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Lecture 7

# Lecture 7, Feb 26.docx

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Brock University

Child and Youth Studies

CHYS 3P15

Patricia Kirkpatrick

Winter

Description

3P15, Feb 26, Lecture 7 (skipped Week 6, that week was the midterm)
Chapter 10
Testing Hypotheses between a Sample and a Population
Learning Objectives
• This chapter will introduce ways to build and test hypotheses. Topics will include
• null and research hypotheses;
• hypothesis testing with one large sample and a population;
• hypothesis testing with one small sample and a population.
What’s a Hypothesis?
• A research or alternative hypothesis is a stated relationship between two or more
variables (independent variables (x) and dependent variables (y)).
• A null hypothesis is a stated non-relationship between two or more variables.
• Hypotheses must be mutually exclusive, exhaustive, and falsifiable.
• Hypotheses stating causal relationships should indicate direction of causality.
What’s a Hypothesis? (cont’d)
• For two interval/ratio or ordinal level measures: the greater the x (IV), the greater/less
the y (DV).
• Research example: Among Protestants, the greater the education, the greater the
income. Null: there is no relationship between education and income among Protestants.
What’s a Hypothesis? (cont’d)
• For one categorical and one continuous measure: category x1 (IV1) will have a
higher/lower score on y (DV) than category x2 (IV2).
• Research example: males will have higher educational attainment than females. Null:
males will not have higher educational attainment than females.
What’s a Hypothesis? (cont’d)
• For two categorical variables:
o For two categorical measures: category x1 will be more likely to have
characteristic y than category x2.
o Example: males are more likely to have a 4-year college degree than females.
Null form: males are not more likely to have a 4-year college degree than
females.
Errors in Testing Hypotheses
• Type I error: reject null hypothesis (0 ) even though it is true (mistakenly think you have
a relationship—“false knowledge”).
• Type II error: do not reject 0 even though it is false (mistakenly think you do not have a
relationship—“unrecognized relationship”).
Hypothesis Summary
• Null Hypothesis (H 0
o The difference is caused by random chance or sampling error.
o The H 0lways states there is “no significant difference.”
• Alternative hypothesis (H1)
o The difference is real.
o H always contradicts the H
1 0.
• One (and only one) of these explanations must be true. How do we choose?
The Sampling Distribution of Differences between Means as a Normal Distribution
• In repeated samples, the differences between sets of sample means assume a normal
distribution.
• The null hypothesis is that the mean of differences is zero. • If there are significant deviations (α=0.05, 0.01, 0.001, etc.) from the mean of
differences, we can reject the null hypothesis.
• The probability of observing mean differences by chance is unlikely.
One-Tailed and Two-Tailed Hypothesis Tests
• The type of difference you are looking for between your sample and your population will
guide you when choosing between a one-tailed or two-tailed test.
• If you are hypothesizing directionality, then you’re likely looking at a one-tailed test.
• If you’re not interested in directionality, then it’s probably a two-tailed test you’re after –
or unsure of directionality
o E.g., Brock students will do better than Brock students as a whole would be one-
tailed… if you are unsure what group will do better, unsure of directionality, two-
tailed
Single-Sam

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