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Unformatted text preview: Inferential Statistics Inferential Statistics How do you know that what you see in the sample is not just due to chance? Can take two approaches: Assume that the differences are "real" until demonstrated otherwise Assume that the differences are spurious until demonstrated otherwise!!!! Hypothesis testing in statistics Null hypothesis (H0) Alternative Hypotheses (H1, H2, H3) that the differences you see in your sample are due to chance In other words, probabilistic equivalence holds everywhere in your study that the differences you see in your sample are not due to chance, that they are generalizable Hypothesis testing (cont.) Accept H1 when: you can reasonably reject H0 (in other words, the null hypothesis has to be so bad that only the alternative hypothesis is probable) The level to reject is quantified by: Alpha = .05 or .01 .05 = 5% chance that null is really true .01 = 1% chance that null is really true Correlation What is the relationship between between motivation and achievement? You do a study with 50 people and find that the correlation is r = .50
What is the null hypothesis? What is/are the alternative hypothesis? Correlation review: When do you use correlation? When variables are continuous!! r falls between 1 and +1
r = 1 means perfect negative relationship r = 1 means perfect positive relationship r = 0 means no relationship Positive Relationship Negative Relationship No Relationship Clarification on Correlations What affects you ability to reject null hypothesis Size of the effect Sample Size True for ALL statistics Table 1 Intercorrelations among motivation and achievement
Achievement Motivation Achievement 1.0 Motivation 0.1 1.0 Note: N = 50, * p < .05 Table 1 Intercorrelations among motivation and achievement
Achievement Motivation Achievement 1.0 Motivation 0.9 1.0 Note: N = ??, * p < .05 Combination of effect size and sample size determines Power Power = the ability to correctly reject the null hypothesis Table 1 Inter-correlations among motivation and achievement
Achievement Motivation Achievement 1.0 Motivation 0.1* 1.0 Note: N = 50000000, * p < .05 Figure? Table 1 Intercorrelations among motivation and achievement and stress
Motiv Motiv Ach 1.0 .6* 1.0 .4* Ach Stress Stress .2 1.0 Note: N = 100, * p < .05 Figure
Ach .6* Motiv .2 * p <, .05 .4* Stress Results presented in Figure 1 suggest that stress correlates significantly with achievement (r = .4) but not motivation (r = .2). In addition, achievement significantly correlates with motivation (r = .6).
Ach .6* Motiv Sample .4* Stress .2 NOTE CAN'T SAY THAT STRESS CORRELATES HIGHER WITH ACH THAN MOTIV CAN SAY THAT STRESS CORRELATES SIGNIFCANTLY GREATER THAN ZERO WITH ACHIEVEMENT CAN SAY THAT STRESS DOES NOT CORRELATE SIGNIFICANTLY GREATER THAN ZERO WITH MOTIVATION Conclusions Goals of stats = 1) Describe your sample 2) see if your results generalize Inferential stats = reject null effects only when there is good evidence (only 5% chance you are wrong to reject null hypothesis) Ability to reject null hypothesis affected by sample size and effect size (together makes up power) ...
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This note was uploaded on 08/26/2009 for the course BB H 310W taught by Professor Saltsman,brian during the Spring '07 term at Penn State.
- Spring '07