Topics for Today
Review and Midterm Prep
Stat203
Fall2011 – Week 12, Lecture 1
Page 1 of 21
Topics:
Hypothesis tests
For means
For Proportions
For Distributions
Correlations
Correlation – interpretation
Regression – construction and interpretation
For all hypothesis tests, Correlation, and Regression,
be able to interpret SPSS output!
Stat203
Fall2011 – Week 12, Lecture 1
Page 2 of 21
For all Hypothesis Tests
Construction of hypotheses:
- identify the parameter, µ, p, f, or ρ (rho = correlation)
- identify 1 or 2-sided hypotheses
- based the above, you should then know how to look up
the p-value, or at least determine whether it is greater or
less than .
- with a p-value and , you should be able to determine
whether we reject or fail to reject the null hypothesis
(W8L2, pg 10)
Stat203
Fall2011 – Week 12, Lecture 1
Page 3 of 21
Understand and be able to interpret:
p-value
on Assignment 3, you had to interpret the p-value in the
context of a particular problem … ensure you
understand this.

Not the value of  (ie: 0.05), and not that it ‘is compared
to the p-value’ … actually understand what it
represents.
Stat203
Fall2011 – Week 12, Lecture 1
Page 4 of 21
Finding p-values
Know how to look things up in Table A, Table C and Table
E.
Remember:
- 2-sided hypotheses the p-value is the area in
__________
- 1-sided hypotheses with alternative hypothesis >, then
the p-value is the __________________1-sided
hypotheses with alternative hypothesis <, then the pvalue is the ________________
Stat203
Fall2011 – Week 12, Lecture 1
Page 5 of 21
Hypothesis Tests for Means
If the question involves variables which are ________ or
_____, then we are doing a test for means.
There are 4 tests for means we have learned … all are ttests (ie: look up p-value in the t-table).
1. 1-sample t-test
2. 2-sample t-test assuming _____ standard deviation
3. 2- sample t-test assuming _______ standard deviation
4. ______ t-test (_______ t-test)
Stat203
Fall2011 – Week 12, Lecture 1
Page 6 of 21
1 – sample t-test
Prime Example: “Is the DRP in our school district higher
than 32?”  ____
The null and alternative always involve some ‘________’
value for the mean (like 32 in the DRP example).
Ensure that you’ve correctly identified the research
hypothesis and can write a statistical alternative
hypothesis (ie: using the parameters) that’s consistent with
the research hypothesis.
Degrees of freedom = _____.
Know how to use both pages of Table C!
Stat203
Fall2011 – Week 12, Lecture 1
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How do you identify a ________ test?
- The research hypothesis (as in the DRP example)
mentions only _________ of people, and
____________.
- The problem only provides a single ____, single
___________, and single __________________
Be able to calculate the test statistic (t) using the sample
size, and sample mean.
Stat203
Fall2011 – Week 12, Lecture 1
Page 8 of 21
2 – sample t-test
Prime Example: “Is the # of BFFs different for teenaged
boys and girls?”  ____
The null and alternative compare means for two groups (ie:
comparative test rather than involving a proposed value of
the mean)
Remember that SPSS gives ONLY the p-value for the 2sided hypothesis … you should be able to calculate pvalues by hand using the
Degrees of freedom = ____________
Know how to use both pages of Table C!
Stat203
Fall2011 – Week 12, Lecture 1
Page 9 of 21
From the SPSS output,
- know how to identify the test – statistic and p-value
- know whether to use the ___ for equal variances or
unequal variance _____________________________
Stat203
Fall2011 – Week 12, Lecture 1
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Paired t-test
Prime Example, Paired t-test: “Do the same city blocks
have a different number of 911 calls before and after
instituting a neighbourhood watch?”  ____
Identify the individuals, note whether each individual is
measured twice or once. If individuals are measured more
than once, samples are _________.
Understand how to interpret the SPSS output.
Degrees of freedom = _____ … where n is the number of
individuals, or pairs of individuals.
Stat203
Fall2011 – Week 12, Lecture 1
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Prime Example, Matched t-test: “Is the remission time for
individuals receiving Drug A different than remission times
for age/gender/ethnicity/geographically matched individuals
receiving Drug B?”  ____
Samples are ___________ if they are selected randomly
from their respective populations. Samples are _________ if
the sample from one population depends in any way on the
members of the sample from the other population.
Stat203
Fall2011 – Week 12, Lecture 1
Page 12 of 21
1 – sample z-test for Proportions
Prime example: “Is the proportion of people experiencing
an adverse symptom < 10%?”  ____
As with tests of means, a 1-sample test involves a single
group of individuals with a single _______ or _______
variable.
This test statistic is calculated by hand – NO SPSS output
for tests of proportions!
NOTE: the test statistic is normally distributed! Look up the
p-value in Table A!
Stat203
Fall2011 – Week 12, Lecture 1
Page 13 of 21
2 – sample z-test for Proportions
Prime example: “Are the proportion of men supporting
more strict gun laws different from the proportion of
women?”  ____
As with the 1-sample test, we did this by hand and looked
up the test statistic in Table A.
Remember, proportion is the same as percent!
This type of question is identified by comparing
___________ or ________ in two
_____________________.
Stat203
Fall2011 – Week 12, Lecture 1
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Chi-Square test for Distributions
Prime example: “Are dogs colour blind?” (do dogs show a
colour preference among food dishes?)  ____
Look for a _______ or _______ variable with _______
categories and a question that is related to whether all
categories are equally likely.
We did this test statistic by hand!
Compare the test statistic to the values in to 0.05 or 0.01
column in Table E.
Chi-square test statistics are always positive!
Stat203
Fall2011 – Week 12, Lecture 1
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t-test for Significant Correlation
Prime example: “Is there a significant correlation between
Alcohol Consumption from Wine and Deaths due to Heart
Disease?”  _____
The goal will be to identify a ‘____________’.
yes … another t-test. SPSS output shows significance level
… this test is ONLY 2-sided. We don’t do _______ tests of
correlation.
Remember that a non-significant correlation doesn’t
mean that the variables aren’t related, it just means
they’re not linearly related!
Stat203
Fall2011 – Week 12, Lecture 1
Page 16 of 21
Interpreting Correlation
Understand what a large ________ or ________
correlation implies about the relationship between two
variables.
Ensure you can guess the correlation from a scatterplot.
Understand the relationship between correlation and the
slope from the linear regression.
Stat203
Fall2011 – Week 12, Lecture 1
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Linear Regression
Know how to write the ___________________ from the
SPSS output.
Understand interpretation of the _____ and _________.
Prime Examples:
1. Alcohol and Heart Disease
2. Poverty and Teen Pregnancy
Interpret R2.
Be able to _______ a Y from a given value of X.
Stat203
Fall2011 – Week 12, Lecture 1
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For both Correlation and Regression
Understand the difference between an ___________ and a
______ relationship.
Does poverty _____ teenage pregnancy, or is there
something __________ that links both of these variables?
Stat203
Fall2011 – Week 12, Lecture 1
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INTERPRETATION IS KEY
Turn a statistical hypothesis test into a sensible sentence in
the _______ of the problem.
Interpret the slope and intercept of a regression model in
terms of the _________.
Stat203
Fall2011 – Week 12, Lecture 1
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Midterm Format
Similar to in-class examples
15% of the midterm will be tricky multiple-choice questions
Remainder of the midterm will be short answer or single
sentence answers.
Review Assignments and in-class examples!
Stat203
Fall2011 – Week 12, Lecture 1
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