Transcript Introduction to Biometrics

Three Types of Statistical
Analysis
Stickrath
Three Types
1. Standard Deviation
– Used for: examination of one set of data
– Essential question: How much variability is in my data?
– Teaching example: For a class of students, how much did their
individual scores vary from the class average?
2. T-test
– Used for: comparison of two sets of data
– Essential question: Which set of data is higher?
– Teaching example: One group of students used computers
everyday and a second group of students never used
computers, which group scored higher on the exam?
3. Chi-squared Analysis
– Used for: comparison of observed data to expected data
– Essential question: Does my observed data fit with my
expectations?
– Teaching example: I expected 15% of my students to score an
A, 25% of my students to score a B, 40% of my students to
score a C, 15% of my students to score a D, and 5% of my
student to score an F. Do the actual scores fit with my
expectations?
Standard Deviation
• An examination of the
variability of data
– a low standard
deviation indicates the
data is spread closely
around the mean value
– a high standard
deviation indicates a
wider spread around
the mean
• Which curve fits the
large schools? Small
schools?
Standard Deviation
• What does standard
deviation mean?
– Think of your
upcoming exam
– If I find a high standard
deviation among the
scores of my students
what does that mean?
– If I find a low standard
deviation among the
scores of my students
what does that mean?
Standard Deviation
• For example, if you wished to see if a red blood cell
count was normal, you could see whether it was within 2
SD of the mean of the population as a whole. Less than
5% of all red blood cell counts are more than 2 SD from
the mean, so if the count in question is more than 2 SD
from the mean, you might consider it to be abnormal.
T-test
• Used to compare the means of two distinct
groups
T-test
• Comparison must take the variability of the
data into account
• Otherwise you end up with the Gates
mistake
Chi-Squared Analysis
• Suppose I bet you $1,000 that I can
predict whether heads or tails will turn up
each time you flip a coin.
• The first time I say, “heads” you flip the
coin and it is heads.
• I got lucky
• The second time I say, “heads” you flip the
coin and it is heads
Chi-Squared Analysis
• The third time, fourth time, fifth time, sixth time,
seven time, eighth time, and so on I predict
heads. Each time you flip heads.
• At what point do you suspect that I am using a
two-headed coin?
• When do you stop chalking it up to chance and
accuse me of using a two-headed coin?
• You can use statistics to back up your
accusations and save yourself $1,000
Three Types
1. Standard Deviation
– Used for: examination of one set of data
– Essential question: How much variability is in my data?
– Teaching example: How many students scored an A, B, C, D, or
F on this exam
2. T-test
– Used for: comparison of two sets of data
– Essential question: Which set of data is higher?
– Teaching example: One group of students used computers
everyday and a second group of students never used
computers, which group scored higher on the exam?
3. Chi-squared Analysis
– Used for: comparison of observed data to expected data
– Essential question: Does my observed data fit with my
expectations?
– Teaching example: I expected 15% of my students to score an
A, 25% of my students to score a B, 40% of my students to
score a C, 15% of my students to score a D, and 5% of my
student to score an F. Do the actual scores fit with my
expectations?