Professor : Dr. Dana

Presented by : Omid Sanaei

Nonexperimental Research :Correlational Methods

Correlational research describes the linear relationship between two or more variables without any hint of attributing the effect of one variable on another.

As a descriptive technique, it is very powerful because this method indicates whether variables (such as number of studying and test score) share something in common with each other. If they do, the two are correlated (or co – related) with one another.

*Correlational Research

*The Relationship Between Variables

The most frequent measure used to assess degree of relatedness is the correlation coefficient, which is a numerical index that reflects the relationship between two variables.

Correlation coefficient is expressed as a number between -1.00 and +1.00, and it increases in strength as the amount of variance that one variable shares with another increases.

Correlations can be direct or positive, meaning that as one variable changes in value, the other changes in the same direction, such as the relationship between the number of hours you study and your grade on an exam. Generally, the more you study, the better your grade will be. Likewise, the less you study, the worse your grade will be.

Correlations can also reflect an indirect or negative relationship, meaning that as one variable changes in value in one direction, the other changes in the opposite direction, such as the relationship between the speed at which you through multiple-choice items and your score on the test. Generally, the faster you go, the lower your score; the slower you go, the higher your score.

Example The correlation is and Y … If X …

The taller one gets (X),the moreone weighs (Y).

Positiveor direct

Increases in value

Increases in value

The fewer mistakesone makes (X), the fewer hours of remedial work(Y) one participates in.

Positive or direct

Decreases in value

Decreases in value

The better one behaves (X), the Fewer in-class suspensions (Y) one has.

Negative or indirect

Decreasesin value

Increasesin value

The less time onespends studying (X), themore errors onemakes on the test (y).

Negativeor indirect

Decreasesin value

Decreasesin value

Table 9.2 Two types of correlations: positive or direct, negative or indirect

*What Correlation Coefficient Look Like

The most frequently used measure of relationships is the Pearson product moment correlation, represented by letter r followed by symbols representing the variables being correlated. The symbol represents a correlation between the variables X and Y.

Scattergram : A scattergram is a plot of scores in pairs, in other words the scattergram is a visual representation of the correlation coefficient of the relationship between two variables.

2 3 4 5 6 7 8 9 100

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4

6

8

10Data Set A

3 35 66 76 87 78 69 77 98 89 9

2 3 4 5 6 7 8 9 100

2

4

6

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10Data Set B

3 35 66 76 57 78 39 77 98 59 9

𝑟 𝑥𝑦=.70

𝑟 𝑥𝑦=.32

2 3 4 5 6 7 8 90

2

4

6

8

10

2 3 4 5 6 7 8 9 100

1

2

3

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6

Data Set C3 95 86 76 77 68 39 37 48 95 8

Data Set D3 25 46 56 47 38 49 57 48 29 3

𝑟 𝑥𝑦=−. 82

𝑟 𝑥𝑦=−.15

*Computing the Pearson Correlation Coefficient

The easiest manual way to compute the correlation between two variables is through the use of the raw score method. The formula for ( where xy represents the correlation between x and y ) is as follows:

Where = the correlation coefficient between x and y∑ = the summation sign n = the size of the sampleX = the individual’s score on the X variable Y = the individual’s score on the Y variableXY = the product of each X score times its corresponding Y score = the individual X score, squared = the individual Y score, squared

𝑟 𝑥𝑦=𝑛∑ 𝑥𝑦−∑ 𝑥∑ 𝑦

√¿¿¿

If you have n variables, then you will have “n taken two at a time’’ pairs of relationship.

*Interpreting the Pearson Correlation Coefficient

The correlation coefficient reflects the degree of relationship between variables.

There are two ways to interpret these general indicators of relationships.

The first method is the “eyeball’’ method, in which correlations of a certain value are associated with a certain nominal degree of relationship such that:

Are said to be Correlations between

Very strong .8 and 1.0

Strong .6 and .8

Moderate .4 and .6

Weak .2 and .4

Very weak .0 and .2

A sounder method for interpreting the correlation coefficient is to square its value and then compute the coefficient of determination. This value, , is the amount of variance that is accounted for in one variable by the other.in other words, it allows you to estimate the amount of variance that can be accounted for in one variable by examining the amount of variance in another variable.

If the correlation between two variables is .40, then the coefficient of determination is .16. Sixteen percent (16%) of the variance on one variable can be explained by the variance in other variable; 84% (100% - 16%)of the variance is unexplained. This portion of unexplained variance is referred to as the coefficient of alienation.

Table 9.4 Differences in the amount of variance accounted for as a function of different values of the correlation coefficient.

0 0.2 0.4 0.6 0.8 1 1.20

0.20.40.60.81

1.2

Value of correlation coefficient

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Figure 9.2 The proof is the seeing --- relationship between increases in the correlation coefficient and increases in the amount of variance explain the relationship between two variables.

Thanks for Your Kind Attention