POSC300 Lecture Notes - Lecture 15: Null Hypothesis, Confidence Interval, Statistic
3 Dec 2018
School
Department
Course
Professor
Hypothesis Testing
● What are we doing?
● “On a scale of 0-100, How do you feel towards illegal immigrants?”
○ •Democrats gave average rating of 50
○ •Republicans gave average rating of 25
● We conclude that Democrats are more favorably disposed to illegal immigrants.
○ But how do we know for sure?
○ Question 1 - How do we know these estimates (50, 25) are an accurate
representation of the population?
○ Question 2 - How do we know this difference wasn’t just random chance or a
function of sampling error?
● Statistical Inference
● Point/Interval Estimates (Question 1)
● Estimate unknown population parameters from known sample statistics.
● We develop a “confidence interval” around these estimates which tells us how
confident we are in their accuracy.
○ i.e. We are 95% sure that Democrats in the population also give a rating
of 50 to illegal immigrants
● Hypothesis Testing (Question 2)
○ Statistically testing whether there is a real difference between our
estimates
○ i.e. We are confident that Democrats and Republicans in the population
have different opinions on illegal immigrants
○ Research Hypothesis
■ This is the hypothesis you have been developing.
■ It is a precise statement of the relationship between two variables
(IV and DV)
■ You generally want to indicate the direction of this relationship.
● i.e. Democrats have a higher evaluation of illegal
immigrants than Republicans (H1: D > R)
● But – technically – indicating a direction for the relationship
is not required
● i.e. Democrats have a different evaluation of illegal
immigrants than Republicans (H2: D ≠ R)
● Null Hypothesis
○ Falsified version of your hypothesis
○ It is also a precise statement about the relationship between two variables
(IV and DV)
○ Generally – it is the hypothesis that there is no effect or no difference
(zero = null) i.e. There is no difference in evaluation of illegal immigrants
between Democrats and Republicans. (H0 : D = R)
● Tricky Interpretation
○ Goal is to reject the Null Hypothesis and accept the Research Hypothesis.
○ These are 2 distinct evaluations
■ Just because we reject the Null Hypothesis doesn’t mean that our
Research Hypothesis is true
● i.e. There may be a significant difference between D and R
(reject null hypothesis) but D is not significantly greater
than R (reject research hypothesis)
■ Two Types of Inference Errors
● Type I Error
○ Rejecting a TRUE Null Hypothesis
■ i.e. In the real world – Republicans and
Democrats have the same evaluation of
illegal immigrants (H0: D = R). But we
have falsely concluded that this is not true.
● i.e. We have incorrectly concluded
that Democrats have a more
favorable opinion than Republicans.
● Type II Error
○ Accepting a FALSE Null Hypothesis
○ Better to think of it as incorrectly rejecting your
○ Research Hypothesis.
■ i.e. In the real world – Democrats have
higher evaluations of illegal immigrants than
■ Republicans (H1: D > R). But we have
falsely concluded that this is not true.
● i.e. We have incorrectly concluded
that they have the same opinion of
illegal immigrants
● Testing for Inference Errors
○ We always focus on Type I Errors
■ That we have rejected a True Null Hypothesis
■ i.e. That we have incorrectly concluded there to be a difference
between D and R.
■ “Statistical Significance” refers to the probability that the Null
Hypothesis has been rejected incorrectly.
● i.e. It refers to the probability that D = R
● i.e. It refers to the probability that our results are wrong
● Levels of Significance
○ Three Levels of Significance
■ (.05) (.01) (.001)
● Probability (p) that we have made a Type I Error
○ i.e. The difference between D and R is significant at
.05 level.
○ i.e. We have a 5% chance of incorrectly rejecting
the null hypothesis. Or that there is only a 5%
chance that D = R
● One or Two Tailed Test
Document Summary
On a scale of 0-100, how do you feel towards illegal immigrants? : democrats gave average rating of 50, republicans gave average rating of 25. We conclude that democrats are more favorably disposed to illegal immigrants. Estimate unknown population parameters from known sample statistics. We develop a confidence interval around these estimates which tells us how confident we are in their accuracy. i. e. we are 95% sure that democrats in the population also give a rating of 50 to illegal immigrants. Statistically testing whether there is a real difference between our estimates i. e. we are confident that democrats and republicans in the population have different opinions on illegal immigrants. This is the hypothesis you have been developing. It is a precise statement of the relationship between two variables (iv and dv) You generally want to indicate the direction of this relationship. i. e. democrats have a higher evaluation of illegal immigrants than republicans (h1: d > r)
