CORRELATIONAL RESEARCH: LANGUAGE LEARNING / TEACHING

ATTITUDES

GROUP 3

PREMALATHA P. CHELLADORAI PGP110028NORAZLINA BINTI RAFI AHMADPGP110020 SITI AISHAH BINTI SAHAIRI PGP110013

Research In Second Language Acquisition (PBGS 6113)

What is

CORRELATIONAL RESEARCH

According To J.D. Brown & T.S Rodgers (2009), Second Language Research,

How things fit together, how things are related

DEFINITION OF CORRELATIONAL

RESEARCH

For example :

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

Collect data

Compile data

Calculate a statistic calledCORRELATION COEFFICIENT

ANALYZING CORRELATIONAL DATA

The degree of relationship between two sets of numbers represented as the ratioof go – togetherness to total score variation

CORRELATION COEFFICIENT

CORRELATION

CORRELATION COEFFICIENT

Magnitude

- Tells the degree of relationship between the two sets of numbers (0.00 – 1.00)

Sign

- Indicates the direction of the relationship (positive/negative)

CORRELATION COEFFICIENT

STUDENT

SET A SET B

Marie 9 8

Jose 8 7

Jeanne 7 6

Hachiko 6 5

Raphael 5 4

Yuka 4 3

Hossein 3 2

Tamara 2 1

Hans 1 0

Example 1:

The number of words spelled correctly in a spelling test of ten items (TEST 1)

Correlation : 1.00 - Magnitude : Perfect relationship - Sign : Positive

CORRELATION COEFFICIENT

STUDENT

SET A SET B

Marie 9 1

Jose 8 2

Jeanne 7 3

Hachiko 6 4

Raphael 5 5

Yuka 4 6

Hossein 3 7

Tamara 2 8

Hans 1 9

Example 2 :

The number of words spelled correctly in a spelling test of ten items (TEST 2)

Correlation : -1.00 - Magnitude : Perfect relationship - Sign : Negative

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

STEPS IN CORRELATIONAL

RESEARCH

In a language studies, there are THREE kinds of scales

1) Rank – ordered scales 2) Continuous scales 3) Categorical

Figure out the types of scaleSTEP

1

Scales that arrange or sort the values according to order

For example : 1st, 2nd, 3rd

RANKED ORDER SCALES

Instead of ranking order, we use number values to organize data

For example : 100, 90, 80, 70

CONTINUOUS SCALE

CATEGORICAL SCALE

Scales that organize the data into category / groups

For example :

MARKS CATEGORY90 – 100 Excellent80 – 89 Very good70 – 79 Good

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

There are THREE types of correlational coefficient

1) Spearman (rho, or ρ) - Analyzing 2 sets of numbers if they are both rank ordered scales

Decide and calculate correlation coefficient

STEP 2 & 3

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

TYPES OF CORRELATION COEFFICIENT AND

SCALES

TYPE OF CORRELATION COEFFICIENT

WHAT SCALES CAN IT ANALYZE?

Spearman (rho, or ρ) Two sets of rank – ordered data

Phi (Φ) Two sets of categorical data

Pearson / product – moment (r)

Two sets of continuous data

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

SPEARMAN (rho, or ρ)

The equation :

SPEARMAN (rho, or ρ)

16

12

2

NN

D

where ρ = Spearman rho correlation

D = the differences between the ranks

N = the number of cases

For example :

Two teachers’ rankings of overall course performance for one group of 11 students

SPEARMAN (rho, or ρ)

SPEARMAN (rho, or ρ)TEACHER

A

1

2

3

4

5

6

7

8

9

10

11

TEACHER B

4

3

1

2

5

6

8

9

7

11

10

STUDENT

Maria

Juanita

Toshi

Raul

Anna

Jaime

Hans

Hachiko

Tanya

Jacques

Serge

DIFFERENCE

-3

-1

2

2

0

0

-1

-1

2

-1

1

D²

9

1

4

4

0

0

1

1

4

1

1

TOTAL : 0 TOTAL : 26

ρ =

=

=

=

SPEARMAN (rho, or ρ) 1

61

2

2

NN

D

The result based on the ranks is high

The rankings of both teachers are highly related

ρ )1121(11

2661

1320

1561

1181818.1

88.8818182.

D² = 26 / N = 11

It is designed to estimate the degree of relationship between two categorical variables with two possible possibilities each.

PHI COEFFICENT (φ)

The equation :

DBCADCBA

ADBC

PHI COEFFICENT (φ)

To calculate, arrange your data in a two - by - two table like this.

PHI COEFFICENT (φ)

A B

C D

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)

PHI COEFFICENT (φ)

PHI COEFFICENT (φ)

A B

C D

FEMALEMALE

Convert your data into this table

I like to share things with other people [Y/N]

YES

NO

2 14

111

φ =

=

=

= =

PHI COEFFICENT (φ) DBCADCBA

ADBC

)114)(112)(111)(142(

)112()1114(

)15)(13)(12)(16(

2154

37440

152

49.193

15279.7855703.

Relationship in this group of graduate students between male and female, answering yes or no to the question about sharing is not highly related.

A = 2 / B = 14 / C = 11 / D = 1

Is designed to estimate the degree of relationship between two sets of continuous scale data.

PEARSON / PRODUCT – MOMENT (r)

The equation :

PEARSON /PRODUCT – MOMENT (r)

yx

yx

SNS

MYMXr

X = the values for the X variable

Y = the values for the Y variable

= the mean for the X variable

= the mean for the Y variable

= the standard deviation for the X variable

= 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)

PEARSON / PRODUCT – MOMENT (r)

yx

yx

SNS

MYMXr

xM

xS

yS

where :

yM

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

PEARSON /PRODUCT – MOMENT (r)

Doing Second Language Research, Page 174

r =

=

=

PEARSON / PRODUCT – MOMENT (r)

yx

yx

SNS

MYMXr

)53.14)(37(.30

76.149

283.161

76.149

93.9285541.

Shows similarity / high – related / more – less – equivalent

Both sets of numbers must be the same.

The pair of numbers within a data set must be independent.

INTERPRETING 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).

EXAMPLE OF CORRELATIONAL

RESEARCH

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.

SUBJECT Part two students from three UiTM

campuses in the Northern region.

INSTRUMENTATION Questionnaire (adopted and adapted

from Gardner and Lambert - 1972).

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).

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.

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.

THE END…