Eye Color 1 2 3 4 5 1 143 30 58 15 12 7.67540 0.41799 -5.88169 -0.63925 -0.31451 2 90 45 215 30 20 -2.57141 0.29019 1.72235 0.49189 -0.08246 3 28 15 190 10 10 -5.39425 -2.34780 6.28154 -1.76376 -0.80382 4 30 15 10 10 5 2.06116 2.71589 -4.05540 2.37402 0.75993 5 5 10 5 15 5 5 -0.52195 0.33262 -0.94192 1.36326 2.07578 – Expected)² Σ (Observed Expected = 223.6 P-value <0.00001 Hair Color
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Eye and hair color A survey of 1021 school-age
children was conducted by randomly selecting children
from several large urban elementary schools. Two of the
questions concerned eye and hair color. In the survey, the
following codes were used:The Statistics students analyzing the data were asked to
study the relationship between eye and hair color.
a) One group of students produced the output shown
below. What kind of analysis is this? What are the
null and alternative hypotheses? Is the analysis
appropriate? If so, summarize the findings, being
sure to include any assumptions you’ve made and/or
limitations to the analysis. If it’s not an appropriate
analysis, state explicitly why not.
s = 1.112 with 1021 - 2 = 1019 degrees of freedom
Variable Coefficient SE(Coeff) t-ratio P-value
Intercept 1.99541 0.08346 23.9 ...0.0001
Hair 0.211809 0.03372 0.28 ...0.0001
b) A second group of students used the same data to
plays counts and standardized residuals in each cell.
If so, summarize the findings, being sure to include
any assumptions you’ve made and/or limitations to
the analysis. If it’s not an appropriate analysis, state
explicitly why not.
1 = Blond 1 = Blue
2 = Brown 2 = Green
3 = Black 3 = Brown
4 = Red 4 = Grey
5 = Other 5 = Other
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