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Essay on General Mathematics: Calculation of the Pearson’s Correlation Coefficient

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Correlation analysis is a statistical measure that indicates the extent to which two or more variables fluctuate together. It helps us in determining the degree of relationships between variables, according to, Hazewinkel, (1994). It does not, however, tell us anything about the cause and effect of the relationship, for instance, if there is a high degree of correlation between the variables. A variable in statistics is any characteristic number, or quantity that can be measured or counted. It is unknown value usually represented by X or Y. Correlation can be positive or negative. An increase in one variable associated with an increase in another correlation is said to be positive. On the other hand, a decrease in one variable associated with an increase in another is negative correlation.

The characteristic of correlation is that values range between -10 to 0 to +1, where 0 shows no relationship.

There are three methods of determining whether two variables are correlated or not.: The Scatter Diagram, Karl Pearson’s of coefficient correlation and the Rank Order. This assignment will look at Pearson’s. Karl Pearson (1867-1936) a British Biometrician developed the coefficient of correlation. The Pearson’s method, popularly known as the Pearsonian coefficient method of correlation is the most extensively used quantitative methods in mathematical practice. It is known as the best method of measuring the association between variables of interest because it is based on the method of covariance. It gives information about the magnitude of the correlation, as well as the direction of the relationship. Covariance in statistics is the mean value of the product of the deviations of two variates from their respective means, according to the Concise Oxford English Dictionary.

The scenario for this assignment is on a researcher interested in the effectiveness of two different methods of punishing teenage children’s antisocial behavior. Method A consisted of locking the children in a small room for ten minutes whenever they behave anti socially. Method B consisted of depriving the other child of their MP3 player for ten minutes. Each child received a week of each treatment, illustrated in a table as under:

Subject A: number of anti-social acts committed after being punished by imprisonment.

Subject B: Number of anti-social acts committed after being punished by loss of MPP3 player.

Calculate the Pearson’s correlation between A and B, using the table below: There are five steps to calculating Pearson’s coefficient correlation as under:

Subject

A: Number of anti-social acts committed after being punished by imprisonment

B: Number of anti-social acts committed after being punished by loss

1

10

2

15

3

3

12

5

4

14

14

5

13

6

6

10

8

7

17

4

8

15

3

9

15

6

10

21

7

X

Y

XY X2 Y2

1

10

2

15

3

3

12

5

4

14

14

5

13

6

6

10

8

7

17

4

8

15

3

9

15

6

10

21

7

The second step involves multiplying X and Y together to fill the XY. For instance, 10×0=0 to be put on the XY.

x

Y

XY

X2 Y2

1

10

2

15

3

45

3

12

5

60

4

14

14

196

5

13

6

78

6

10

8

80

7

17

4

68

8

15

3

45

9

15

6

90

10

21

7

147

X

Y

XY

X2

Y2

1

10

100

2

15

3

45

225

3

12

5

60

144

4

14

14

196

196

5

13

6

78

169

6

10

8

80

100

7

17

4

68

289

8

15

3

45

225

9

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15

6

90

225

10

21

7

147

441

The fourth step involves taking the squares and put the results in the Y2 columns.

X

Y

XY

X2

Y2

1

10

100

2

15

3

45

225

9

3

12

5

60

144

25

4

14

14

196

196

196

5

13

6

78

169

36

6

10

8

80

100

64

7

17

4

68

289

16

8

15

3

45

225

9

9

15

15

90

225

225

10

21

7

147

241

49

X

Y

XY

X2

Y2

1

10

100

2

15

3

45

225

9

3

12

5

60

144

25

4

14

14

196

196

196

5

13

6

78

169

36

6

10

8

80

100

64

7

17

4

68

289

16

8

15

3

45

225

9

9

15

15

90

225

225

10

21

7

147

441

49

142

65

809

2114

629

Bless, (1990), provides the sixth step of correlation coefficient formula written as:

n(∑xy) – (∑x) (∑y)

r = [n∑x2 – (∑x)2] [n∑y2 – (∑y)2]

10(809) -(142) (65)

r = [10×2114 – (142)2] [10×629 – (65)2]

80r=10(809) -(142) (65)

8090 – 9230

r = [21140 – 20164] [6290 – 4225]

-1140

r = [976] [2065]

-1140

r = 2015440

r = -1140

1419.661932

r = -0.803008078

In conclusion, as with most kinds of research, there are both advantages and disadvantages to coefficient correlation studies. Used a lot in psychology inquiries, coefficient correlation is used as a pointer for further, more detailed research, according to Ingule, (1996). Secondly, they are easy to work with and easy to interpret. Correlational studies can be conducted on variables that can be measured and not manipulated. A correlation can also demonstrate the presence or absence of a relationship between two factors so it is good for indicating areas where experimental research could not take place and show further results.

On the other hand, disadvantages of the coefficient correlation are that it can only measure linear relationships between X and Y and for any relationship to exist, any change in X has to have constant proportional change in Y. If the relationship is not linear then the result is inaccurate, in addition, to this the correlation is meaningless particularly if it is about categorical data. No cause and effect can be established in correlational research as it is not certain that one variable caused the other to happen. As a disadvantage, a correlational analysis can only be used when variables are two on a scale, McLeod, (2018).

References

  1. Concise Oxford English Dictionary. (11th.ed.).
  2. Hazewinkel, M. (1994). (eds.). “Correlation in Statistics.” Encyclopedia of Mathematics. Springer science + business media B.V/ Klawer Academic Publishers.
  3. Ingule, F & Gatumu, H. (1996). Essentials of Educational Statistics. Nairobi: East African Educational Publishers.
  4. McLeod, S.A. (2018). Correlations. Simply Psychology. https://www.simplypsychology.org/correlation.html

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Essay on General Mathematics: Calculation of the Pearson’s Correlation Coefficient. (2022, September 27). Edubirdie. Retrieved February 6, 2023, from https://edubirdie.com/examples/essay-on-general-mathematics-calculation-of-the-pearsons-correlation-coefficient/
“Essay on General Mathematics: Calculation of the Pearson’s Correlation Coefficient.” Edubirdie, 27 Sept. 2022, edubirdie.com/examples/essay-on-general-mathematics-calculation-of-the-pearsons-correlation-coefficient/
Essay on General Mathematics: Calculation of the Pearson’s Correlation Coefficient. [online]. Available at: <https://edubirdie.com/examples/essay-on-general-mathematics-calculation-of-the-pearsons-correlation-coefficient/> [Accessed 6 Feb. 2023].
Essay on General Mathematics: Calculation of the Pearson’s Correlation Coefficient [Internet]. Edubirdie. 2022 Sept 27 [cited 2023 Feb 6]. Available from: https://edubirdie.com/examples/essay-on-general-mathematics-calculation-of-the-pearsons-correlation-coefficient/
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