
1/25/2023 2:04 PM 2
EDUC 606

3. METHODS OF EDUCATIONAL RESEARCH
Independent samples t test
• Example of research question: Is
there a significant difference in the
mean self – esteem scores for
males and females?
• What you need: Two variables:
• One categorical, independent
variable(males/females)
• One continuous, dependent
variable(self- esteem scores)
1/25/2023 2:04 PM 3
EDUC 606

4. METHODS OF EDUCATIONAL RESEARCH
Paired- samples t test
• Example of research question: Is there a
significant change in participants’ Fear of
Statistics Test scores following participation in
an intervention designed to increase
students’ confidence in their ability to
successfully complete a statistics course?
• Additional assumption: The difference
between the two scores obtained for each
subject should be normally distributed. With
samples of 30+, violation of this assumption is
unlikely to cause any serious problems.
1/25/2023 2:04 PM 4
EDUC 606

5. METHODS OF EDUCATIONAL RESEARCH
One- way between- groups ANOVA
• Example of research question: Is there
a significant difference in optimism
scores for young, middle- aged and
old participants?
• What you need: Two variables:
one categorical iv with 3 or more
distinct categories or continuous.
One continuous dv.
1/25/2023 2:04 PM 5
EDUC 606

6. METHODS OF EDUCATIONAL RESEARCH
ONE- WAY REPEATED MEASURES
• Example of research question: Is there a
change in confidence scores over the three
time periods?
• What you need:
• One group of participants measured on the
same scale on three different occasions or
under three different conditions, or each
person measured on three different questions
or items using the same response scale. This
involves Two variables:
one iv (categorical)
One dv (continuous)
1/25/2023 2:04 PM 6
EDUC 606

7. METHODS OF EDUCATIONAL RESEARCH
Two- way between groups ANOVA
• Example of research question:What
is the impact of age and gender on
optimism?
• What you need: Three variables:
two categorical iv’s
One continuous dv
1/25/2023 2:04 PM 7
EDUC 606

8. METHODS OF EDUCATIONAL RESEARCH
Statistical techniques to explore
relationships among variables
• Pearson correlation coefficient
(r).(Zero- order correlation)
• Example of research question: Is
there a significant relationship
between age and performance?
• What you need: Two variables: both
continuous or one continuous and
one dichotomous (two values)
1/25/2023 2:04 PM 8
EDUC 606

9. METHODS OF EDUCATIONAL RESEARCH
Partial correlation
• Partial correlation- allows you to explore
the relationship between two variables,
while statistically controlling for( getting
rid of) the effect of another(confounding)
variable that you think might be
contaminating or influencing the
relationship.
• What you need: Three continuous
variables:
Two variables that you wish to explore the
relationship
One variable that you wish to control
1/25/2023 2:04 PM 9
EDUC 606

10. METHODS OF EDUCATIONAL RESEARCH
Regression Analyses:
• Simple linear
• Multiple ( standard or simultaneous,
hierarchical or sequential,stepwise)
• ASSUMPTIONS:
*Sample size (N=50+8m, m is the number of iv’s) or
104+m.
* multicollinearity and singularity of iv’s
* outliers
* normality, linearity, homoscedasticity,
independence of residuals( residuals are the
differences between the obtained and the
predicted dv scores.
1/25/2023 2:04 PM 10
EDUC 606

11. METHODS OF EDUCATIONAL RESEARCH
T- test examples
– The following are the scores of 10 males and 10 female students in
spelling. Test the null hypothesis that there is no significant
difference between the performance of male and female students in
the said test. Use the t test at .05 level of significance.
Male female
14 12
18 9
17 11
16 5
4 10
14 3
12 7
10 2
9 6
17 13
1/25/2023 2:04 PM 11
EDUC 606

12. METHODS OF EDUCATIONAL RESEARCH
T test for dependent or correlated samples
An experimental study was conducted on
the effect of programmed materials in
English on the performance of 20
selected students. Before the program
was implemented, the pre-test was
administered and after 5 months the
same instrument was used to get the
post-test result. The following is the
result of the experiment.
1/25/2023 2:04 PM 12
EDUC 606

13. METHODS OF EDUCATIONAL RESEARCH
• Pre- test( x1):
20,30,10,15,20,10,18,14,15,20,18,15,
15,20,18,40,10,10,12,20.
• Post- test(x2):
• 25,35,25,25,20,20,22,20,20,15,30,10,
16,25,10,45,15,10,18,25.
1/25/2023 2:04 PM 13
EDUC 606

14. METHODS OF EDUCATIONAL RESEARCH
ANOVA examples
A sari-sari store is selling 4 brands of
shampoo. The owner is interested if
there is a significant difference in the
average sales for one week. The
following data are recorded:
Brand A: 7,3,5,6,9,4,3.
Brand B: 9,8,8,7,6,9,10.
Brand C: 2,3,4,5,6,4,2.
Brand D: 4,5,7,8,3,4,5.
Perform one way anova at .05 alpha level
1/25/2023 2:04 PM 14
EDUC 606

15. METHODS OF EDUCATIONAL RESEARCH
Example of two way ANOVA
Teacher factor
A B C
Method1 40 50 40
41 50 41
40 48 40
39 48 38
38 45 38
Method 2 40 45 50
41 42 46
39 42 43
38 41 43
38 40 42
Method 3 40 40 40
43 45 41
41 44 41
39 44 39
38 43 38
1/25/2023 2:04 PM 15
EDUC 606

16. METHODS OF EDUCATIONAL RESEARCH
Pearson correlation and Regression examples
Below are the midterm (x) and the final (Y)
grades.
X: 75,70,65,90,85,85,80,70,65,90.
Y: 80,75,65,95,90,85,90,75,70,90.
Is there a significant relationship between the
midterm and the final grades of students in
Mathematics? Use alpha at .05 level of
significance.
Suppose the midterm report is 88 (x=88), what
is the value of the final grade?
1/25/2023 2:04 PM 16
EDUC 606

17. METHODS OF EDUCATIONAL RESEARCH
Multiple regression example
• The following are data on the ages and incomes of a
random sample of 5 executives working for in ABC
corporation and their academic achievements while
in college.
• Age Academic Income
achievement ( in thousand pesos)
x1 x2 Y
38 95 81.7
30 90 73.3
46 92 89.5
40 92 79.0
32 85 69.9
Do age and academic achievement predict income?
1/25/2023 2:04 PM 17
EDUC 606

18. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 18
EDUC 606

19. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 19
EDUC 606

20. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 20
EDUC 606

21. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 21
EDUC 606

22. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 22
EDUC 606

23. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 23
EDUC 606

24. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 24
EDUC 606

25. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 25
EDUC 606

26. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 26
EDUC 606

27. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 27
EDUC 606

28. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 28
EDUC 606

29. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM
EDUC 606

30. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 30
EDUC 606

31. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 31
EDUC 606

32. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 32
EDUC 606

33. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 33
EDUC 606

34. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 34
EDUC 606

35. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 35
EDUC 606

36. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 36
EDUC 606

37. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 37
EDUC 606

38. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 38
EDUC 606

39. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 39
EDUC 606

40. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 40
EDUC 606

41. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 41
EDUC 606

42. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 42
EDUC 606

43. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 43
EDUC 606

44. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 44
EDUC 606

45. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 45
EDUC 606

46. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 46
EDUC 606

47. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 47
EDUC 606

48. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 48
EDUC 606

49. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 49
EDUC 606

50. METHODS OF EDUCATIONAL RESEARCH
1/25/2023 2:04 PM 50
EDUC 606
Prepared by:
© 2018
REY M. REGIDOR
Student, School of Education
Ateneo de Zamboanga University