**ABOUT US**

We are a group of students from Occupational therapy in Nanyang Polytechnic! Hope you enjoy our research presentation:)

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**INTRODUCTION** This site is created to blog about our Statistics project on:

*Is there a relationship between the length of our foot and the length of our forearm?** *

There has always been a belief about how different parts of our body proportions are similar to each other like the circumference of our neck is equivalent to waist size or the **length of our foot is equivalent to the length of our forearm**.

** Goals for research:** To prove any relationship that maybe present between the variables

To understand the process of gathering data and analysing relationship between valuables

To reflect on the research process, evaluate and explore room for improvements in future data gathering processes.

** Importance of this finding:** 1. To find a suitable feet size for a prosthetic leg that looks proportionate to the body in cases of bilateral below knee-amputation(BKA).

2. We will be able to see if our forearm length for shoe size testing when going shopping!

If it is true, then no more trying for shoes outside!

*Our Hypothesis**:*

**H _{1}**:

**There is a positive relationship between the length of the foot and the length of the forearm**

**H _{0}** :

**There is no significant relationship between the length of the foot and the length of the forearm**

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We’ll be collecting data on these “vital statistics” from friends around our cohort, analyse them and come up with a conclusion.

We hope that the data and the analysis gathered at the end of this project will let us see how true this is.

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**LITERATURE REVIEW**

Leonardo di ser Piero da Vinci was a famous Renaissance Italian man who is celebrated for his unquenchable curiosity which was equalled only by his invention and painting. Some of the world renowned paintings such as the ‘Mona Lisa’ and ‘The Vitruvian Man’ are illustrious even till today.

During the 1480s, when he was working on the equestrian monument to Francesco Sforza, Leonardo also embarked on the first time on extensive groups of studies on the proportion of the human body, on anatomy and physiology. Thus in April 1489 he began a book with the title “On the human figure”. During the project, he made systematic studies of two young men. After what must have been months of taking measurements, as he was doing at almost exactly the same time with the horses belonging to his patron Ludovico il Moro, he arrived at a systematic overview of human proportions, at which point he then started to look at the proportion of sitting and kneeling figures. He then compared the results of his anthropometric studies – taking human measurements – with the only surviving theory of proportions from Antiquity, namely the Vitruvian man. Vitruvius, a moderately successful architect and engineer during the days of the Roman Empire had written a treatise on architect which included in its third book a description of the complete measurements of the human body. These led him to conclude that a man with legs and arms outstretched would fit into the square and the circle, perfect geometric figures.

Vitruvius mentioned a formula of body proportion as fashioned by nature in his book; de Architectura book III chapter three. He proposed the use of this formula in the construction of the sacred temple of the immortal gods to truly call it a well-designed, symmetrical, proportional beauty of a building (Pollio, n.d., p30).

With the formula described by Vitruvius, da Vinci produced the Vitruvian Man which clearly illustrates the body proportion of different parts of the body to one another. With the Vitruvian Man, da Vinci came up with a “golden proportion”, a relationship between two ratios which was expressed mathematically as 1: 1.61803, commonly known to the Greek as phi (Place, 2000).

A comparison of two body part proportion ratio also mentioned by Place, which will be the focus of our research is:

The length of foot is the same as the length of forearm, demonstrating a golden relationship between the hand and the foot (Place, 2000).

Interestingly, other literature review also mentioned this hypothesis. In the article “The King’s Foot”, dewitt mentioned the evolution of measurement based on correspondences to various parts of the body, usually the King’s body.

He said: “One apocryphal but likely account of the origins of the *foot* is that it was the distance from the king’s elbow to his wrist–whoever this king may have been.” (n.d.).

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**METHODOLOGY** This is how we carried out our research!

**Sample population**: 30 randomly chosen subjects from the occupational therapy cohort (Cluster sampling)

**Variables**: Dependent – forearm length (cm)

Independent – feet length (cm)

**Measuring instruments/ tools**:

- Measuring tape to measure foot and forearm (x4)
- Masking tape to secure the measuring tape to the floor(x1)
- Chairs for subjects to sit when measuring forearm (x2)
- Thick books for accurate measurement (x2)
- List of subjects that we are to measure (x2)

**How did we carry out measurements?**

In order to collect data for the most accurate length, instructions for measurements must be standardized among the data collectors

*Forearm*

*Foot *

**Factors to ensure validity, reliability and consistency of data**

- Start and end point of measurements were standardised among data collectors
- Position of subjects when measurements were taken:
- All forearm measurement done in sitting
- Feet measurements done standing
- Subjects were required to remove all accessories from their arm for accurate data collection
- Time of the day- to cater to the expansion of the feet throughout the day
- All data was collected on one occasion and at the same time of the day
- Tools were standardised as well:
- We compared the tape measures to make sure there are no discrepancies in the units and also to start from the 10cm mark to increase inter-rater reliability

It has to be taken into account that the measurements may vary across the 4 data collectors. Thus, prior to the data collection, data collectors did a “trial and error” to maximize inter-rater reliability. We assigned 4 data collectors for measurement, 2 for forearm length and 2 for feet length. The data collectors collected data for left and right sides of the forearm and foot. 2 other data collectors were assigned to the forearm and feet sections respectively to help with data recording. Data collected for foot and hand were then collated by 2 individuals respectively. **Figure 1** below shows the set up of the station for data collection.

**Figure 2** below shows the headings for the record sheet that we used for data collection

To increase accuracy, we took the average of the 2 readings per side of the forearm and feet.

**The tedious process of our group members…**

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**STATISTICAL ANALYSIS**

Figure 4. shows the variable list

**Variables are defined as:**

Sex: 0= male, 1=female (nominal)

Age: (scale)

Left forearm: first and second reading, average reading (scale)

Right forearm: first and second reading, average reading (scale)

Left foot: first and second reading, average reading (scale)

Right foot: first and second reading, average reading (scale)

Therefore, in order to find out whether the length of our forearm is the same as our foot, our group use the Pearson’s correlation coefficient as a symmetric measure of association for interval level variables.

**Assumptions of the Pearson’s r:**

- Assumption 1- All observations must be independent of each other
- Assumption 2- The dependent variable should be normally distributed at each value of the independent variable
- Assumption 3- The dependent variable should have the same variability at each value of the independent variable
- Assumption 4- The relationship between the dependent and independent variables should be linear

In our case,

Assumption 1 is fulfilled because the samples were taken independently and randomly.

Assumption 2 needs to be verified by doing a QQ plot.

From the QQ plots, it can be seen that they are all normal and do not violate this assumption. Most of the points are close to the best fit line For Assumptions 3 and 4, to verify them, scatterplots are used to confirm homogenous variance and that there is a linear relationship between R forearm and R foot and between L forearm and L foot.

From the scatter plot, it appears to follow a general positive linear trend. From table 1, a Pearson’s correlation coefficient of 0.749 indicates a moderately strong relationship between the length of the left forearm and foot. There is thus a positive, moderate, and significant association between left forearm and foot. (r= 0.749, p<0.05, N=30)

From the scatter plot, it appears to follow a general positive linear trend. From table 2, a Pearson’s correlation coefficient of 0.778 indicates a moderately strong relationship between the length of the right forearm and foot. There is thus a positive, moderate, and significant association between right forearm and foot. (r= 0.778, p<0.05, N=30)

The *stem and leaf plot* is useful as it provides a summary of the data and also shows the extra details, in this case, gender and also shows the outliers clearly if needed.

From the stem and leaf plots, some outliers may be identified in the males’ data for the left forearm. This might be because of their proportion to their height or other genetic factors. The graph for the males also tend to have a higher but narrower range of values as compared to the females graph. This is due to the fact that the males tend to be bigger in size and thus their forearm and feet are bigger too.

Our group decided to see whether the distinctions still exist if we plot it on a scatter plot with markers.

From the scatter plots, it shows a positive linear trend regardless of gender, thus there is still a linear relationship between the length of the forearm and foot.

It is to be taken into consideration that our group only took a random sample of 30, thus a more accurate measurement to prove our hypothesis should include more.

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**CONCLUSION**

From our findings, we conclude that there is a positive relationship between the length of forearm and feet and thus we can accept H_{1}, and reject H_{0. }Even though there is a positive relationship with the two variables, it does not show that forearm length is of equal length with the foot length, thus only can be served as a good gauge when it comes to measurements of shoe sizes and prosthetics for patients.

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**GROUP EVALUATION**

Our group felt that there are some areas that we could improve on. However, due to limitations in time and resources , we were not able maximise the potential of our research findings.

Areas of improvement includes:

- A larger sample group for a better representation of data
- Substituting standardised electronic measuring instruments in place of subjective manual measuring instruments.

Further research can be done in areas such as applying results of this statistical analysis to clinical practice.

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**REFLECTIONS**

*Benjamin’s Reflection*

Statistic module gave me a better understanding of the process of research and act as a step up from research methodology module we undertook in year one. It is definitely very helpful to understand the SPSS programme which is an asset in statistical data analysis.

This project has stimulated our creative thinking incorporating the knowledge we learned last year in research methodology to come up with appropriate methodology for our research. The thinking process involved is definitely very fulfilling and will aid us in the future.

*Samantha’s reflection*

I have learnt alot from doing this project. I thought using a blog instead of a presentation was quite interesting. This project had certainly enriched me in ways by allowing me to explore statistics and apply what I have learnt in class. Working with classmates through the various processes was tedious but exciting. The SPSS definitely helped us quite abit in our project. Hopefully what we have learnt will help us in our FYP next year!

*Shamaine’s reflection*

I have learnt a lot while doing this project. From choosing an agreeable topic to work on with my group members, gathering the data, and analyzing them, leading to our final conclusion. The Spss helped us a lot with our statistical analysis. This has been an enriching experience and certainly prepared us with the basics for the FYP next year. Maybe in future, it might be able to help us with our evidence-based practice as well!

*Szesze’s reflection*

As our group aim to improve the interrelator results, 2 data collectors took turns to measure a subject, the tedious process in order to prove the reliability of our project made me feel the importance of data collection extremely important. I enjoyed the process with my other group mates thoroughly and gained much knowledge using the Spss.

*Nirma’s reflection*

This project has allowed me to see the application of statistical methods to a real research topic.

The idea of setting up a blog is a creative method to allow students to share their research findings.

It was a good experience in that we had to find ways to collate data in the most effective way possible and also gave us an opportunity to work on spss as a form of practice. I hope to be able to effectively integrate the knowledge received in upcoming research projects.

*Mohsin’s reflection*

From our project I felt that we needed better and more accurate ways to measure the feet of our subjects. What could be done better was to ensure proper positioning of the heel. Instead of using a book to rest the heel on, we could have used the wall to judge heel position. This method would have increased accuracy of measurement for heel length.

I also feel that briefing of data collectors are important so as to ensure that readings collected could be used for our measurements as accurately as possible.