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

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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%

BIVARIATE LINEAR REGRESSION

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.

RECOMMEND STUDYING ASSIGNMENTS. PURPOSE OF FINAL TEST: all of the stuff we

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

formulas.

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.

Presentation

NYC

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