Examples: Toasting time, Temperature settings, etc. 3 What is
random variation in the distribution of a population? POPULATION 1:
Little to no variation (e.g., product manufacturing) In engineering
situations such as this, we try to maintain quality control i.e.,
tight tolerance levels, high precision, low variability. But what
about a population of, say, people?
Slide 4
POPULATION 1: Little to no variation (e.g., product
manufacturing) Density What is random variation in the distribution
of a population? POPULATION 2: Little to no variation (e.g.,
clones) 4 Most individual values population mean value Examples:
Gender, Race, Age, Height, Drug Response (e.g., cholesterol level),
NOT REALISTIC!!! Very little variation about the mean!
Slide 5
POPULATION 2: Little to no variation (e.g., clones)POPULATION
3: Much variation (more realistic) Examples: Gender, Race, Age,
Height, Drug Response (e.g., cholesterol level), What is random
variation in the distribution of a population? Density 5 Much more
variation about the mean!
Slide 6
GLOBAL OPERATION DYNAMICS, INC. What are statistics, and how
can they be applied to real issues? Example: Suppose a certain
company insists that it complies with gender equality regulations
among its employee population, i.e., approx. 50% male and 50%
female. 6 To test this claim, let us select a random sample of n =
100 employees, and count X = the number of males. (If the claim is
true, then we expect X 50.) etc. Sample size n partially depends on
the power of the test, i.e., the desired probability of correctly
rejecting a false null hypothesis ( 80%). The larger the n, the
higher the power.
Slide 7
GLOBAL OPERATION DYNAMICS, INC. What are statistics, and how
can they be applied to real issues? Example: Suppose a certain
company insists that it complies with gender equality regulations
among its employee population, i.e., approx. 50% male and 50%
female. 7 To test this claim, let us select a random sample of n =
100 employees, and count X = the number of males. (If the claim is
true, then we expect X 50.) etc. X = 64 males (+ 36 females)
Questions: If the claim is true, how likely is this experimental
result? (p-value) Could the difference (14 males) be due to random
chance variation, or is it statistically significant?
Slide 8
The experiment in this problem can be modeled by a random
sequence of n = 100 independent coin tosses (Heads = Male, Tails =
Female). It can be mathematically proved that, if the coin is fair
(unbiased), then in 100 tosses: probability of obtaining at least 0
Heads away from 50 is = 1.0000 certainty probability of obtaining
at least 1 Head away from 50 is = 0.9204 probability of obtaining
at least 2 Heads away from 50 is = 0.7644 probability of obtaining
at least 3 Heads away from 50 is = 0.6173 probability of obtaining
at least 4 Heads away from 50 is = 0.4841 probability of obtaining
at least 5 Heads away from 50 is = 0.3682 probability of obtaining
at least 6 Heads away from 50 is = 0.2713 probability of obtaining
at least 7 Heads away from 50 is = 0.1933 probability of obtaining
at least 8 Heads away from 50 is = 0.1332 probability of obtaining
at least 9 Heads away from 50 is = 0.0886 probability of obtaining
at least 10 Heads away from 50 is = 0.0569 probability of obtaining
at least 11 Heads away from 50 is = 0.0352 probability of obtaining
at least 12 Heads away from 50 is = 0.0210 probability of obtaining
at least 13 Heads away from 50 is = 0.0120 probability of obtaining
at least 14 Heads away from 50 is = 0.0066 etc. 0 8 The =.05 cutoff
is called the significance level. 0.0066 is called the p-value of
the sample. Because our p-value (.0066) is less than the
significance level (.05), our data suggest that the coin is indeed
biased, in favor of Heads. Likewise, our evidence suggests that
employee gender in this company is biased, in favor of Males.......
..from 0 to 100 Heads..
Slide 9
GLOBAL OPERATION DYNAMICS, INC. What are statistics, and how
can they be applied to real issues? Example: Suppose a certain
company insists that it complies with gender equality regulations
among its employee population, i.e., approx. 50% male and 50%
female. 9 To test this claim, let us select a random sample of n =
100 employees, and count X = the number of males. (If the claim is
true, then we expect X 50.) etc. X = 64 males (+ 36 females)
Questions: If the claim is true, how likely is this experimental
result? (p-value) Could the difference (14 males) be due to random
chance variation, or is it statistically significant? HYPOTHESIS
EXPERIMENT OBSERVATIONS
Slide 10
The experiment in this problem can be modeled by a random
sequence of n = 100 independent coin tosses (Heads = Male, Tails =
Female). It can be mathematically proved that, if the coin is fair
(unbiased), then in 100 tosses: probability of obtaining at least 0
Heads away from 50 is = 1.0000 certainty probability of obtaining
at least 1 Head away from 50 is = 0.9204 probability of obtaining
at least 2 Heads away from 50 is = 0.7644 probability of obtaining
at least 3 Heads away from 50 is = 0.6173 probability of obtaining
at least 4 Heads away from 50 is = 0.4841 probability of obtaining
at least 5 Heads away from 50 is = 0.3682 probability of obtaining
at least 6 Heads away from 50 is = 0.2713 probability of obtaining
at least 7 Heads away from 50 is = 0.1933 probability of obtaining
at least 8 Heads away from 50 is = 0.1332 probability of obtaining
at least 9 Heads away from 50 is = 0.0886 probability of obtaining
at least 10 Heads away from 50 is = 0.0569 probability of obtaining
at least 11 Heads away from 50 is = 0.0352 probability of obtaining
at least 12 Heads away from 50 is = 0.0210 probability of obtaining
at least 13 Heads away from 50 is = 0.0120 probability of obtaining
at least 14 Heads away from 50 is = 0.0066 etc. 0 10 The =.05
cutoff is called the significance level. 0.0066 is called the
p-value of the sample. Because our p-value (.0066) is less than the
significance level (.05), our data suggest that the coin is indeed
biased, in favor of Heads. Likewise, our evidence suggests that
employee gender in this company is biased, in favor of Males.......
ANALYSIS CONCLUSION
Slide 11
Classical Scientific Method Hypothesis Define the study
population... Hypothesis Define the study population... Whats the
question? Whats the question? Experiment Designed to test
hypothesis Experiment Designed to test hypothesis Observations
Collect sample measurements Observations Collect sample
measurements Analysis Do the data formally tend to support or
refute the hypothesis, and with what strength? (Lots of juicy
formulas...) Analysis Do the data formally tend to support or
refute the hypothesis, and with what strength? (Lots of juicy
formulas...) Conclusion Reject or retain hypothesis; is the result
statistically significant? Conclusion Reject or retain hypothesis;
is the result statistically significant? Interpretation Translate
findings in context! Interpretation Translate findings in context!
Statistics is implemented in each step of the classical scientific
method! 11