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PSYC 2360 (100)
Chapter 8


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PSYC 2360
Mark Fenske

Chapter 8: Hypothesis Testing and Inferential Statistics Probability and Inferential Statistics - any pattern of data that might have been caused by a true relationship between variables might instead have been caused by chance - why research never actually “proves” hypothesis or theory - Hypothesis Testing Flow Chart: Develop Research Hypothesis Set alpha (Usually α=.05) Calculate power to determine sample size that is needed Collect Data Calculate statistic and p-value Compare p-value to alpha(.05) p < .05 p > .05 Reject Fail to Reject Null Hypothesis Null Hypothesis - Those previous procedures involve - use of probability - statistical analysis - Inferential Statistics -- statistical procedures that use sample data to draw inferences - about true state of affaires Sampling Distributions and Hypothesis Testing - directly testing whether a research hypothesis is correct or incorrect NOT achievable goal - not possible to specify what observed data would look like if hypothesis was true - possible to specify in statistical sense, what observed data would look like if hypothesis was not true - Sampling Distribution -- distribution of all the possible values of a statistic - each statistic has associated sampling distribution - there is a sampling distribution for: - mean - standard deviation - correlation coefficient - Binomial Distribution -- distribution of correct and incorrect guesses - as sample size ↑, extreme values are less likely to be observed - as sample size ↑, distribution becomes narrower - Null Hypothesis - Null Hypothesis (H ) 0- assumption that the observed data reflects only what - would be expected under the sampling distribution - specifies the least-interesting possible outcome - the hope in an experiment is to REJECT the null hypothesis - to be able to conclude that observed data was caused by something other than chance - Testing for Statistical Significance - Setting Alpha - observed data must deviate substantially from what is to be expected in order to reject null hypothesis - Significance Level (alpha) -- standard that the observed data must - meet - alpha normally = 0.05 - rejecting null hypothesis if observed data = so unusual that they would have occurred by chance at max. 5% of the time - as alpha ↓, ↑ stringent the standard - Comparing p-value to Alpha - Probability Value (p-value) -- shows likelihood of an observed statistic - occurring on basis of sampling distribution - indicates how extreme data scores are in terms of caused by chance - Statistically Significant -- if the p-value is less than alpha (p < .05) - REJECT null hypothesis - Statistically Nonsignificant -- if the p-value is greater than alpha - (p > .05) - FAIL TO REJECT null hypothesis - p-value for given outcome is found through examination of sampling distribution of statistic - Using One- and Two-Sided p-values - One-sided p-values -- unusual outcomes occur in only one way - Two-sided p-values -- unusual outcome occur in more than one way - p-value is always 2x bigger than one-way p- value - because binomial distribution is symmetrical - provide more conservative statistical test - allow us to interpret statistically significant relationships - even if differences are not in direction originally predicted in hypothesis Reduction of Inferential Errors REJECT FAIL TO REJECT Null Hypothesis Null Hypothesis Null Hypothesis is Type 1 Error Correct Decision TRUE Probability = α Probability = 1 - α Null Hypothesis is Correct Decision Type 2 Error FALSE Probability = 1- β Probability = β **POWER** - Type 1 Errors - Type 1 Error -- reject null hypothesis when it was actually true - should have failed to reject null hypothesis - we know we will make a Type 1 error no more than 5% of the time (if α = .05) - you never know for sure whether or not you make a Type 1 error - it is possible that data that interpreted as rejecting null hypothesis are cause by random error and that the null hypothesis is really true - by setting alpha, it allows us to assure that a Type 1 error has not been made - Type 2 Errors - Type 2 Error -- fail to reject null hypothesis when it was actually false - should have rejected null hypothesis ▯ - missing true relationship - Statistical Power - Power -- probability that the research will reject the null hypothesis given that - the null hypothesis is actually false - correctly rejecting null hypothesis - Power = 1 - β - depends in part of how big the relationship being searched for actually is - bigger it is, easier to detect - Effect Size - beta can only be estimated - Effect Size -- size of relationship between variables - indicated by a statistic - indicates the magnitude of relationship - 0 = no relationship between variables - large & positive = strong relationship between variables - because researcher can never know ahead of time the exact effect size of relationship - cannot exactly calculate power
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