Our Reflection

We appreciate each other more after doing this project because we only have four members. Compared to teams which have six members, we seem to lack in manpower, but we helped each other and I am very happy to see that we have this spirit in my team, and we really had a great time when doing this project, although we faced a lot of difficulties. For example, we are not sure the data that we measure are reliable and for the new users like us to SPSS, we are not sure how to use the linear regression and so on. We are glad to have Ms Chia as our lecturer to guide us and make sure we are at the right track. After consulting her, we have a clear idea on how to go about it.
Last but not least, we would like to thank all the participants for helping us in our project. And dear Ms Chia, thank you for your teaching we will never forget you and especially your life stories shared with us.

Statistical Conclusion

Based on our group findings, we will reject the null hypothesis because the correlation between arm-span and height is significant, strong and positive. Hence, we conclude that there is a relationship between height and arm-span.

Analysis of Data Part 3

We look at the R square, means 80.5% of our data are relevant, the 19.5% may due to other factors.

Predicted variable (heights) = slope * arm-spans + intercept

Predicted value of "heights" = 0.731 X value of arm-spans + 43.492

Analysis of Data Part 2

Statistical Methods

For our data analysis, we used Statistical Package for Social Sciences (SPSS) 14.0 for Windows Integrated Student version.

Of Linearity and Homogeneity and Scatter Plots

To find out if an association exists between arm-span and height, and if yes, the degree of association, requires a correlational analysis. Because there is only one independent variable, and both independent and dependent variables (for the reason as to their selection, see post titled 'Analysis of Data Part 1') are scale data, and we're interested in their correlation, we've identified Pearson's Correlation Coefficient to be the most appropriate statistical test.


The coefficient of correlation only measures linear relationship. Thus, first we need to ascertain with a scatter diagram, whether arm-span and height are linearly related, and if a constant error variance exists.

We've plotted the scatter diagram of arm-span and height for the sample here. A copy is enclosed here as well.

The R square linear is 0.805. We interpret this to mean the goodness of fit of the line, ie 80.5% of the variation in height can be explained by the fitted line.

As a linear relationship exists between arm-span and height, we proceed to compute Pearson's correlation coefficient. This is the results from SPSS.

Since the p value (0.000) is less than 0.05, we reject the null hypothesis, and conclude there is a very strong, positive, and significant association between arm-span and height. [where r = 0.897, p < 0.05 and N = 30]

We are also interested to find out how the association looks when the sample is stratified by gender. Thus, we plotted the scatter diagram again, but setting gender as marker field. The scatter diagram of arm-span and height for females and males in the sample is available here. A copy is enclosed below as well.

R square linear of male and female samples is 0.759 and 0.638 respectively. In other words, 75.9% and 63.8% of the variation in height can be explained by the fitted line for male and female samples respectively. We take it that the fit lines for both genders are sufficiently linear and have homogeneous variance.


A linear relationship exists between arm-span and height for the two genders, so we proceed to compute Pearson's correlation coefficient. This is the results from SPSS.







For female Since the p value (0.000) is less than 0.05, we reject the null hypothesis, and conclude there is a very strong, positive, and significant association between arm-span and height for the women sampled. [ where r = 0.799, p < 0.05 and N = 23]


For male Since the p value (0.011) is less than 0.05, we reject the null hypothesis, and conclude there is a very strong, positive, and significant association between arm-span and height for the men sampled. [ where r = 0.871, p < 0.05 and N = 7 ]

Analysis of Data Part 1

Of variables and measurements

We're interested in conducting our own investigation to see if arm-span is indeed correlated with height, and if it does, what is the nature, significance and magnitude of this association.

Based on our literature review, we saw there is a clinical relevance of estimating height of a person using the arm-span. This estimation is useful in the following cases -

• to quantify age-related loss in stature


• to identify clients with disproportionate growth abnormalities and skeletal dysplasias


• to quantify the alteration in height as a result of progressive spinal deformities


• as a substitute measurement where height measurement is not feasible, such as clients' lower limbs have been amputated

Therefore, for the purposes of statistical analysis, we've identified arm-span to be our independent variable, and height, the dependent variable.

The following data elements are collected in the course of measuring our sampling units.

1. age (level of measure: scale)


2. gender (level of measure: nominal, where 1='female', 2='male')


3. height (level of measure: scale)


4. armspan (level of measure: scale)

Sampling method

We've not employed probability sampling in our selection of sampling units. Our chosen sampling method is coincidental sampling. We've allocated for our group one week to collect the necesary data, and on day 1, we went around the class during 2 15-minute breaks in between lessons, asking for classmates' permission to allow our group to measure their height and arm-span.



Three timeslots are identified over the next 4 days from which they are welcome to indicate their preference to turn up for the measurement process. In this manner, we managed to enlist the help of 26 classmates, and including the 4 of us, we had the minimum sample size of 30.




In a subsequent literature review, we found the rationale for why Ms Chia has stipulated 30 as the minimum sample size. Creswell (2008, p.370) explained that "The group needs to be of adequate size for use of the correlational statistic, such as N = 30; larger sizes contribute to less error variance and better claims of representativeness."


We looked up on this internet site recommended by Ms Chia, during one of the research methods' lecture. (http://www.custominsight.com/articles/random-sample-calculator.asp) Using the calculator provided, and given a population size of 46 that is the total size of our cohort for HSNF01, our sample size of 30 yields a sampling error of 8.9%, 10.6%, and 13.9% at 90%, 95% and 99% confidence interval respectively.

-METHODOLOGY-

Methodology
The focus of this preliminary study was primarily on confirming if the measurement of arm span is related to a person’s height. A detailed experiment was done aimed at determining the effects of arm span and height.

A.Subjects
The study was conducted at Nanyang Polytechnic based on convenience sampling. There are 30 subjects in total for this study with 7 males and 23 females, ranging from 21 to 50 years old (mean age is 31.93 years old).

Inclusion Criteria
• Age: 21 - 55
• Ability to comprehend simple instruction
• Able to stand straight
• Able to keep arm at 90 degrees abduction to measure arm span.

Exclusion criteria
• Deformities that affect the height and arm (leg, spine, arm)
• Kyphosis

The subjects arrived at Nanyang Polytechnic, health science block, classroom K612 for the study. The purpose and procedure of the study was explained to subjects and verbal consent was obtained prior to commencement of data collection. 30 of the 30 subjects completed the study.

B.Equipment
Measuring tapes and metal tapes were used for measuring arm span and height respectively. 4 different types of measuring tape were collected and calibrate.

i.Set-up
The 4 measuring tapes were placed side by side at the tip of a straight paper evenly to check for accuracy. There are 0.05 cm differences after the comparison. The four measuring tape were then calibrated against the measuring scale in Nanyang Polytechnic’s gym.







C.Experimental Procedures
The subjects will be going through standing height measurement by twice by 2 different testers. After that subjects will go to another station to measure their arm span again twice by 2 different testers respectively. The purpose of measuring subjects twice by 2 testers is to eliminate biases and determining the level of agreement among raters, measuring the degree of correlation between them (Interrater Reliability)

INTRODUCTION

Welcome to the first blog posting of Sub-group 4.

In this post, we will be introducing to you:
- Our research topic
- The reason behind why we chose this topic
- Independent and dependent variables
- Null and research hypothesis
- Supporting literature review of chosen topic
- Application to our context



Our statistics topic is based on Leonardo Da Vinci's Study of Human Proportions which was made famous by his drawing, the Vitruvian Man.


Traditionally, the human body is represented as being 8 heads tall:

1)From the top of the head to the chin
2)from chin to the nipples
3)from the nipples to the navel
4)from the navel to the crotch
5)from crotch to mid-thigh
6)from mid-thigh to just below the knees
7)from below the knees to the middle of the tibia
8)from mid-tibia to the feet

The wing span or arm span of both arms outstretched is also equal to a person's height from head to toe, evidenced by the square surrounding the Vitruvian Man.

This theory is what we are trying to prove.

Our variables are:
- Independent: The human arm-span from tip of one hand to tip of the other hand
- Dependent: The human height from top of head to bottom of ankles

Our null hypothesis:
There is no relationship between a person's arm span and his height

Our research hypothesis:
There is a relationship between a person's arm span and his height

This is based on our literature review of a research we have found on arm span and height which was proven positive, meaning there is a positive relationship between the two variables.

The importance of our study is to find out the natural height of a person through his arm-span and how his height can change throughout his lifetime due to pubertal growth spurts, spinal deformities, growth deformities or the natural process of aging.