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Test 3 Review.docx

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PSYC 3000
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Inferences about a Population Proportion: * Has the proportion in a group changed over time - Relationship; with confidence interval: approximate hypothesis test using interval; see if p Is in O the value - CI: Two sided: correspond to Two sided Tests Null: comes from context of problem; no effect P value: conditional probability, tells us probability of getting result, given, the null is true - If the p is low: the null must go - It’s the probability of the data; not the null 2 - Big P: Fail to reject the null Statically significant - > Set Alpha level: a: common levels: 0.01 0.05 0.1 (when two sided a/2) Alpha level = significance level “Reject the null at the 5% significant level” Hypothesis testing/confidence go hand in hand; - 95% confidence interval: Alpha 5% - Confidence interval 99%: A: 1% Conditions: - Independence assumption - Randomization condition - 10% Condition - Success Failure condition Making Errors - Type 1: The null hypothesis is true; we reject it (false positive)  Occurs at a level of a: 5% 10% 1% : unusual sample  Probability of type 1: a  Type II: the null is false; but we fail to reject it (guilty person free) False negative  Probability of Type II: B; decrease this by increasing a (but then you have more chance of type I) - Power: test’s ability to detect a false hypothesis  Jurors ability to properly convict  High power; we have looked deep enough  Power: 1 – B (type II) Effect size: the distance between the null: P anO the P - Ask ourselves how big of a difference would matter (flip a coin 50% maybe 60% would mean better than chance) - - Bottom has larger effect size: S tandardized mean difference between the two groups - cohens D: measure of effect size: diff mean sample – mean pop/SD - small D: 0.2 – 0.5 - Medium D: 0.5- 0.80 - Large 0.8 + We can lower alpha to lower chance of Type 1 error: 0.05 - > 0.01 - This increases B: chance for type II error - Therefore this lowers power - Bigger the effect size; more power; two models further apart; less overlap; less likely to make type II error - Increase sample size: Increasing sample size; increases power and decreases probability of Type 1 and type II  Tests with greater likely hood of Type I error: have more power less chance of Type II error Can increase: alpha -> get higher power; but also more chance of Type II Comparing Two Proportions (Two Proportion Z test) - We want to make inference between the difference two group proportions Model: Sampling distribution model for the difference between two proportions Sampling distribution modeled by - normal model - Mean:   p  1 2 - Standard Deviation: SD  1p ˆ2 p1 1 p2 2 n1 n 2 Assumptions and Conditions: - Indpendance assumption - Randomization - 10% condition - Independent Groups Assumption - Success/failure condition How do we test: - Test for no difference - H 0 p1– p 2 0 - What is this null value: P pooled - Then check CI see if it is a plausible value Inferences about means: Quantitate Means - one sample T-test (week 12 for example) - Based on: Student’s T model * if the parent population from which we are sampling is normally distributed: then the random variable has the student’s t distribution with (n-1) degrees of freedom Model: sampling distribution of the mean: centered at the population mean: u - law of large numbers; larger the samples size; closer we get to actual value: closer approaches normal distribution: will look more bell shaped (histogram) -  Now using Student’s T model: - t distribution: lower height; wider spread Objective: to determine whether the mean of sample differs from known/estimated population mean  Data Requirements: One sample/DV (quantative/numerical/Continuous) - As sample size increases the sampling distribution of sample means approaches normal distribution - CLT: sampling distribution of the mean is centered at population mean, μ Conditions: - Independence - Randomization - 10% Condition - Nearly Normal Condition: Make histogram/normal probability Plot  If data is normally distributed; data points will be close to the diagonal line - Large enough sample condition: (5-10) is enough for normal, if skewed minimum 30+ -> check the histogram -> Check the normal probability Plot -> Check Shapiro Wilk: If the P value of the Shapiro wilk test is greater than: 0.01, 0.05, 0.10: it is normal - if it is below these values: The data significantly deviate from normal distribution The Independent Sample’s T Test (week 12) - based on: sampling distribution for the difference between two means - We can first look visually: check out the box plots; see if means are different - See some difference; go to do inferential statistics - Based on Student’s T Model - Objective: Test whether the means of two groups differ significantly on some DV Requirements: - One IV: 2 separate groups - One quantitative DV - 0 not included in CI: reject the null * unlike proportions test; we don’t usually pool here Conditions: - Independent Group Assumption: Two groups must be independent one another - Nearly Normal Condition Check for both groups: Violation either one; violates  Check Separately - Independence assumption - Randomization Condition Parameter of interest: Difference between the two means Dependent Sample T test - Objective: Two test whether the means of two related groups differ significantly on some dependent variables Requirements: - One IV: Two related groups - One quantitative DV  just a one sample t test for the mean of the pairwise differences  once we know data is paired: we examine Pairwise differences  It’s the differences we care about; ignore the original 2 sets Conditions: - Paired Data assumption:  The data are paired - Nearly Normal condition:  Check histogram/normal probability plot of the differences Paired Samples And Blocks - > Scores in one sample related to scores in other sample: samples are dependent - Dependent samples: matched/paired samples - Example #1: Repeated Measures Design: Each Person tested more than once - means from each group of scores; from same sample (ex: focus in light and dark conditions) Example #2: Matched Subject Design - Matched subject design:  Separate groups: however subject in one group matched with an equivalent from another (match based on gpa; two groups; for IQ test)  Because again it is the difference we care about; we treat them as if they were the data Two sample problem becomes one sample problem d 0 tn1 SE d  sd SE d  n - Standard error for the mean applied to the differences Conditions mean: statistic follows: student’s t model: n-1 degrees of freedom Comparing Counts: Inferences About Categorical Data (Chapter 26) Goodness of fit - one group/ one categorical variable - is the observed distribution consistent with a theoretical model Test of Homogeneity - 2+ groups/One categorical variable - are the distributions of a variable the same in 2+ populations Test of independence: - One group/two categorical variables - Is there an association between the 2 categorical variables? Procedure: - Observed frequencies at each level similar to / different from the expected at each level  Observed: Actual frequency obtained for each level  Expected Frequencies: - Frequency values specified by the null hypothesis Frequency you would expect if null were true Chi Square Statistis: - Adding up the squares of the deviations between the observed and expected counts divided by the expected counts  it is a measure of discrepancy between the 2 distributions - if the two distributions are identical: chi square will be zero; the bigger the differe
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