1. Probability in Statistics
Chapter 6
Probability in Statistics

2. The Role of Probability in Statistics : Statistical Significance
A set of measurements or observations in a statistical study is said to be statistically significant if it is unlikely to have occurred by chance
Toss of a fair coin
50-50
30-70
20-80
GED111/CDS111 Statistics in Modern Society

3. From Sample to Population
Opinion poll for the support to a political party
1st poll 49%
2nd poll 51%
In contrast
1st poll 75%
2nd poll 30%
GED111/CDS111 Statistics in Modern Society

4. Quantifying Statistical Significance
If the probability of an observed difference occurring by chance is 0.05 (or 1 in 20) or less, the difference is statistically significant at the 0.05 level
If the probability of an observed difference occurring by chance is 0.01 (or 1 in 100) or less, the difference is statistically significant at the 0.01 level
Statistical significance at almost any level is no guarantee that an effect or difference is present
GED111/CDS111 Statistics in Modern Society

5. GED111/CDS111 Statistics in Modern Society
Time to think
Suppose an experiment finds that people taking a new herbal remedy get fewer colds than people taking a placebo, and the results are statistically significant at the 0.01 level, Has the experiment proven that the herbal remedy works? Explain.
GED111/CDS111 Statistics in Modern Society

6. GED111/CDS111 Statistics in Modern Society
Exercise
Statistical Significance
Q1-4, p236
Dose It Make Sense??
Q5-8, p236
Application
Q22, 23 p237
GED111/CDS111 Statistics in Modern Society

7. GED111/CDS111 Statistics in Modern Society
Basic of Probability
Outcomes
The most basic possible results of observations or experiments
Event
A collection of one or more outcomes that share a property of interest
Expressing Probability
The probability of an event, expressed as P(event), is always between 0 and 1 inclusive.
GED111/CDS111 Statistics in Modern Society

8. Theoretical Probabilities
Count the total number of possible outcomes
Among all possible outcomes, count the number of ways the event of interest, A, can occur.
P(A)
no. of ways A can occur/total no. of outcomes
GED111/CDS111 Statistics in Modern Society

9. Relative Frequency Probabilities
Repeat or observe a process many times and count the number of times the event of interest, A, occurs.
P(A)
No. of times A occurred/total no. of observations
GED111/CDS111 Statistics in Modern Society

10. Subjective Probabilities
Estimate probability using experience, judgment, or intuition
GED111/CDS111 Statistics in Modern Society

11. GED111/CDS111 Statistics in Modern Society
Complementary Events
Negation, Not A
Probability Distributions
Represents the probabilities of all possible events
Tossing a coin 3 times, noting heads
GED111/CDS111 Statistics in Modern Society

12. The law of Large Numbers
Applies to a process for which the probability of an event A is P(A) and the results of repeated trials are independent.
If the process is repeated through many trials, the proportion of the trials in which event A occurs will be close to the probability P(A). The larger the number of trials, the closer the proportion should be to P(A).
GED111/CDS111 Statistics in Modern Society

13. GED111/CDS111 Statistics in Modern Society
Gambler’s Fallacy
The mistaken belief that a streak of bad luck makes a person “due” for a streak of good luck
GED111/CDS111 Statistics in Modern Society

14. GED111/CDS111 Statistics in Modern Society
Exercise
Does It Make Sense??
Q5-8, p
GED111/CDS111 Statistics in Modern Society

15. Focus on Social Science
Are Lotteries Fair? pp
GED111/CDS111 Statistics in Modern Society