CHAPTER 6 (GROUP 3)

1. CORRELATIONAL RESEARCH:
LANGUAGE LEARNING /
TEACHING ATTITUDES
GROUP 3
PREMALATHA P. CHELLADORAI PGP110028
NORAZLINA BINTI RAFI AHMAD PGP110020
SITI AISHAH BINTI SAHAIRI PGP110013
Research In Second Language Acquisition
(PBGS 6113)

2. What is
CORRELATIONAL RESEARCH

3. DEFINITION OF
CORRELATIONAL RESEARCH
According To J.D. Brown & T.S Rodgers
(2009), Second Language Research,
How things fit together, how things are
related

4. For example :
Are big kids really fast runners?
- The relationship between students
height and their speed.

5. ANALYZING CORRELATIONAL
DATA
Collect data
Compile data
Calculate a statistic called
CORRELATION COEFFICIENT

6. CORRELATION COEFFICIENT
The degree of relationship between two
sets of numbers represented as the ratio
of go – togetherness to total score
variation

7. CORRELATION COEFFICIENT
CORRELATION
Sign
Magnitude - Indicates the
direction of the
- Tells the degree of relationship
relationship between (positive/negative)
the two sets of numbers
(0.00 – 1.00)

8. CORRELATION COEFFICIENT
STUDENT SET A SET B
Marie 9 8
Example 1:
Jose 8 7
Jeanne 7 6 The number of words spelled
Hachiko 6 5 correctly in a spelling test of ten
items (TEST 1)
Raphael 5 4
Yuka 4 3 Correlation : 1.00
Hossein 3 2 - Magnitude : Perfect relationship
Tamara 2 1 - Sign : Positive
Hans 1 0

9. CORRELATION COEFFICIENT
STUDENT SET A SET B
Marie 9 1
Example 2 :
Jose 8 2
Jeanne 7 3 The number of words spelled
Hachiko 6 4 correctly in a spelling test of ten
items (TEST 2)
Raphael 5 5
Yuka 4 6 Correlation : -1.00
Hossein 3 7 - Magnitude : Perfect relationship
Tamara 2 8 - Sign : Negative
Hans 1 9

10. STEPS IN CORRELATIONAL
RESEARCH
STEP 1
Figure out what kind of scales you are
dealing with
STEP 2
Deciding on the appropriate correlation
coefficient to calculate
STEP 3
Calculate the appropriate correlation
coefficient

11. STEP 1
Figure out the types of scale
In a language studies, there are THREE
kinds of scales
1) Rank – ordered scales
2) Continuous scales
3) Categorical

12. RANKED ORDER SCALES
Scales that arrange or sort the values
according to order
For example : 1st, 2nd, 3rd

13. CONTINUOUS SCALE
Instead of ranking order, we use
number values to organize data
For example : 100, 90, 80, 70

14. CATEGORICAL SCALE
Scales that organize the data into
category / groups
For example :
MARKS CATEGORY
90 – 100 Excellent
80 – 89 Very good
70 – 79 Good

15. THE COMBINATION OF THE
THREE SCALES
NAME MARKS RANKS GROUPS
Amber 100 1 High
Bernard 94 2 High
Cassey 89 3 High
Dania 86 4 Middle
Eric 78 5 Middle
Fay 76 6 Middle
Georgia 64 7 Low
Hashim 61 8 Low
Indra 55 9 Low

16. STEP 2 & 3
Decide and calculate correlation
coefficient
There are THREE types of correlational
coefficient
1) Spearman (rho, or ρ)
- Analyzing 2 sets of numbers if they
are both rank ordered scales

17. 2) Phi (Φ)
- Is appropriate if the 2 sets of are
numbers are categorical scales
3) Pearson / Product – moment (r)
correlation coefficient
- Is appropriate if the 2 sets of
numbers are continuous scales

18. TYPES OF CORRELATION
COEFFICIENT AND SCALES
TYPE OF CORRELATION WHAT SCALES CAN IT
COEFFICIENT ANALYZE?
Spearman (rho, or ρ) Two sets of rank –
ordered data
Phi (Φ) Two sets of
categorical data
Pearson / product – Two sets of continuous
moment (r) data

19. SPEARMAN (rho, or ρ)
It is conceptually the easiest to
understand
It is designed to estimate the degree of
relationship between two sets of rank-
order data
Also simply called as SPEARMAN RHO

20. SPEARMAN (rho, or ρ)
The equation :
2
6 D
1 2
N N 1
where ρ = Spearman rho correlation
D = the differences between the ranks
N = the number of cases

21. SPEARMAN (rho, or ρ)
For example :
Two teachers’ rankings of overall course
performance for one group of 11
students

22. SPEARMAN (rho, or ρ)
STUDENT TEACHER A TEACHER B DIFFERENCE D²
Maria 1 4 -3 9
Juanita 2 3 -1 1
Toshi 3 1 2 4
Raul 4 2 2 4
Anna 5 5 0 0
Jaime 6 6 0 0
Hans 7 8 -1 1
Hachiko 8 9 -1 1
Tanya 9 7 2 4
Jacques 10 11 -1 1
Serge 11 10 1 1
TOTAL : 0 TOTAL : 26

23. SPEARMAN 6 D 2
1
(rho, or ρ) 2
NN 1
D² = 26 / N = 11
6 26
ρ = 1 11(121 1)
156  The result based on
= 1 the ranks is high
1320
 The rankings of both
teachers are highly
related
= 1 .1181818
= .8818182 .88

24. PHI COEFFICENT (φ)
It is designed to estimate the degree of
relationship between two categorical
variables with two possible possibilities
each.

25. PHI COEFFICENT (φ)
The equation :
BC AD
A B C D A C B D

26. PHI COEFFICENT (φ)
To calculate, arrange your data in a
two - by - two table like this.
A B
C D

27. PHI COEFFICENT (φ)
For example :
I like to share things with other people [Y/N]
(Respondent : several classes of MA level
ESL teachers in training at the University of
Hawaii)

28. PHI COEFFICENT (φ)
Convert your data into this table
I like to share things with other people [Y/N]
MALE FEMALE
A B
2 14 YES
C D
11 1 NO

29. PHI COEFFICENT BC AD
(φ) A B C D A C B D
A = 2 / B = 14 / C = 11 / D = 1
(14 11) (2 11)
φ = (2 14)(11 1)(2 11)(14 1)
154 2  Relationship in this group of
= graduate students between
(16)(12)(13)(15) male and female, answering
yes or no to the question
152 about sharing is not highly
= related.
37440
152
= 193.49
= .7855703 .79

30. PEARSON /
PRODUCT – MOMENT (r)
Is designed to estimate the degree of
relationship between two sets of
continuous scale data.

31. PEARSON /
PRODUCT – MOMENT (r)
The equation :
X Mx Y My
r
NS x S y

32. PEARSON / PRODUCT –
MOMENT (r) r X Mx Y My
NS x S y
where :
X = the values for the X variable
Y = the values for the Y variable
Mx = the mean for the X variable
My = the mean for the Y variable
Sx = the standard deviation for the X variable
Sy = the standard deviation for the Y variable
N = N the number of paired values for the X and Y
variables (often the number of participants)

33. PEARSON /
PRODUCT – MOMENT (r)
For example :
One set of questionnaire (Willing, 1988 :
116)
- This questionnaire results in two
different ways:
a) Mean answers on each four-point
Likert scale item
b) Percentage (%) as best for each
item

34. Doing
Second
Language
Research,
Page 174

35. PEARSON / PRODUCT –
MOMENT (r) X Mx Y My
r
NS x S y
149 .76
r = 30 (. 37 )(14 .53 )
149.76  Shows similarity / high –
= 161.283 related / more – less –
equivalent
= .9285541 .93

36. INTERPRETING
CORRELATIONAL RESEARCH
Both sets of numbers must be the same.
The pair of numbers within a data set
must be independent.

37. EXAMPLE OF
CORRELATIONAL RESEARCH
TITLE
Motivation and Attitude in Learning
English among UiTM Students in the
Northern Region of Malaysia.
RESEARCHERS
Bidin, Samsiah and Jusoff,
Kamaruzaman and Abdul Aziz, Nurazila
and Mohamad Salleh, Musdiana and
Tajudin, Taniza (2009).

38. PUBLICATION
English Language Teaching, 2 (2). pp.
16-20. ISSN 1916-4742.
PURPOSE OF STUDY
Describe the relationship between the
students’ motivation and attitude; and
their English Language performance.

39. SUBJECT
Part two students from three UiTM
campuses in the Northern region.
INSTRUMENTATION
Questionnaire (adopted and adapted
from Gardner and Lambert - 1972).

40. METHOD
- A correlational research design was
used : SPEARMAN RHO RANK-ORDER
CORRELATION COEFFICIENT
- It was used to answer these two
questions (QUESTION 1 & QUESTION 2).

41. QUESTION 1
To find out whether there exists any correlation between
motivation and English language performance.
It is found that there is no significant difference
between motivation and English language performance.

42. QUESTION 2
To find out whether there exists a significant correlation
between the attitude in learning English and English
language performance
It is found that the respondents who obtained an A
(high achievers) have better attitude in learning English
compared to low achievers.

43. THE END…