Correlational Analysis on Quantitative Research.pptx

What is Correlational
Analysis?
• this is the relationship or linkage of two
variables
• Looking at the variables if they co-occur, co-relate,
or go together therefore you will only use
statistical techniques pertaining to this if you want
to find the relationship magnitude, direction, and
significance of two variables.

What is Correlational
Analysis?
Page 03
• This correlation coefficient (r) can take a value of -1 to +1
where a value of zero shows that there is no association
between the two variables. When there is a positive
coefficient or r > than 0, this means that as one variable
increases, so does the value of the other variable. A value
of negative coefficient or r < 0 means that if a variable
increase, the value of the paired variable decreases.
However, correlation does not mean causation (Sowell,
2001; Tabachnick & Fidell, 2013) and the only way to
establish causation is through experiment and logic.

To analyze correlation the ff
statistical techniques can be use
Page 04
1. Pearson Product Moment
Correlation
• We can use Pearson Product Moment Correlation
to measure or prove an existence of relationship
between two variables.
(Pearson Product-Moment Correlation - When You
Should Run This Test, the Range of Values the
Coefficient Can Take and How to Measure Strength
of Association., n.d.)

Assumptions (requirements for
usage of technique)
Page 05
1.
Normality
• Variables should show an approximately bell
curve when plotted on a histogram, practical
implications if this assumption is violated may
lead to degraded solutions and biased results.

usage of technique)
Page 06
2. Absence of Outliers
• If the data is observed, there are no very high
and very low values.
3. Level of Measurement
• Both variables should be either interval or ratio
or what we sometimes call as continuous data.

usage of technique)
Page 11
3. Spearman’s Rank
Correlation
• When your data involves ranked data (1st,
2nd , 3 rd) or follows a hierarchal order (grade
1, grade 2, grade 3) or (child, teen, youth) or
simply when you know that there is an order
for the responses.

usage of technique)
Page 08
1. Level of
Measurement
• Variables are ordinal (5 point scale from very low
to very high), and interval or ratio.
2. Paired Observations
• Observations should be paired, where if you get
the height of a respondent your other data
should also come from the same respondent
such as his birth order in the family

THE FORMULA
FOR PEARSON
PRODUCT
MOMENT
CORRELATION
PR 2

Formula for Pearson Product
Moment Correlation
Page 10

• r= correlation coefficient: this tells us the strength
of relationship as well as the direction of
relationship depending on the value or polarity
(positive or negative)
Moment Correlation
• x = variable x (we call them as such in replacement
of the name of the variable)
• y= variable y (we call them as such in replacement
of the name of the variable)

• x
̅ = mean of variable x (we get it by adding all the
values in x and then divide them depending on
how many there are in the columns x)
Moment Correlation
• y
̅̅ = mean of y (we get it by adding all the values in y
and then divide them depending on how many
there are in the columns y)

Step 1: Create a table like the one shown below and
put the values on x and y columns – the context of this
example is a study between Knowledge and Attitude
towards COVID 19 where x is Knowledge and y as the
Attitude
Steps on How to Use the
Formula

Formula

Formula
Step 2: compute the mean for x
x
̅ = 3 + 4 + 4 + 4 +2 +3 + 3 +2 +1 +
1
10
x
̅ = 2.7
Step 3: compute the mean of y
y
̅ = 3 + 5 + 5 +5 + 3 + 4 + 4 + 3 + 2 + 2
10
y
̅ = 3.6

Formula
Step 4: Fill out the
table by
subtracting the
value of x with x
̅
3 – 2.7 = 0.3
4 – 2.7 = 1.3
4 – 2.7 = 1.3 and so
on

Formula
Step 5: Fill out the
table by
subtracting the
value of y by y
̅ .
3 – 3.6 = -0.6
5 - 3.6 = 1.4
5 - 3.6 = 1.4

Formula
Step 6: compute
for (x-x
̅ ) x (y-y
̅ )
0.3 x -0.6 = -0.18
1.3 x 1.4 = 1.82
Step 7: compute
for sum of (x-x
̅ ) x
(y-y
̅ ) by adding all
the values in its
column
-0.18 + 1.82 + 1.82 + 1.82 + 0.42 + 0.12 +
0.12 + 0.42 + 2.72 + 2.72 = 11.8

Formula
Step 7: compute
for (x -x
̅ ) 2 by
squaring all the
values in (x-x
̅ )
0.3 x 0.3 or (0.3) 2 =
0.09
1.3 x 1.3 or (1.3) 2 =
1.69

Formula
Step 8: compute
for the sum of (x -
x
̅ ) 2 by adding all
the values in its
column
0.09 + 1.69 + 1.69 +
1.69 + 0.49 + 0.09 +
0.09 + 0.49 + 2.89 +
2.89 = 12.1

Formula
Step 10: compute
for the sum of (y-y
̅ )
2 by adding all the
values in its
column
0.36 + 1.96 + 1.96
+1.96 + 0.36 + 0.16
+ 0.16 + 0.36 + 2.56

Formula
Step 11: Substitute
all the values to
our formula

Substitute all the values
in the formula
Multiply 12.1 by 12.4
Substituted:

Substituted:
Get the square root of
150.04
r = .963 Divide 11.8 by 12.25

Interpretation for Positive
Value Result

Interpretation for
Negative Value Result

Since we got .963 as the r value, we can interpret the
relationship as “very high positive correlation” and we can
also say that knowledge and attitude towards COVID 19 has
a very high positive correlation
Now we have the magnitude and direction, the next
phase is to check if the relationship is significant.

Get the significance by solving t
- subsitute the values from the table
.963 is our r
.927 is the result
of .963 being squared
10 is the number of
our samples

073 is the difference of
1 and .927
8 is the difference of 10
and 2
.0091 is the result of
dividing .073 by 8

09
Page 31
.0955 is the result of
getting the root
of .0091
10.08 is the result of
dividing .963 by .0955
.0954

Steps:
Step 1 – compute for Degree of freedom wherein we just
subtract one (1) from the total sample of 10 which is
equals to 9.
Step 2 – look for the column of your alpha value which
is .05
Step 3 – make a cross on the table and you should find
that it meets at 2.262

We can see that the computed t of 10.09 is greater
than our critical value of 2.262. This means that our
computed t is on the rejection region wherein we
can see that there is sufficient evidence to reject the
null hypothesis.

10.09
Page 35
Format for
interpretation:

A ___________ (Statistical technique) was run to find out the
significance, magnitude, and direction of relationship
between ________ (variable A) and ________(variable B).
Results show that _________ (Variable A) and _________
(Variable B) were found to have a ___________ (descriptive
interpretation) ________(Direction) ___________(significance), r
_______ (degree of freedom) ______(r statistic), _____
(computed T) ______ (greater or lesser than sign) ), _____
Data applied in the
format

A Pearson product moment correlation was run to
find out the significance, magnitude, and direction
of relationship between Knowledge and Attitude
towards COVID-19. Results show that Knowledge
and Attitude were found to have a Significant Very
High Positive Correlation, r(8) = .963, t=10.09 >
2.262.
Data applied in the
format

Instruction: Analyze the data given by filling out the
table, using the formula, drawing the table, and writing
the interpretation.
Title: Alcohol Sales and Covid-19 Cases in Davao City
Page 38

36.29
-51.29
-62.29
6.71
37.71
26.71
78.71
=200
=2451.29
-50
-15
-11
-10
10
20
56
1,814.5
769.35
685.19
-67.1
371.1
534.2
4,407.76
=8,521
-1,316.96
-2,630.66
-3,880.04
45.02
1,422.04
713.42
6,195.26
=548.08
-2,500
-225
-121
-100
100
400
3,136
=690

r=
8,521
r =
13.86
8,521
(548.08)(690)
(378,175.2)
8,521
8,521
614.96

Correlational Analysis on Quantitative Research.pptx

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