POL242Y1 Lecture Notes - Null Hypothesis, Point Estimation, Explained Variation

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21 Nov 2012
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Week 11: POL 242 Review-Testing Hypotheses
Testing Hypotheses Alternative Approach
Take a point estimate and then taking the point estimate into a standardized value.
Keep your probabilbility value and take a point estimate into a standized value (for
alternative value)
Compare prob. Values rather than T scores. (it makes more sense)
1.96 makes more sense than 0.04.
Example: Suppose that you want to test the hypothesis that the proportion of the public who
favors some public policy is not equal to 50%. You draw a sample of 1200 Canadians and find
that 53.2% are in favor. Please test this hypothesis using the alternative approach.
Solution: Compare TS and CV. Our P value is less than our alpha value. We reject our null
hypothesis. Our substantive conclusion…
Bi-variate Regression
We use our line of best fit to estimate the type of relationship.
Generally, we use the line that minimized the sume of the square of the residuals
What is a residual? Minimize the distance from the points to the line of best fit.
Regression and Strength
We try to estimate the size of slope coefficient. Essentially, the slop coefficient, how
much change is made to DV when change is made to IV.
Our estimated slope is very small, T value is small and P value is really large.
Regression and inference
Can we generalize any possible relationship that we can find between IV and DV?
Can we infer that there is a true relationship between the population?
When T scores are small, (we are comparing T score and to standized value of 1.96 and -
1.96) . The T score is 8 which is far beyond the standized value of 1.96.
Therefore we reject hypothesized value.
Compare P value to alpha.
All we have to do is TO ALWAYS COMPARE P VALUE TO OUR ALPHA VALUE. This is much
easier to determine whether to reject or accept our null hypothesis. The number -8.202
is much bigger than -0.5.
Regression and goodness of fiti (besides looking at strength of relationship, we often have to
look at the overall goodness of fit)
Estimated line of best fit.
How accurate is our explanation of the dependent value based upon info on our
independent variable?
o In order to do this, we have to look and calculate for coefficient of determination
or R2
R squared= amount of explained variation/ total amount of variation.
Barack Obama average 46.8% job approval during his 14th quarter in office, a slight
improvement from 45.9% in quarter 13.
o What is the problem with this statement in statistics? (first sentence)
Improved from 45.9% to 46.8%
Margin of error? Confidence interval
Think about confidence interval and margin of error:
What is the confidence interval on a sample size of 1000?
Confidence interval: 4-5%
Independent variable and its effect on dependent variables.
Which of these two independent variables seem to have greater effect on citizens’
willingness to support this form of public policy? Why did you draw the conclusion that
you did?
o Income and political ideology
o Political ideology has a steeper slope. And therefore greater effect on citizens’
willingness to support form of public policy.
Final test
1 hour
60 points
20 multiple choice questions (1 min per question)
4 Short answer questions
Up until July 24th 2012. (multivariate regression)
Beginning of class.
learnt in assignments is to know it.
Assignments > lecture (assignments is your backbone)
First 20 multiple choice-> study quizzes
Example: take a look at this output. What does it say substantively?
o Only thing we are give are the standard deviation formula but recognize all
o Understand how to find them in M/C as well.
Continuation of Lesson
Regression diagnostics
No perfect relationship amongst the variables included In the model
P value? What does it mean? we would reject the null hypothesis.