Phase angle measurements, ranging from 2Ëš to 12Ëš, indicate plasma membrane integrity and cellular health. Elevated values represent intact plasma membranes and a high body cell mass (BCM), where lower values signify breakdown of the membranes and energy storage incapability of cells. The research question to be investigated is: "does Phase Angle correlate with Age and Body Mass Index in males with regular physical activity?", as these two variables are known factors affecting bodily health and wellbeing. Two hypotheses were established based on the research question; Hypothesis I stating "As age increases, phase angle decreases", and Hypothesis II: "As BMI increases, phase angle decreases.".
Phase angle measurements were obtained through a Bio- Impedance Analysis (BIA) on every out of 32 men in the experimental sample, carried out by BodystatÂ®1500MDD. Biographical age was used as one variable, and height and weight were used to calculate the body mass index (BMI), the second variable. Data was interpreted on graphs, linear regression plotted, and Spearman's Rank Correlation Coefficient statistical analysis conducted.
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Hypothesis I was supported by the graphical and regression analysis, as data points created a negative correlation. When testing the |RÂ²| value, 0.309, for significance, it was larger than its critical value at 95% accuracy, 0.306, but smaller at 97.5%, 0.364 . Nonetheless, Hypothesis I was supported and accepted.
The graphical and regression analysis of Hypothesis II data did not support it, as there was not visible correlation, and the linear regression was negligible. The same was reflected by the statistical analysis; the |RÂ²| value of 0.059 was considerably smaller than its critical value at 95%, 0.306, therefore Hypothesis II was rejected.
The investigation concluded that, based on the collected data, phase angle decreases with increasing age, and that there is no correlation between phase angle and BMI.
I. I n t r o d u c t i o n
1.1 Phase Angle
1.1.1 Phase Angle & Physics
Phase angle is a concept originating in the electricity branch in physics. It relates to the study of a.c. (alternating current) circuits. In an a.c. circuit, the potential difference (p.d., measured in V) and current (I, measured in amps) will both be oscillating about the same frequency, however, they must not do it simultaneously; they may be out of phase  . The phase angle is, specifically, the angle, in degrees (Ëš), by which the sine curve of the voltage leads or lags the sine curve of the current in the circuit  .
Fig. 1  : Diagram illustrating phase angle (Î¸ = phase angle)
1.1.2 Phase Angle & The Human Body
Phase angle, in a human context, is calculated from Resistance (R) and Reactance (Xc), two bioelectrical parameters  . Resistance indicates tissue hydration; hydrated body cells offer a lower resistance to an a.c. current passing through, compared to less hydrated ones  . Reactance is associated with cellularity (the state of tissue based on degree, quality, or condition of cells present in it  ), cell size, and the state of the cell membranes: integrity, function, and composition  .
The electrical definition for phase angle is: PA = arctangent (Xc/R)  .
Fig. 2  : Definition of phase angle
1.1.3 Plasma Membrane Integrity & Water Distribution
Phase angle has a slightly different meaning when referring to the human body than in electrical circuits. It has been interpreted as "an indicator of membrane integrity and water distribution between the intra- and extra-cellular spaces"  .
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Integrity, in biological terms, may be defined as "an unimpaired condition  ", meaning how undamaged and intact the cell membrane of a body cell is. As it may be deduced from their names, the difference between intra- and extra cellular fluid (ICF and ECF, respectively), is their location. Namely, they are separated by cell membranes  : ICF is found inside cells, whereas ECF is all the remaining fluid.
Extra- cellular fluid may be divided into
interstitial fluid, surrounding cells,
plasma, the liquid component of blood,
fluid in bone and dense connective tissue, and
transcellular fluid, in the epithelium of cells, produced from transport activities  (e.g. gases need to be dissolved before they may diffuse across plasma membranes).
The ratio of ICF to ECF is 55:45  . However, this ratio may change, especially in individuals with wasting, dialysis patients, and obese individuals  , Hence, phase angle, is an indicator of cellular health  .
ICF and ECF are also a measure of body cell mass (BCM). BCM represents all cellular and metabolically active tissue in the body, and is constituted of muscle tissue, organ tissue, bone tissue, ICF, and ECF  . This brings us back to cellular health: BCM is dependent on cell hydration (the amount of ICF and ECF) and severe dehydration results in depletion of BCM. This is a common feature of chronic diseases including AIDS and terminal cancer  .
Phase angle incorporates all these factors to give a reliable indication of how unimpaired and intact body cells are.
Phase angle ranges between 2Ëš and 12Ëš  . Low phase angle measurements indicate cell membrane breakdown and an inability of cells to store energy; a high phase angle value indicates that the membranes of the cells are intact and BCM is high  , therefore the higher the value of phase angle, the healthier the cells are  .
Fig. 3  : Graph illustrating phase angle in relation to cellular health
The research question was expounded on this concept of cellular health and formulated according to two possible factors affecting it: how worn out cells are (age) and amount of adipose tissue (BMI): "Does Phase Angle correlate with Body Mass Index and Age in males with regular physical activity?". Background and justifications for selection of these variables follow:
1.2.1 The Concept of Biographical Age
'Biographical age' has been chosen, from the two types of age: biographical and biological. Biographical refers to the age of a person in numbers, where biological age indicates the bodily condition  . For example, the biological age may be low for certain (healthy) individuals with a high phase angle, where their biographical age is older than others  . As these two concepts easily differ form each other, biographical age was selected and used in this study as it is the most obvious and more easily measured than biological age. Further in the investigation, only 'age' instead of 'biographical age' will be used for convenience reasons.
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1.2.2 Age & Phase Angle
When we age, the body changes; organs malfunction, arterial problems such as atherosclerosis increase, joints become painful, bone and muscle tissue deteriorates, which limits execution of physical activity; the immune system also depreciates as less immune cells are produced  , and elderly people get sick much more easily than young ones. All these aspects indicate that phase angle, measuring cellular health, should decrease with age.
In new-borns, the amount of ECF compared to ICF is much greater than in adults  . Water distribution differs between a younger and elderly person's body. This shows that age has an influence on phase angle. As life and death are part of the natural cycle, cells in our bodies, and any other living organisms, degenerate in time, become less efficient, and even mutate, until natural death occurs. Phase angle, being a measurement of cellular health, will consequently be significantly affected by age; older individuals are expected to have a lower, 'worse', phase angle reading than younger ones.
These assumptions lead to the first hypothesis:
1.2.3 Hypothesis I
"As age increases, phase angle decreases."
1.3 Body Mass Index
1.3.1 Body Mass Index: The Theory
The body mass index is a measure of obesity, and takes into account weight and height of a person to give an indication of the amount of adipose tissue  . It is calculated using the formula: . 
1.3.2 Body Mass Index & Phase Angle
Most tissues contain 70 - 80% water, with an exception being adipose, fat, tissue, which contains only 10 - 15%  . Individuals with a large amount of adipose tissue have a lower ratio of intracellular fluid. This shows that water distribution is also affected by the amount of adipose tissue in their body, in other words, phase angle is affected by the body mass index (BMI). Obese individuals are at a much higher risk of suffering chronic diseases as cardiovascular disease, type 2 diabetes, musculoskeletal disorders (osteoarthritis), and endometrial, breast and colon cancer  . This illustrates that phase angle, as a measurement of cell wellbeing, deteriorates with an increasing BMI, and a second hypothesis may be suggested:
1.3.3 Hypothesis II
"As BMI increases, phase angle decreases."
1.4 Bio Impedance Analysis
Bio Impedance Analysis (BIA) is a measurement based on how strongly bodily fluids oppose the flow of an a.c. current in the body, also called impedance, which varies between lean tissue, for example muscles with long cylindrical cells and a high fluid and electrolyte content, and adipose tissue, for example, which is contains globular cells and has a low water content  . This is how body composition, or total body water (TBW) are measured: a current is passed through the body between electrodes attached to the skin, and the drop of voltage from one electrode to the other represents impedance  . By using predictive equations, ECF, ICF, and TBW may be calculated, from which, extra- cellular mass (ECM) and BCM are deduced  . As mentioned in the introduction, these are factors affect phase angle, which is calculated from reactance and resistance (see section 1.1.3).
II. M e t h o d o l o g y
2.1 Data Collection
2.1.1 Raw Data Collection
Data collection is done through BIA, using the bio- impedance analyser, BodystatÂ®1500MDD, on the whole experimental sample. Each individual was asked for personal details first; those which were used in this procedure were age, height, and weight. The details were entered into a database, and into the computer application, where the Bodystat device based calculations on these details. The individual was asked to lie down on a deckchair, and two electrodes from the device were connected by crocodile clips to each, the right hand and right foot. The device was set, and the BIA started, and took about 10 minutes each time to gather all necessary information.
Fig. 4  : Demonstration of electrodes attached during a BIA.
Phase angle is calculated and reproduced by the device, hence no further calculations were necessary. BMI was derived from dividing weight by the square of the height. This was done using a spreadsheet. The age is recorded manually in the database with the other data.
(see Appendix A and B for raw data collection, and Appendix F for an example of a BIA conducted throughout the investigation).
2.1.2 The Experimental Sample
The sample of people used in the investigation consists of 32 men at different ages (see Fig. 5 for age distribution) who regularly (at least three times a week) undergo rigorous physical activity. The sample is random, and simply of those who chose to have a BIA done for personal use.
Fig. 5: Pie chart displaying distribution of ages in the experimental sample (see Appendix A for data table).
The reason for limiting the sample down to men who exercise at least three times a week is to make the investigation as fair as possible.
Men and women have a different BMI and phase angle, as women naturally have more adipose tissue than men at any age  , therefore a mixed sample would not allow for useful results to be obtained. The male gender was chosen for the investigation as there were simply more men as the device was newly bought at that time.
The regular and frequent physical activity underwent by all men in the sample indicates good health and similar conditioning. This makes the sample more homogenous, where the variables, age and BMI may more efficiently be investigated.
All subjects agreed to have their measurements used in this investigation, as no sensitive personal data has been used.
2.2 Data Analysis
2.2.1 Graphical & Regression Analysis
The first step of analysing correlation of both sets of data involves plotting scatter grams and drawing a linear regression line, or line of best fit. The graphs are created using the Chart Wizard, and the regression lines drawn with help of the Trendline function of the spreadsheet application, Microsoft Office Excel. Graphing the data allows visualization of the distribution of points, and a trendline helps determine if a correlation is present, as well as distinguish whether it is positive or negative.
2.2.2 Statistical Analysis
Further analysis is statistical, and will conclude whether the correlation is significant or must be ignored. This will be done using the Spearman's Rank Correlation Coefficient, a statistical test designed specifically to test the strength of correlation between two data sets  . Because both the hypotheses state the direction of correlation, a one- tailed test will be used when testing the RÂ² value for significance.
There was a choice of several statistical tests for correlation: Chi- Squared Test, Pearson Product- Moment Correlation Coefficient, and Spearman's Rank Correlation Coefficient. The Chi- Squared Test was not chosen as the data was not at the categorical level, which would be necessary for it to be performed. Because it was not known if both data sets were normally distributed (which is also very unlikely), the Pearson Product- Moment Correlation Coefficient could not be used either. Spearman's Rank Correlation Coefficient is the most suitable statistical test as it works for data at the interval level which must not be normally distributed, and hence was the one to be further used in the investigation.
4.2 Interpretation of Statistical Analysis
4.2.1 Hypothesis I
The Spearman's Rank Correlation Coefficient for the data is -0.309. On the coefficient scale from -1.0 to 1.0, -0.309 is considered a weak negative correlation. This supports Hypothesis I, "as age increases, phase angle decreases". However, such a weak correlation between phase angle and age is not as substantial as previously anticipated, or that it may have occurred by chance. This speculation is elaborated by testing the |R2| value (0.309) for significance. It is bigger than its critical value at 95%, but smaller at 97.5% meaning less than 5, but more than 2.5 errors in 100 trials would occur. Consequently the correlation for the data collected is substantial enough to support the hypothesis, and it may be stated that there is a significant correlation between phase angle and age.
4.2.2 Hypothesis II
The R2 value for the data is -0.059. As a coefficient value of 0 represents no correlation, and on the coefficient scale from -1.0 to 1.0, -0.059 indicates a negligible correlation. As the R2 value is not exactly 0, the null hypothesis, "There is no significant correlation between phase angle and BMI", must be rejected. However when the |R2| is tested for significance, 0.059 is considerably smaller than the critical value at 95%, 0.309. Hence, Hypothesis II, "As BMI increases, phase angle decreases", must be rejected, and the null hypothesis accepted. There is, therefore, no significant correlation between phase angle and BMI from the data collected, and the coefficient illustrating negative correlation is too inconsequential and may have occurred by chance.
4.3 Validity of Experiment
The experiment may be considered a reliable inquiry of the correlation of phase angle with age and BMI. The data the experiment is based on is a primary source and was obtained through personal data collection, eliminating any inaccuracies or adjustments made, as it may be the case in secondary or official data. Because any analysis solely included obtained data, it may be declared that it is based on hard facts, instead of assumptions as it is the case when extrapolating or interpolating graphs, using moving averages, or predicting trends. Furthermore, all data is definitive, as it is composed of quantitative measurements, making the investigation much more consistent than if it were based on quantitative and virtual measurements, such as feelings or emotions.
These factors considerably strengthen the validity of this experiment.
The data on phase angle obtained through data collection is extremely reliable, as BodystatÂ®1500MDD is a professional piece of equipment, and returns accurate and consistent results.
Height and weight were not measured, but the individuals were asked about them. This is where errors might have occurred: people may not have been completely honest about these details. Height and weight are relatively sensitive pieces of information, and, as one knows from every- day experience, frequently adjusted to sound better. However, as the BIA was done for each person's own interest and at their request, providing false details would be their loss only. Additionally, everyone who chose to do a BIA knew the specialists conducting it, which demonstrates there was no need for false details and pretense. This suggests that information about height and weight was provided accurately.
A benefit of asking people about their weight is that they gave their normal average weight. If weight was measured before, it might not be as accurate, considering daily variations occur based on the amount of food and drink ingested, egested, the previous day or shortly preceding the BIA.
Considering these arguments, the collected data on height and weight is very reliable.
Details about age were definitely accurate, as age does not vary on daily basis. There was no reason for the individuals to not honestly answer, especially as men are not as sensitive about age as women tend to be. It must also be kept in mind that all measurements were done in privacy and kept private, which supports the assumption that people were honest when providing the details needed.
A source of error may have, however, been for how long the men have been the age they were at the BIA. Some might have only recently turned the age, and some might have celebrated their birthdays shortly subsequent to the BIA. This may have influenced the data and the correlation between phase angle and age; it may have been stronger or weaker. A weaker correlation would have affected the investigation, as the RÂ² value (0.309) was only vaguely larger than its critical value (0.306), and easily made it insignificant. A stronger correlation, or larger RÂ² value would have increased significance, may be to 97.5% or even 99% accuracy.
The minute significance and insignificant correlation Hypothesis I and Hypothesis II data, respectively, might also be justified by the varying occupations of the men. Even though all exercised at least three times a week, some were professional athletes, while some were ordinary managers. This greatly influenced data for both hypotheses, as professional sportsmen are physically not comparable to ordinary men who only exercise a fair amount. Their bodies will be much fitter and healthier for their age compared to those of individuals working in a sedative manner, in offices for example, meaning that phase angle could be higher for an older athlete than for a younger manager. Additionally, muscle tissue is denser than adipose tissue, hence it will weigh more  . This greatly affects Hypothesis II results, as an athlete with a lot of muscle will weigh more and have a higher BMI, even though he is very healthy, and have a high phase angle. But a non-athlete, may weigh less and have a lower BMI, but have more adipose tissue and not be as healthy, with a lower phase angle reading. This might have made the results insignificant, even though with the right data collection, the opposite might have occurred.
It must, however, also be kept in mind that a correlation does not assume a causal relationship. This means that even though Hypothesis I was supported by a significant correlation between phase angle and age, this correlation might not be a real relationship, and only occurred by chance. A decreasing phase angle with increasing age does not necessarily mean that they affected each other, or have an impact on each other. Based on logic and theoretical background, a correlation between the two variables should also be a causation. Nevertheless, this must be considered.
Data collection and processing might be more accurate and reliable if the units of 'age' would be different. Using months instead of years would eliminate the previously discussed inaccuracy, and make results of phase angle in relation to age more reliable. Furthermore, a larger experimental sample would give more space for correlations to show up, and eliminate experimental error. Also, narrowing down the sample to a certain group of men, based on their life experience with sports. Either, only men who recreationally exercise, or sportsmen and athletes who have done sport to a rigorous level for a major part of their life should be included in the experimental sample. This would reduce uncertainties originating in differenced in amount of lean and fat tissue of athletes and non-athletes. Also, instead of the BMI used as a measure of obesity, the Waist- To- Hip Ratio (WTH ratio) could be used, which might allow for more suitable data for the investigation to be collected.