MATH IA - IB MATH STUDIES.docx

Investigating the Relationship Between Short Term Memory Capability and Gender IB Mathematical Studies SL Internal Assessment School: Brent International School Subic Word Count: 1815 words Candidate Name: Jezi Christia Mari Llamas Candidate Number: 004812-0004 Graduation Year: May 2014 Date Submitted: February 12, 2014

Table of Contents

Introduction

Page 1

Methodology

Page 2

Data Processing

Pages 3

Main Essay

Pages 2-15   

Bibliography Appendix

Methodology Data Collection and Processing Conclusion and Evaluation

Page 2 Pages 3-14 Page 15 Page 16 Page 17-18

Introduction From time immemorial, it has already become obvious that the male and female races are born with distinct characteristics which are unique to their gender. The differences which make each gender what it is has become a factor wherein debates could be formulated. This especially happens when the abilities of men and women are compared. In the modern world, women have gained a much more admissible standing in society, gaining more and more rights to what men have over the past few years. Men had been a superior race for centuries before women began to stand up against them and show that women were just as capable as men. Despite the fact that women have risen in terms of social standing, they still rank somewhat below men. In the United States, the unemployment rate for women is much lower at 6.3%, as opposed to that of the men’s which ranks at 7.1%. The smaller percentage of employed men is observed to be in higher ranking jobs. Acceptance rates of women in those higher ranking jobs which men currently hold are significantly low (Oursler). Being an avid fan of psychology with great interest on the differences between the male and female mind, it was not entirely difficult to choose a topic for this investigation. What had started initially as a short argument between my parents became the basis for my investigation. For this particular project, I decided to look into the possible relationship between the short term memory of a person and their gender. This being said, it is predicted that there will be a relationship between the two variables mentioned earlier, and that women will possibly have a greater short term memory capacity, seeing as how more women are able to attain jobs that require cognitive skill. This investigation aims to study the relationship between a spatial and logical aspect, such as short term memory capacity, and gender in order to possibly come to a conclusion that women are just as able as men or are capable of even surpassing them in certain aspects. The results of this investigation may prove to become a small, yet significant study, which may possibly prove the worth and value of women in the workforce, as well as break the gender barriers which cloud the judgement of the majority.

Methodology 1

A person’s short term memory lasts approximately 20 to 30 seconds. The amount of information, or the capacity of a person’s short term memory, can vary depending on many different factors, such as age and the amount of information that needs to be recalled (McLeod). In order to eliminate possible variances in the data to be processed, the age range of the samples will be limited to 15-20 year old males and females, whose brains are close to full development, as well as possess the sufficient synapses in order to transmit signals within the brain. Each gender will have 50 samples, all of whom are within the said age group. The short term memory capacity of the samples will be tested using a word memorization test, wherein the sample will be asked to memorize as many words possible within thirty seconds. To improve the precision of the testing, all the samples will be asked to memorize the same set of words within the same time span. The number of words that each sample memorizes will be recorded and the average of the values will be categorized per gender. In order to determine whether there is a correlation between the short term memory capacity of a person and the gender of a person, I will be using a series of numerous mathematical processes, which will include the chi-squared test for independence and Pearson’s correlation coefficient.

Data Collection and Processing 2

In total, 100 people were asked to participate in the investigation. 50 of the samples were female and 50 were male. The raw data was then organized into a table dividing the male and female samples. The average numbers of words retained by the male and female samples were then averaged by using the mean. This was achieved by adding all of the collected values of one group together, then dividing them by the number of participants. The averages were then put into a table, then, these were translated into a chart which shows the difference between the results. Table 1: Average Number of Words Retained (Mean) Men Women

6.92 7.68

At first glance, it seems to be obvious that women are capable of retaining more information in their short term memory capacity than men. The possible relationship, though, was disproved when the data was also subject to a chi-squared test for independence in order to determine whether or not the average number of words retained by men and women, which conveys the limits of their short term memory capacity, is dependent or independent of the gender of the person. Table 2: Collected Data *Raw Data found in Table 4 Maximum Number of Words Retained

3-4

5-6

7-8

9-10

Male

5

17

18

10

50

Female

3

11

17

19

50

Totals

8

28

35

29

100



Totals

Chi-squared test for Independence: o

The survey was conducted in order to determine whether the short term memory capacity, is independent of the students’ gender. The collected results of the investigation are tabulated above. 3

o

The null hypothesis for this particular problem is: 

H0- The short term memory capacity of a person is independent to their gender.

The alternative hypothesis will then be: 

Hi- The short term memory capacity of a person is not independent to their gender.

Table 3: Expected Values Maximum Number of Words Retained

3-4

5-6

7-8

9-10

Males

4

14

17.5

14.5

Females

4

14

17.5

14.5

To calculate for the chi-squared value, the values in the table above must be calculated through the use of this equation: (Observed – Expected)²/Expected = x² (5-4)² / 4 = 0.25 (3-4)² / 4 = 0.25 (17-14)² / 14 = 0.6428571429 (11-14)² / 14 = 0.6428571429 (18-17.5)² / 17.5 = 0.0142857143 (17-17.5)² / 17.5 = 0.0142857143 (10-14.5)²/ 14.5 = 1.396551724 (19-14.5)²/ 14.5 = 1.396551724 x² = 4.607389163 p = 0.798595491 df = 8

4

Figure 1:

(Elgin) Based on the table below, the critical value for the chi squared distribution with 8 degrees of freedom at 5% significance level is 15.51. Since the x² value is less than the critical value, the null hypothesis is not rejected. The null hypothesis states that the short term memory capacity of a person is independent to their gender. Taking this into account, the results show that there is no correlation between the short term memory capacity of a person and their gender, since the chi squared test for independence shows that the two variables are independent of each other. To verify these results, the data was subject to

5

the Pearson’s Correlation Coefficient, assuring that there is no correlation between the two variables as the chi-squared test for independence had conveyed. Maximum Number of Words Retained

3-4

5-6

7-8

9-10

Male

5

17

18

10

50

Female

3

11

17

19

50

Totals

8

28

35

29

100

Totals

Table 4: Maximum Number of Words Retained Men

Women

4

4

4

4

4

4

4

5

4

5

5

5

5

5

5

5

5

5

5

5

5

5

5

6

5

6

5

6

5

7

6

6

7

6

7

6

7

6

7

6

8

6

8

6

8

7

8

7

8

7

8

7

8

7

8

7

8

7

8

8

8

8

8

8

9

8

9

8

9

8

9

8

9

8

9

8

9

8

10

8

10 7

8

10

9

10

9

10

9

10

9

10

10

10

10

10

10

10

10

10

10

10

10

10

Using the table provided above with all the raw data, I was able to find the correlation coefficient r, which tells us about the strength of the correlation of these two variables. I had used my TI-84 Graphic Display Calculator, or GDC in order to find the value of r. (See Appendix A for Instructions on finding the r value using the TI-84) From there, the value of r was found to be -0.0000737516624.

Figure 2:

8

(Statisticshowto) The x values refer to the codes 1 and 2 which referred to the gender; “1” being the females and “2” being the males. The y values refer to the maximum number of words retained after thirty seconds. N refers to the number of items on the list. The x² and y² values were then calculated in order to solve manually for the value of r. (See Appendix B: Table 5 for the table of calculations for the x² and y² values)

In this case, this refers to the 100 people that were asked to participate in the experiment. In order to find the r value, the formula below must be used. When the values are inputted into the formula, it will show the following:

(

) (

)) (

) ][(

)

r=

(

√[((

√[

][

(

)) (

) ]

]

9

√[

][

]

r r r = 0.0000737516624 Figure 3:

(Blythe 224) According to a section in our Mathematical Studies SL book, when the value of r is between 0.25 to 0.5, there is a weak correlation. Since r is -0.0000737516624, it shows that there is a very weak or almost no correlation between the short term memory capacity of a person and their gender. This information allowed me to deduce that the results from the chi-squared test of independence proved right. The two variables are independent of each other and do not have any correlation.

10

Conclusion Though at first glance, there seems to be a relationship between the short term capacity of a person and their gender. Through the investigation, I was able to falsify this theory and show that there was actually no correlation between the two factors. The two mathematical processes that I had used to process my raw data, the chi squared test for independence and the Pearson’s correlation coefficient, allowed me to have a more accurate result in terms of my observation. I had used the chi squared test for independence, only to find out that the two variables are independent; however, I wanted to double check this result by using the Pearson’s correlation coefficient. To my dismay, the results remained to show that the two variables do not have a relationship. Had I not done this and based my observations solely on the averages of the maximum words retained by each gender, I may have been led to believe that there was at least a moderate correlation between the short term memory capacity of a person and the person’s gender. Although I was quite disappointed to obtain the results which had disproved my hypothesis of females having a greater short term memory capacity, I am still confident in the results that I had obtained, as I had double checked them both in my graphic display calculator (GDC) and manually. Initially, the process of calculating the values manually proved to be a challenge to me since I was handling a large amount of data. It was also very easy to commit mistakes due to the occasional confusions that I would have when I was processing the data. The errors, however, were minimized through the process of repeating the calculations in order to assure its precision. I am well aware that the results of my investigation may not be a 100 percent accurate, as certain factors may affect the person’s ability to remember the words, such as tiredness, lack of interest in the experiment, variation in personal mental capabilities and so on. These factors are things that are beyond my control; however, due to the large sample size, I am confident that I may have at least gotten a semi-accurate set of results. Should this investigation be done again by another, I would recommend that these issues be addressed, and that the sample is limited only to those who are willing and have a sound mental condition in order to participate in the study. Also, it may be more helpful to increase the sample size for each gender, but still remaining an equal number of males and females in order to assure the accuracy of the results. 11

To conclude, this investigation had failed to prove the initial hypothesis, wherein women have a better short term memory capacity, thereby failing to achieve the initial aim of this investigation. I was though, able to use different mathematical processes in order to get to the conclusion that there is no relationship between the short term memory capacity and the gender.

12

Bibliography Blythe, Peter. "Correlation." Mathematical Studies Standard Level Course Companion. Oxford: Oxford UP, 2012. 224. Print. McLeod, Saul. "Short Term Memory." - Simply Psychology. N.p., n.d. Web. 21 Nov. 2013. . Oursler, Alyssa. "Unemployment Rate — Women Are Winning, Until You Look at Wages." Investor Place. FinancialContent Services, Inc., n.d. Web. 2013. . "Section 9.3: Confidence Intervals for a Population Standard Deviation." Chapter 9. N.p., n.d. Web. 21 Nov. 2013. . Wordpress. "Statistics How To." Statisticshowto.com. Wordpress, n.d. Web. 2013. .

13

Appendix 

[A]: Finding the r value using the TI-84 Calculator o Using the calculator, the data was put into a list in the TI-84 calculator by pressing the STAT button, then selecting EDIT. The x values, which refers to the gender, which were placed into L1. Since the gender of the person is not a quantitative value, a qualitative value needs to be assigned to each gender. The females have been assigned the number “1”, whereas the males have been assigned the number “2”. The y-values, which are the number of words retained within the 30 seconds, were put into L2. Afterwards, the STAT button pressed, then I went to the CALC menu, then selected option 4: which corresponds to LinReg.



[B]: Table 5- Values of x, y, x², y² and xy for use with Pearson’s Correlation Coefficient

Participants

x

y

x²

y²

xy

1

1

4

1

16

4

2

1

4

1

16

4

3

1

4

1

16

4

4

1

5

1

25

5

5

1

5

1

25

5

6

1

5

1

25

5

7

1

5

1

25

5

8

1

5

1

25

5

9

1

5

1

25

5

10

1

5

1

25

5

11

1

5

1

25

5

12

1

6

1

36

6

13

1

6

1

36

6

14

1

6

1

36

6

15

1

7

1

49

7

16

1

7

1

49

7

14

17

1

7

1

49

7

18

1

7

1

49

7

19

1

7

1

49

7

20

1

8

1

64

8

21

1

8

1

64

8

22

1

8

1

64

8

23

1

8

1

64

8

24

1

8

1

64

8

25

1

8

1

64

8

26

1

8

1

64

8

27

1

8

1

64

8

28

1

8

1

64

8

29

1

8

1

64

8

30

1

8

1

64

8

31

1

8

1

64

8

32

1

9

1

81

9

33

1

9

1

81

9

34

1

9

1

81

9

35

1

9

1

81

9

36

1

9

1

81

9

37

1

9

1

81

9

38

1

9

1

81

9

39

1

10

1

100

10

40

1

10

1

100

10

41

1

10

1

100

10 15

42

1

10

1

100

10

43

1

10

1

100

10

44

1

10

1

100

10

45

1

10

1

100

10

46

1

10

1

100

10

47

1

10

1

100

10

48

1

10

1

100

10

49

1

10

1

100

10

50

1

10

1

100

10

51

2

4

4

16

8

52

2

4

4

16

8

53

2

4

4

16

8

54

2

4

4

16

8

55

2

4

4

16

8

56

2

5

4

25

10

57

2

5

4

25

10

58

2

5

4

25

10

59

2

5

4

25

10

60

2

5

4

25

10

61

2

5

4

25

10

62

2

5

4

25

10

63

2

5

4

25

10

64

2

5

4

25

10

65

2

5

4

25

10

66

2

6

4

36

12 16

67

2

6

4

36

12

68

2

6

4

36

12

69

2

6

4

36

12

70

2

6

4

36

12

71

2

6

4

36

12

72

2

6

4

36

12

73

2

7

4

49

14

74

2

7

4

49

14

75

2

7

4

49

14

76

2

7

4

49

14

77

2

7

4

49

14

78

2

7

4

49

14

79

2

7

4

49

14

80

2

8

4

64

16

81

2

8

4

64

16

82

2

8

4

64

16

83

2

8

4

64

16

84

2

8

4

64

16

85

2

8

4

64

16

86

2

8

4

64

16

87

2

8

4

64

16

88

2

8

4

64

16

89

2

8

4

64

16

90

2

8

4

64

16

91

2

8

4

64

16 17

92

2

9

4

64

18

93

2

9

4

64

18

94

2

9

4

64

18

95

2

9

4

64

18

96

2

10

4

100

20

97

2

10

4

100

20

98

2

10

4

100

20

99

2

10

4

100

20

100

2

10

4

100

20

Totals

150

754

250

6016

1070

18

4