What is the Relationship between Female Weight and Male Weight - Research Proposal Example

What is the Relationship Between Female Weight and Male Weight [Name] [Institutional Affiliation] [Date] Table of Contents List of Tables 2 List of Figures 2 Introduction 3 Aim 3 Hypothesis 3 List of Tables Table 1: Sample Data 5 Table 2: Mean, Standard deviation, Mode and the 5 number summary 6 Table 3: Values for Computation of Linear Regression 10 List of Figures Figure 1: Side-by-side Box Plots 6 Figure 2: Normal Probability Plot for Female Weight 7 Figure 3: Normal Probability Plot for Male Weight 8 Figure 4: Scatter Plot for Female Weight 12 Figure 5: Scatter Plot for Male Weight 13 Introduction Statistics is plays a central role in data analysis (Donley, 2012) and (Malim and Ann, 1997). A number of early researchers have tried to establish the relationship existing between male and female in terms of weight. In order to establish such a relationship, it requires the input of statistical analysis aimed at comparing a random data for male and female and then performing some linear regression analysis, mode, mean, and median, standard deviation, maximum and minimum, among other statistical analysis tools. Scatter plots are important in illustrating the weight distribution for male and female, especially as to whether the weights show any linear relationship. Aim The aim of this statistical report is to investigate the relationship the weight of females and the weight of male. Hypothesis The research hypothesis shall be based on the investigation as to whether the weight for female and male are related positively, negatively or not related at all. Data Collection Sampling technique is necessary when sorting large population data (Sapsford and Victor, 2006). The data obtained for this research was obtained randomly from weights of over 150 persons and then sorted into a sample of 100 persons with 50 male and 50 female. The data collected for 50 male and 50 female is as shown in Table 1 below. Female weight in pounds Male Weight 1 180 130 2 130 123 3 123 139 4 195 153 5 170 190 6 175 160 7 135 160 8 163 160 9 190 160 10 161 160 11 138 160 12 135 160 13 118 152 14 130 118 15 159 147 16 118 147 17 130 132 18 160 143 19 100 124 20 160 126 21 160 167 22 130 143 23 140 145 24 140 143 25 120 134 26 187 153 27 130 147 28 143 154 29 134 125 30 154 163 31 133 170 32 145 171 33 145 152 34 134 124 35 134 153 36 142 135 37 117 153 38 147 163 39 162 125 40 172 142 41 142 126 42 162 151 43 126 163 44 135 134 45 135 176 46 153 162 47 146 153 48 146 123 49 154 152 50 163 123 Table 1: Sample Data Discussion and Analysis Five Number Summary According to Ware and Charles (1999) and Walker (2010), five number summary technique entails the use of sample minimum, sample maximum, lower quartile, median and upper quartile. The medium expresses the information to do with location, the range is explained by both minimum and maximum whereas the spread is explained by the quartiles. Table 2 below illustrates the mean, standard deviation, mode and the 5 number summary. Female Male Mean, Standard Deviation and Mode Mean 146.02 147.38 Standard Deviation 20.29928118 16.47371437 Mode 130 160 Five Number Summary Median 142.5 151.5 Maximum 195 190 Minimum 100 118 First Quartile 133.25 134 Third Quartile 160 160 Table 2: Mean, Standard deviation, Mode and the 5 number summary From Table 2, the median weight for male is more than that for female. The maximum weight of female is more than that for male whereas the minimum weight for the male is more than that for female. Most of the weights for female and male are located at 130 and 160 respectively. The lower quartile shows that male weight is more than that for female but the upper quartile shows equal weights. Side-by-side Box Plots The Side-by-side Box Plots is as shown in Figure 1 bellow Figure 1: Side-by-side Box Plots Normal probability plot (NPP) Figure 2: Normal Probability Plot for Female Weight Figure two indicates that female weight data does not exhibit the properties of normal distribution. Figure 3: Normal Probability Plot for Male Weight The plot in Figure 3 indicates that the data does not exhibit the properties of normal distribution. How best the Data can be Explained This data can best be explained by the use of five number summary which considers the upper quartile (Q3), median, maximum, lower quartile (Q1) and minimum. The data is best explained using the five numbers because the two variables do not have a strong correlation. Therefore, each data should be looked at independently. Five number summary is more detailed than the use of mean and standard deviation. Relation between Female Weight and Male Weight Linear Regression Model Table 3 below offers the basis for calculation of the linear regression model as shown herein. No Weight of Female (Y) Weight of Male (X)   XY 1 180 130 16900 23400 2 130 123 15129 15990 3 123 139 19321 17097 4 195 153 23409 29835 5 170 190 36100 32300 6 175 160 25600 28000 7 135 160 25600 21600 8 163 160 25600 26080 9 190 160 25600 30400 10 161 160 25600 25760 11 138 160 25600 22080 12 135 160 25600 21600 13 118 152 23104 17936 14 130 118 13924 15340 15 159 147 21609 23373 16 118 147 21609 17346 17 130 132 17424 17160 18 160 143 20449 22880 19 100 124 15376 12400 20 160 126 15876 20160 21 160 167 27889 26720 22 130 143 20449 18590 23 140 145 21025 20300 24 140 143 20449 20020 25 120 134 17956 16080 26 187 153 23409 28611 27 130 147 21609 19110 28 143 154 23716 22022 29 134 125 15625 16750 30 154 163 26569 25102 31 133 170 28900 22610 32 145 171 29241 24795 33 145 152 23104 22040 34 134 124 15376 16616 35 134 153 23409 20502 36 142 135 18225 19170 37 117 153 23409 17901 38 147 163 26569 23961 39 162 125 15625 20250 40 172 142 20164 24424 41 142 126 15876 17892 42 162 151 22801 24462 43 126 163 26569 20538 44 135 134 17956 18090 45 135 176 30976 23760 46 153 162 26244 24786 47 146 153 23409 22338 48 146 123 15129 17958 49 154 152 23104 23408 50 163 123 15129 20049 Sum ∑Y = 7301 ∑X = 7369 ∑ = 1099341 ∑ XY = 1079592 Table 3: Values for Computation of Linear Regression A linear correlation coefficient is significant in measuring the strength of the relationship between any two sets of variables, and for indication of the direction of such relationship. The value of the linear correlation, r, coefficient can thus be interpreted accordingly. If the value of r is near to positive +1, then the relationship between female and male height will be said to be more positive. This applies in case where an increase in one variable leads to an increase in the other variable. However, for values near -1, it illustrates negative correlation whereby as one variable increases the other decreases. The other expected scenario is where there is no correlation at all, if the value for correlation coefficient is zero. In perfect correlation, all value lie on a straight line. As a general principle, a correction coefficient more than 0.8 is regarded strong whereas the one less than 0.5 is regarded weak. The values depend on the data type under examination. The model for linear regression such as is suitable for simple regression but in multiple regression, the model of is applied. In either cases, the values for and are obtained by simultaneously solving equations (i) and (ii) below: ……………………………….. (i) ………………………. (ii) The coefficient of correlation is given by: Where: R = coefficient of correlation n = population size for each variable X = Weight of male Y = Weight of female Therefore, R = = 0.0002 This is almost zero. Therefore, this draws to the conclusion that there is no correlation between male weight and female weight. Scatter Diagrams Figure 4: Scatter Plot for Female Weight The weight of female is not linearly distributed as shown in Figure 5. Figure 5: Scatter Plot for Male Weight The weight for male is not linearly distributed as shown in the scatter plot in Figure 5. Statistical investigation into the relationship between the weight of female and male exhibits a number of errors. For example, the computation of numbers involves the rounding off of numbers. Further, data collection took into consideration the population sample of adults only. In this case, demographics matter in the sense that people chosen should be from a certain group, that is ,where a common genes can apply so that we would investigate, if the genes factor is a constant, what happens to the two variables. Further, the data is obtained by way of measuring and recording. Such process is prone to experimental errors such as errors in the weight measuring instruments and human errors in recording the numerous data for different people. Conclusion This research analysis considers a random sample of 50 male and 50 female as a general representation of the entire population. The data is evaluated under different statistical techniques but the experimental and scientific methods should be put in place to explain the differences. The major disadvantages of mean, mode and median is that they do not indicate the extreme conditions that would otherwise distort the overall meaning of the results. Therefore, standard deviation and linear regression analysis come in to perform the crucial role of deviations from the mean and to illustrate the nature of correlation between the two variables. Works Cited Top of Form Bottom of Form Top of Form Bottom of Form Top of Form Bottom of Form Top of Form Bottom of Form Top of Form Donley, Amy M. Research Methods. New York: Infobase Pub, 2012. Internet resource. Malim, Tony, and Ann Birch. Research Methods and Statistics. London: Macmillan Press, 1997. Print. Sapsford, Roger, and Victor Jupp. Data Collection and Analysis. London: SAGE Publications in association with the Open University, 2006. Internet resource. Walker, Ian. Research Methods and Statistics. Houndmills, Basingstoke, Hampshire: Palgrave Macmillan, 2010. Print. Ware, Mark E, and Charles L. Brewer. Handbook for Teaching Statistics and Research Methods. Mahwah, N.J: Lawrence Erlbaum Associates, 1999. Print. Bottom of Form Read More