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PSYC512: Research Methods PSYC512: Research Methods Lecture 9 Brian P. Dyre University of Idaho

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PSYC512: Research Methods Lecture 8 Outline Exam Next Week Exam Next Week Will cover all lecture material, all material in Howell Chapters 1- 5, broad concepts assumptions from Howell Chapters 6-11 Will cover all lecture material, all material in Howell Chapters 1- 5, broad concepts assumptions from Howell Chapters 6-11 What do I mean by “broad concepts?” What do I mean by “broad concepts?” which tests are associated with which types of scaling properties of variables? which tests are associated with which types of scaling properties of variables? What variants of the tests exist and why? What variants of the tests exist and why? What assumptions underlie the test? What assumptions underlie the test? Questions about material covered in Lecture 8 Questions about material covered in Lecture 8 Describing Data Describing Data The Normal Distribution The Normal Distribution Testing Hypotheses Testing Hypotheses Inferential Statistics Inferential Statistics

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PSYC512: Research Methods Review: The Normal Distribution What is the difference between a normal distribution and a standard normal distribution? What is the difference between a normal distribution and a standard normal distribution? What is the difference between a raw score and a standardized score? What is the difference between a raw score and a standardized score? What are confidence intervals? What are confidence intervals?

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PSYC512: Research Methods Testing Hypotheses Hypothesis testing is the process by which hypothetical relationships between intervening variables are assessed Hypothesis testing is the process by which hypothetical relationships between intervening variables are assessed Hypotheses are always tested relative to one- another or to a “null” hypothesis Hypotheses are always tested relative to one- another or to a “null” hypothesis Examples Examples Comparing groups Comparing groups Assessing performance interventions Assessing performance interventions Assessing relationships between variables Assessing relationships between variables

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PSYC512: Research Methods Null-Hypothesis Testing and Inferential Statistics 2 possible realities 2 possible realities Relationship between your variables does not exist—a null relationship (H o, the null hypothesis) Relationship between your variables does not exist—a null relationship (H o, the null hypothesis) Relationship between the two variables in question actually exists (H 1, the experimental or alternative hypothesis) Relationship between the two variables in question actually exists (H 1, the experimental or alternative hypothesis) 2 possible decisions when looking at the data 2 possible decisions when looking at the data Conclude that a relationship exists (reject the null hypothesis, H o DISCONFIRMATION!) Conclude that a relationship exists (reject the null hypothesis, H o DISCONFIRMATION!) Conclude that no relationship exists (do not reject the null hypothesis CONFIRMATION? NO!) Conclude that no relationship exists (do not reject the null hypothesis CONFIRMATION? NO!)

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PSYC512: Research Methods Null-Hypothesis Testing and Inferential Statistics H o True H o False Reject H o (conclude there is an effect) Type I error (false alarm) Correct Decision Do not Reject H o (conclude there is NOT an effect) Correct Decision Type II error (miss) Decision True State of the World 2 realities by 2 decisions form a 2 x 2 matrix of 4 possibilites

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PSYC512: Research Methods Null-Hypothesis Testing and Inferential Statistics Why might we observe a difference between two groups if no difference actually exists (null is true; samples are drawn from the same population)? Why might we observe a difference between two groups if no difference actually exists (null is true; samples are drawn from the same population)? Each sample may have a unique mean due to sampling error Each sample may have a unique mean due to sampling error Frequency 1 Population 2 samples

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PSYC512: Research Methods Null-Hypothesis Testing and Inferential Statistics How does this change if a difference actually exists between my groups? How does this change if a difference actually exists between my groups? Each sample has a unique mean that represents both sampling error and the differences between the 2 populations Each sample has a unique mean that represents both sampling error and the differences between the 2 populations Frequency 2 Populations Frequency

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PSYC512: Research Methods Hypothesis Testing: Probability and Statistics Problem: How do we distinguish real differences or relationships from measurement noise? Problem: How do we distinguish real differences or relationships from measurement noise? Probability and statistics may be used to assess (descriptive statistics) or compare (inferential statistics) the relative magnitude of different types of variability Probability and statistics may be used to assess (descriptive statistics) or compare (inferential statistics) the relative magnitude of different types of variability Effect (treatment) Variance Effect (treatment) Variance Variability due to relationship between variables or effect of different levels of independent variable (treatments) Variability due to relationship between variables or effect of different levels of independent variable (treatments) “Good” variance that we want to maximize “Good” variance that we want to maximize Error Variance Error Variance Variability in measure due to factors other than the treatment Variability in measure due to factors other than the treatment “Bad” variance that we want to minimize “Bad” variance that we want to minimize

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PSYC512: Research Methods Hypothesis Testing: Inferential Statistics All inferential statistics are evaluating this ratio: All inferential statistics are evaluating this ratio: Effect (good) Variance Test statistic = -------------------------------------- Error (bad) Variance Error (bad) Variance Example test statistics: Chi-square, t, F Example test statistics: Chi-square, t, F These test statistics have known distributions that then allow us to estimate p, the probability of a Type I error (inappropriately rejecting the null hypothesis) These test statistics have known distributions that then allow us to estimate p, the probability of a Type I error (inappropriately rejecting the null hypothesis) Decision to reject null is made by comparing p to some generally accepted criterion for Type I error probability, Decision to reject null is made by comparing p to some generally accepted criterion for Type I error probability,

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PSYC512: Research Methods How is the probability of a Type I error, p, calculated? It depends on… Scaling properties of your dependent variable (DV) Scaling properties of your dependent variable (DV) DV is interval or ratio parametric tests DV is interval or ratio parametric tests DV is nominal or ordinal non-parametric tests DV is nominal or ordinal non-parametric tests Research design Research design Experimental – test differences on measure between conditions or groups t-test, ANOVA, sign test, Mann-Whitney Experimental – test differences on measure between conditions or groups t-test, ANOVA, sign test, Mann-Whitney Correlational – test relations between different measures Pearson product-moment correlation, point-biserial correlation, etc. Correlational – test relations between different measures Pearson product-moment correlation, point-biserial correlation, etc. Manner in which you phrase your hypotheses Manner in which you phrase your hypotheses One tailed vs. two-tailed tests One tailed vs. two-tailed tests

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PSYC512: Research Methods Examples?

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Next Time… Topic: Review of broad concepts related to power, Chi-square, t-tests, and correlation Topic: Review of broad concepts related to power, Chi-square, t-tests, and correlation Be sure to: Be sure to: Review Howell chapters 6-10 Review Howell chapters 6-10 Bring questions! Bring questions! Continue searching and reading the scientific literature for your proposal Continue searching and reading the scientific literature for your proposal

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