Statistics for Life Math 1462 Assessing Normality Lab 6

1. 1
Assessing Normality Lab 6
Laura Sandoval
Texas A&M University-Corpus Christi
Statistics for Life Math-1442-W01
March 21, 2015
Assessing Normality Lab 6
Summary
This lab identifies normality and considers the various methods used for normalizing transformations of data.
The random sample was created using the JMP Statistical Software, a subset of 150 observations form the Small
Town.xls file, and then an analysis of distribution for each continuous variable was constructed and displayed
with a histogram and a normal quantile plot graph. Using these graphs an analysis for approximately normal
distribution were determined by visual inspection of the histogram to see if the data was roughly bell-shaped,
identifying any outliners, and then using the normal quantile plot to conclude if the data distribution was
normal. The normal quantile plot is used if the histogram is basically symmetric and number of outliers is 0 or
1. The criteria for a normal distribution of a population is normal if the pattern of the points is reasonably close
to a straight line and the points do not show some systematic pattern that is not a straight-line pattern. For a
distribution that has not normal criteria the points do not lie reasonably close to a straight- line and the points
show some systematic pattern that is not a straight-line pattern. The Q-Q plot follows approximately a straight
line pattern and the dots are located within the red discontinuous curves. There is no presence of an obvious
pattern on the Q-Q plot, therefore we can accept normality of the sampling distribution of the means as
predicted by the central limit theorem.

2. 2
The continuous variables are labeled as Figures 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7 and consist of a histogram and a
normal quantile plot which graphs the points of original data as the x value and the y value as the corresponding
“z” score. The criteria for determining a normality was used with the findings summarized, label as Table 1.1,
and show each numeric continuous variable, if the data was normal or not normal distribution, and if any
transformation was applied for achieving normality. Using visual analysis Age, Weight, Height, Sys_BP,
Salary, and Charity were non-normal and a transformation was used to produce results with a normal
distribution. The mathematical functions such as; logarithmic function, square root, or inverse or reciprocal
transformation enable recalculation of the data for results that are normally distributed. Variable transformation
allows analysis of data that before mathematical manipulations was not normally distributed, and converts the
data into a new set of scores which are useable for analysis. The transformation used for each non-normal
continuous variable were as follows; Age and Salary used Johnson SU Probability, Height used Generalized
Log Probability, SYS_BP used Gamma Quantile and Charity used Weibull 2 Parameters Estimates.
The variable with a normal distribution is shown at Figure 1.4 BMI, the criteria for determining
normality was met by the histogram showing a bell-shaped curve and having less than 1 outliner, the Q-Q plot
also meets these requirements with the data plots for the population distribution forming a pattern that is
reasonably close to a straight line and within the dotted red curves.
Using BMI as my normal distribution with a mean of 25.51 and a standard deviation of 3.02, a random
normal distribution was simulated for 100 observations. Using the JMP software this formula was used
(Random Normal (25.338, 3.1362907)), and using the formulas 𝑥1 = 𝑥̅ − 1.5𝑠 and 𝑥2 = 𝑥̅ + 1.2𝑠 for
calculation of probability that one observation is between these standard deviations and then dividing the total
number of occurrences by the number of observations (100). These results were in agreement and the numbers
agree when comparing between the true and simulation probability. The true BMI was calculated for P(-
1.5<z<1.2) =.83 and the simulated BMI was P(-1.5<z<1.2) =.818, the true probability and the simulated
probability were close in value.

3. 3
Figure 1.1
AGE
Figure 1.2
HEIGHT
Figure 1.3
WEIGHT
Figure 1.4
BMI

4. 4
Figure 1.5
SYS_BP
Figure 1.6
SALARY
Figure 1.7
CHARITY

5. 5
Table 1.1
Variable
Normal or
Non
Normal
Transformation
Age Non normal Johnson SU Probability
Weight Normal None
Height Non normal General Log Probability
BMI Normal None
SYS_BP Non normal Gamma Quantile
Salary Non normal Johnson SU Probability
Charity Non normal
Weibull
2 Parameter Estimates
Figure 2.1
Diagnostic Plot
Figure 2.3
Diagnostic Plot

6. 6
Figure 2.2
Diagnostic Plot
Figure 2.4
Diagnostic Plot
Figure 2.5
Diagnostic Plot