Correlational Research Info

8/11/2019 Correlational Research Info.

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CORRELATIONAL RESEARCH

This is also a type of descriptive research in which we try to study the existing relationships

between two or more variables. It should be remembered that the main aim of educational

research is not only to discover what is presently unknown but also to predict the future

relationships between various variables. These predictions are comparatively easy andpossible to be made if we explore the existing strong relationships between certain

variables. In order to explore these relationships we conduct correlational studies.

1. Purposes of Correlational Research

The major aim of a correlational research is to explore the correlation between or

among the variables. These correlations help us better understand the conditions and

events in a meaningful way, and in making predictions about the future conditionsand events. These research studies ultimately enable us to explain, predict and, up to

some extent, control certain conditions and events.

For example, to B. F. Skinner, a great behavioral psychologist, most events could beexpressed as: X (f) Y, i.e. X is the function (f) of Y, and this is possible only

because both are correlated. In his experiments, X refers to the behaviour of the

pigeon and Y refers to the reinforcement given to the pigeon after it performs some

particular behavior (e.g., pecking at a tray). The pigeon learns to peck at the traybecause it leads to some reward (food). On the basis of his experiments, he

concluded that one thing caused another that is, the proper administration of

reinforcement led or caused the bird to behave in a certain manner.Now, on the basis of this information and knowledge, we can conduct some

correlational study in the educational and/or classroom settings and predict the

behaviour of the students and up to some extent we can control their behaviour by

applying various types or schedules of reinforcements.

2. Major Topics of Correlational ResearchIn the educational settings, correlational research is targeted toward the following

four broad categories of topics :

Researching various human traits related to learning, viz. personality,

motivation, intelligence, etc.

Researching various classroom conditions related to learning, viz. class size,

teacher behaviour, peer interaction, etc.

Researching various teaching practices, procedures, and materials related tolearning.

Researching the validation of educational tests and measurements.3. Sources of Data for Correlational Research

Actually, correlational research requires only a few sources of data, but these

sources must provide or supply two measures or scores for each subject studied. For

example, if we want to explore the relationship between the level of anxiety andstudent performance, we essentially need scores on these two variables each for all

the subjects of the sample.


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4. Types of Correlations

As is just described, we require pairs of test scores for each subject to calculate

correlation between these pairs. But the nature of these pairings (or data obtained)

requires us to calculate correlation by any of the following different methods ofcorrelation :

Pearson r : It is the most commonly used correlational procedure. In this, we need

pairs of raw scores on two tests, one pair for each subject of the sample, e.g. marks

obtained by a student in the tests of science and math.

Spearman r : Sometimes we cannot obtain raw scores but we obtain the ranking ofthe subjects. Then, we have to calculate Spearman's rank order correlation. For

example, to explore the relationship between self-confidence and leadership we

shall have to use this method. Here we may be unable to obtain the raw scores of the

subjects on these two variables but we may rank them on these.Biserial r : It is calculated when we have scores of the subjects on one variable or

trait, but on the second variable, we have to put them into a dichotomy

(dichotomous means 'cut into two parts'), which means that we have to place themin either this or another category. For example, we may plan to explore the

relationship between mental age (M.A., a measurable variable into scores) and

number of parents in the family (dichotomous variable-either one parent i.e. eithermother or father or two i.e. both mother and father).

Tetrachoric r : In biserial r, we have one continuous variable (expressed in test

scores) and second dichotomous variable (a two-fold classification). But sometimes

we may get both the variables dichotomous (or a 2 x 2 or four-fold table). Then wehave to compute tetrachoric r. Here our both variables are not measured in scores

but are capable of being separated into two categories. For example, we may wish to

discover the relationship between intelligence (above average/below average) andself-confidence (above average/below average). Here we have, as per our research

objectives, decided to study the relationship between two categories of intelligence

and two categories of self-confidence.

Partial Correlation : In correlational approach, mostly the third variable problemrefrains us from drawing inferences on the basis of the observed r between two

variables. According to Christensen (1994), "the third variable problem refers to the

fact that the two variables may be correlated not because they are causally relatedbut because some third variable caused both of them." For example, it is found that

reading ability and vocabulary are highly correlated, but, in fact, both of these

variables are strongly affected by intelligence. Hence, if anybody wants to study the

actual correlation between these two variables, he must first partial out the effect ofintelligence which is done by the method of partial correlation.

5. Research Tools

As you have just read, in correlational research, we require data in the form ofnumbers, rankings or dichotomies. To obtain these types of data, as per our research

design, we may use "standardized tests" (like intelligence tests), "other measuring

devices" (e.g., heart beat, pulse rate, etc.), or "established criteria" (to be used in

making rankings and dichotomies).


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6. Steps in Correlational Research

The correlational research is very simple and uncomplicated to conduct. It involves

the following steps, most of which you will find a little bit similar to other research

methods :

Selecting and Defining a Problem : Like other types of research,

correlational research also requires first of all a researcher to select anddefine his/her research problem. Here the researcher should select at least"two variables" (one can select even more).

Formulating Hypothesis : Generally, null hypothesis is formulated in

correlational research because it seems much easier to reject a nullhypothesis than to retain a research hypothesis. It simply states, "No

relationship exists between A and B."

Data Collection : As per the nature of the variables, the next step of this

research method is to collect the data in pairings of scores, rankings, or

groupings by applying the appropriate research tools.

Data Compilation : After collecting the data, we must next compile it in

such a way that two measures (i.e. scores, rankings, or groupings) can be

shown for each subject of the sample.

Analysis and Interpretation of Data : Our next step is to treat the data

statistically by applying appropriate correlational technique to compute the

correlation between the two sets of scores. Then we interpret our findings inthe light of (i) the size of the correlation, (ii) the direction of the correlation

(positive or negative), and (iii) its significance level.

a. The Size of the Correlation: The degree or size or strength of therelationship between two variables is expressed by the coefficient of

correlation. Whether positive or negative, the more the coefficient

the stronger or closer the relationship. It should be noted that,

irrespective of the correlational procedures followed, the range of thecoefficient lies in between 0 (means no relationship at all) to 1.00

(means perfect correlation). However, in research, these values of 0

and/or 1.00 are never or rarely obtained.b. The Direction of the Correlation: You can find the two variables

correlated in either positive or negative direction. The direction of

the correlation is independent of the size of the correlation, and both

have nothing to do with each other. Correlations of +.62 and -.62 areof exactly the identical size but show a different type of relationship

(the former is positive correlation and the latter shows negative

correlation). Positive correlations indicate that increase or decrease

in one variable tends to accompany the increase or decrease inanother variable in parallel fashion. If, on the other hand, increase in

one variable tends to decrease in another and vice versa, it indicates a

negative correlation. The higher or lower the correlation (eitherpositive or negative), the more accurately we can predict one

variable from the other.

c. Significance Level of Correlation: And, as far as the significancelevel of obtained correlation is concerned, we first compute the

standard error (SE) of the correlation and then multiply this SE by


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correlation coefficient moves toward either -1 or +1,

the relationship gets stronger until there is a "perfect

correlation" at either extreme.

The direction of the relationship is indicated by the "-

" and "+" signs. A negative correlation means that asscores on one variable rise, scores on the other

decrease. A positive correlation indicates that the

scores move together, both increasing or bothdecreasing.

A student's grade and the amount of studying done,for example, are generally positively correlated.

Stress and health, on the other hand, are generally

negatively correlated.

2. REGRESSION AND

PREDICTION

If there is a correlation between two variables, and we

know the score on one, the second score can bepredicted. Regression refers to how well we can make

this prediction. As the correlation coefficients

approach either -1 or +1, our predictions get better.

For example, there is a relationship between stress

and health. If we know my stress score, we canpredict my future health status score.

3. MULTIPLE

REGRESSION

This extends regression and prediction by adding

several more variables. The combination gives us

more power to make accurate predictions.

What we are trying to predict is called the

CRITERION VARIABLE.

What we use to make the prediction, the known

variables, are called PREDICTOR VARIABLES.

If we know not only my stress score, but also a healthbehavior score (how well I take care of myself) andhow my health has been in the past (whether I am

generally healthy or ill), we can more closely predict

my health status. Thus, there are 3 predictors--stress,

health behavior, and previous health status--and onecriterion--future health.


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CROSS-LAGGED PANEL DESIGNS measures 2

variables at two points in time. It has been used, forexample, to show that watching violence on TV leads

to violent behavior, more than the other way around.

6. SYSTEMS ANALYSISThis involves the use of complex mathematical

procedures to determine dynamic processes, i.e.,changes over time, feedback loops, and the elements

and flow of relationships.

It has been used, for example, to diagram the

differences between successful and unsuccessful

elementary schools. Some of the elements in these

systems are teachers' expectations of studentperformance, teaching effort, and student

performance. Each of these affects the other andchanges over time.

Purpose

The correlation is a way to

measure how associated orrelated two variables are.

The researcher looks atthings that already exist

and determines if and in

what way those things arerelated to each other. The

purpose of doing

correlations is to allow us

to make a prediction aboutone variable based on what

we know about another

variable.

For example, there is a

correlation betweenincome and education. We

find that people with

higher income have moreyears of education. (You

can also phrase it that


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variable also increase.

Likewise, as the value ofone of the variables

decreases, the value of the

other variable also

decreases. The exampleabove of income and

education is a positivecorrelation. People with

higher incomes also tend

to have more years ofeducation. People with

fewer years of education

tend to have lower income.

Here are some examples of

positive correlations:

1. SAT scores and college

achievementamong

college students, thosewith higher SAT scores

also have higher grades

2. Happiness and

helpfulnessas peoples

happiness level increases,

so does their helpfulness(conversely, as peoples

happiness level decreases,

so does their helpfulness)

This table shows somesample data. Each person

reported income and years

of education.

Participant

Income

Years

ofEducation

#1125,000

19

#2100,000

20


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#340,00

016

#435,00

016

#5 41,000 18

#629,000

12

#735,000

14

#824,00

012

#950,000

16

#1060,000

17

In this sample, thecorrelation is .79.

We can make a graph,

which is called ascatterplot. On the

scatterplot below, each

point represents one

persons answers toquestions about income

and education. The line is

the best fit to those points.All positive correlations

have a scatterplot that

looks like this. The linewill always go in that

direction if the correlation

is positive.


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Negative correlati on

In a negative correlation, as the values of one of the variables

increase, the values of the second variable decrease. Likewise,

as the value of one of the variables decreases, the value of theother variable increases.

This is still a correlation. It is like an inverse correlation.The word negative is a label that shows the direction of the

correlation.

There is a negative correlation between TV viewing and class

gradesstudents who spend more time watching TV tend to

have lower grades (or phrased as students with higher grades
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tend to spend less time watching TV).

Here are some other examples of negative correlations:

1. Education and years in jailpeople who have more years of

education tend to have fewer years in jail (or phrased as peoplewith more years in jail tend to have fewer years of education)

2. Crying and being heldamong babies, those who are held

more tend to cry less (or phrased as babies who are held lesstend to cry more)

We can also plot the grades and TV viewing data, shown inthe table below. The scatterplot below shows the sample data

from the table. The line on the scatterplot shows what a

negative correlation looks like. Any negative correlation will

have a line with that direction.

ParticipantGPA

TV inhours

perweek

#1 3.1 14

#2 2.4 10

#3 2.0 20

#4 3.8 7#5 2.2 25

#6 3.4 9

#7 2.9 15

#8 3.2 13

#9 3.7 4

#10 3.5 21

In this sample, the correlation is -.63.


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trength

Correlations, whether positive or negative, range in theirstrength from weak to strong.

Positive correlations will be reported as a number between 0and 1. A score of 0 means that there is no correlation (the

weakest measure). A score of 1 is a perfect positive

correlation, which does not really happen in the real world.

As the correlation score gets closer to 1, it is getting stronger.So, a correlation of .8 is stronger than .6; but .6 is stronger

than .3.

The correlation of the sample data above (income and years of

education) is .79.

Negative correlations will be reported as a number between 0
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and -1. Again, a 0 means no correlation at all. A score of1 is

a perfect negative correlation, which does not really happen.As the correlation score gets close to -1, it is getting stronger.

So, a correlation of -.7 is stronger than -.5; but -.5 is stronger

than -.2.

Remember that the negative sign does not indicate anything

about strength. It is a symbol to tell you that the correlation isnegative in direction. When judging the strength of a

correlation, just look at the number and ignore the sign.

The correlation of the sample data above (TV viewing and

GPA) is -.63.

Imagine reading four correlational studies with the followingscores. You want to decide which study had the strongest

results:

-.3 -.8 .4 .7

In this example, -.8 is the strongest correlation. The negative

sign means that its direction is negative.

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Advantage

1.An advantage of the correlation method is that we can make

predictions about things when we know about correlations. Iftwo variables are correlated, we can predict one based on the

other. For example, we know that SAT scores and college

achievement are positively correlated. So when collegeadmission officials want to predict who is likely to succeed at

their schools, they will choose students with high SAT scores.

We know that years of education and years of jail time are

negatively correlated. Prison officials can predict that people

who have spent more years in jail will need remedial

education, not college classes.

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Disadvantage

1.The problem that most students have with the correlation

method is remembering that correlation does not measurecause. Take a minute and chant to yourself: Correlation is not

Causation! Correlation is not Causation! I always have my in-class students chant this, yet some still forget this very crucial

principle.

We know that education and income are positively correlated.

We do not know if one caused the other. It might be that

having more education causes a person to earn a higher

income. It might be that having a higher income allows aperson to go to school more. It might also be some third

variable.

A correlation tells us that the two variables are related, but we

cannot say anything about whether one caused the other. This

method does not allow us to come to any conclusions aboutcause and effect.

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Correlational Research Info