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Lecture 7

Lecture 7, Feb 26.docx

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Brock University
Child and Youth Studies
Patricia Kirkpatrick

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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