xcdhvjbkhnjlm;,

2. HYPOTHESISTESTING
1.TESTINGTHE ASSUMPTION ON 1
POPULATION MEAN AND PROPORTION
2.TESTING IFTHERE IS A SIGNIFICANT
DIFFERENCE BETWEEN 2 POPULATION
MEANS

3. RESEARCH QUESTIONS FROM
PRACTICAL RESEARCH OUTPUTS
SAMPLE OUTPUTS:
ISTHERE A SIGNIFICANT DIFFERENCE ONTHE
RESPONDENTS’ PERCEIVED STRESS LEVELWHEN
GROUPED ACCORDINGTO SEX?
ISTHERE A SIGNIFICANT DIFFERENCE BETWEEN MALES
AND FEMALES INTERMS OF SOCIAL MEDIA ADDICTION?

4. “SIGNIFICANT RELATIONSHIP”

5. Suppose you are a researcher and you want to know
whether there is a significant relationship between a
person’s number of hours spent in playing online
games and his/her level of aggressive behavior,
how are you going to establish this relationship?
SITUATIONAL ANALYSIS

6. LINEAR
CORRELATION
CORRELATION

7. ATTHE END OFTHE LESSON, IWOULD BE ABLETO:
 1. DIFFERENTIATE UNIVARIATE AND BIVARIATE DATA
 2. IDENTIFY DEPENDENT AND INDEPENDENTVARIABLES
 3. CONSTRUCT A SCATTER PLOT
 4. ESTIMATE STRENGTH OF ASSOCIATION BETWEENTHE
VARIABLES BASED ON A SCATTER PLOT
 5. CALCULATETHE PEARSON’S SAMPLE CORRELATION
COEFFICIENT
 6. SOLVE PROBLEMS INVOLVING CORRELATION ANALYSIS

9. NATURE OF BIVARIATE DATA
o Univariate data – a study that involves only one
variable
Ex: Investigating the average speed of 30 cars
o Bivariate data – a study that examines the relationship
between two variables.
Ex: Relationship between the performances in Statistics and
Probability and General Mathematics of the senior high school

10. DEPENDENT AND INDEPENDENT VARIABLES
o Independent Variable– a standalone variable, which means that
its value can change without reference to another variable.
o Dependent Variable – a variable that changes as a result of the
change in the independent variable.
Example:
An educational researcher tests the effects of using a
particular teaching strategy on the performance in mathematics of
college students.

11. DEPENDENT AND INDEPENDENT VARIABLES
Identify the independent and dependent variables in the following
situations.
1. A college professor studies how attitude affects the
math performance of engineering students.
2. The principal wants to determine on how age correlates to the
attention span of the students.

12. SCATTER
PLOT

13. SCATTER PLOT
o shows the relationship of the variable in a bivariate
data
o it consists of a series of points plotted on a
rectangular coordinate plane
• x-axis (independent variable)
• y-axis (dependent variable)

14. CONSTRUCTING A SCATTER PLOT
Example 1:
Construct a scatter plot for the
given data.
x 10 14 19 23 28
y 34 65 81 115 124
y
x
0 7 14 21 28 35
0
30
60
90
120
150

15. SCATTER PLOTS
RELATIONSHIP AND INTERPRETATION
RELATIONSHIP AND INTERPRETATION

16. y
x
Dependent
variable
Independent
variable
y
x
Dependent
variable
Independent
variable
PERFECT POSITIVE
CORRELATION
POSITIVE
CORRELATION
-indicated by an upward trend of the points

17. PERFECT POSITIVE
CORRELATION
POSITIVE
CORRELATION
EXAMPLE
1. Income and Educational Attainment of
Employees
2. Number of hours studied and score
obtained in a test

18. y
x
Dependent
variable
Independent
variable
NO
CORRELATION
-points are scattered in the plane

19. NO
CORRELATION
EXAMPLE
1. Sense of humor and Shoe size of a
person
2. IQ and Height of a person

20. y
x
Dependent
variable
Independent
variable
y
x
Dependent
variable
Independent
variable
PERFECT NEGATIVE
CORRELATION
NEGATIVE
CORRELATION
-indicated by a downward trend of the points

21. PERFECT NEGATIVE
CORRELATION
NEGATIVE
CORRELATION
EXAMPLE
1. Number of workers and number of
days to complete a job
2. Amount of rainfall and amount of
agricultural harvest

22. SCATTER PLOT
Example 2
The table shows the time in hours spent by
five students in playing computer games and
scores these students got on a Math test.
Construct and interpret the scatter plot for the
given data.
Time(x) 1 2 3 4 5
Score (y) 25 20 15 10 5
y
x
0 1 2 3 4 5
0
5
10
15
20
25
Interpretation:
The scatter plot represents a perfect negative
correlation since, as the amount of time spent in
paying computer game increases, the score in Math
test decreases.

23. SCATTER PLOT
Example 3
The table shows the number of selfies
posted online by students and scores sthey
obtained from a Science test. Construct and
interpret the scatter plot for the given data.
Number of
Selfies (x)
1 3 5 7 9
Score (y) 25 5 50 35 15
Interpretation:
The scatter plot shows no pattern. Thus, it can
be said that there is no correlation between the
number of selfies posted online and the scores
obtained from a Science test.
y
x
0 1 3 5 7 9
0
10
20
30
40
50
2 4 6 8

24. CORRELATION
PEARSON PRODUCT MOMENT
PEARSON PRODUCT MOMENT
CORRELATION COEFFICIENT
CORRELATION COEFFICIENT

25. PEARSON PRODUCT MOMENT CORRELATION COEFFICIENT
o also called as Pearson’s r, in honor of the
English mathematician Karl Pearson who
developed the formula in the 1880s.
o a statistical tool that determines the existence,
strength, and direction between two variables.

26. FORMULA: Pearson’s r

27. FORTHE INTERPRETATION OFTHE RESULT:
Pearson r Qualitative Interpretation
+ 1 Perfect
+0.80 – +0.99 Very High
+0.60 – +0.79 Moderately High
+0.40 – +0.59 High
+0.20 – +0.39 Moderately Low
+0.01 – +0.19 Very Low
0 No Correlation

28. EXAMPLE 1
JM, an educational researcher at a science high school, wants to know
whether a student’s physics grade depends on his math grade. He collects a
sample of 5 students and gathered their grades in math and science. The math
and science grade of the students are five in the table below:
Can JM conclude a strong positive relationship between the math and
physics grades?
Math Grade
(x)
76 82 87 92 95
Physics Grade
(y)
75 83 88 89 93

29. EXAMPLE 1: SOLUTION
5, 700
6, 806
7, 656
8, 188
8, 835
5, 776
6, 724
7, 569
8, 464
9, 025
5, 625
6, 889
7, 744
7, 921
8, 649
TOTAL:

30. EXAMPLE 1: SOLUTION
Interpretation:
Therefore, JM can say that there is a strong positive relationship
between the math and physics grades.

31. EXAMPLE 2
The table shows the time in hours spent by five students in
playing computer games and scores of these students got on a
Math test. Solve for the Pearson’s r and describe the result.
Time(x) 1 2 3 4 5
Score (y) 25 20 15 10 5

32. EXAMPLE 2: SOLUTION
25
40
45
40
25
1
4
9
16
25
625
400
225
100
25
TOTAL:

33. EXAMPLE 2: SOLUTION
Interpretation:
Therefore, we can say that there is a perfect negative relationship between
the time spent in playing computer games and the score in a Math test. .

34. EXAMPLE 3
Loida studies if age correlates with the average number of hours of sleep,
so she selected a random sample size 6 and surveyed the needed data. The
gathered data are given below. Can Loida conclude a strong positive
relationship between a person’s age and the number of hours he or she
sleeps?
Age(x) 8 15 22 27 34 40
Sleep (y) 8 8 7 7 5 6

35. PAGE 301- #3 A-C

36. IWAS ABLE TO:
1. DIFFERENTIATE UNIVARIATE AND BIVARIATE DATA
2. IDENTIFY DEPENDENT AND INDEPENDENTVARIABLES
3. CONSTRUCT A SCATTER PLOT
4. ESTIMATE STRENGTH OF ASSOCIATION BETWEENTHE
VARIABLES BASED ON A SCATTER PLOT
5. CALCULATETHE PEARSON’S SAMPLE CORRELATION
COEFFICIENT
6. SOLVE PROBLEMS INVOLVING CORRELATION ANALYSIS

37. HYPOTHESISTESTING USING
PEARSON’S R

38. STEP 1: NULL AND ALTERNATIVE HYPOTHESIS
Ho: r=0 ;There is no significant
relationship…
Ha: r≠0 ;There is a significant
relationship…

39. STEP 2: SIGNIFICANCE LEVEL
ɑ=.05 or .10 or .01

40. STEP 3: CRITICALVALUES OFT
df= n-2
Refer to the t-table

41. STEP 4: FORMULA FOR T

42. STEP 5: DECISION
FAIL TO REJECT OR REJECT Ho

43. STEP 6: INTERPRETATION
Thus at 5% significance level,
(there is or there is no) significant
relationship between …

44. NOTE
If there is no significant relationship, end of
solution
If there is a significant relationship, you can
predict the value of y given x (REGRESSION
ANALYSIS)

45. REGRESSION
ANALYSIS

46. REGRESSION ANALYSIS IS ONLY APPLICABLE IFTHERE IS A
SIGNIFICANT RELATIONSHIP BETWEEN X ANDY
• It gives the regression equation that enables
us to predict the value of the dependent (y)
variable given the value of the independent
(x) variable

47. REGRESSION LINE (LINE OF BEST FIT)

49. YOU CAN USE THE FORMULA TO
PREDICT THE DEPENDENT (Y)
VARIABLE USING THE
INDEPENDENT (X)VARIABLE

50. PAGE 315 ; # 5
SOLVE FOR R
TEST THE SIGNIFICANT
RELATIONSHIP
REGRESSION LINE

51. QUESTION
Perform the steps of Hypothesis Testing to test if
there is a significant difference between number of
hours spent on social media and a person’s happiness
index (scale from 1-10, 10 being the highest)
Ask at least 5 respondents