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r_to_t_approximation_Sp08BB

# r_to_t_approximation_Sp08BB - Steps for Hypothesis Testing...

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Unformatted text preview: Steps for Hypothesis Testing 1. H1 and H0 2. Determining the nature of the dependent variable 3. Choosing the appropriate test statistic 4. Setting Type I & Type II error rates 5. Determining sample size 6. Collecting data 7. Conducting appropriate statistical tests 8. Calculate observed effect sizes 9. Decision Making Steps to Hypothesis Testing r-to-t Approximation Example Step 1: State the Hypotheses Null Hypothesis: =0 Research Hypothesis: 0 1 #1 Visual Cliff Example H0 = The ratings of the mother's expressions have no effect on the baby's movement (r=0) H1 = The ratings of the mother's expression have an effect on the baby's movement. (r0) The higher the mother's score on the negative scale, the less forward movement by the baby. #1 Visual Cliff Example Even though using a directional hypothesis, will still use a 2-tailed distribution Conservative measure chance could go in the other direction Step 2: Visual Cliff Example DV#1: Ratings of mother's negative expression on a scale of 0 - 6 #2 Visual Cliff Example DV #2: Measurement of forward movement in centimeters (cm) out of a possible 1,000cm 0 3 6 Ratio! Interval! 2 Step 3: Chose test statistic 2 DVs No IV Interval/Ratio Data Step 3: Chose Test Statistic We are using r as an approximation of t, so we'll be using the t-distribution Correlation! Step 4: Setting Error Rates Correlation using the r as an approximation of t Type I Errors: PC () = 0.05 PW = ()(1) = 0.05 EW = [1 (1-)1] = 0.05 Step 4: Setting Error Rates Not basing this study on past research Sticking with conventional value: = 0.20 3 #5 Determining the Sample Size Not basing it on past studies, so base it on moderate values: rMEI = 0.25 = 0.20 Power = (1-) = 0.80 Sample Size = ? #5 Visual Cliff Example If don't know N: Usually the case when conducting an actual experiment. If already know N: Usually the case for this class b/c working with existing data sets. N = (/rMEI)2 + 1 ( WHERE is related to 0.80 power rMEI = minimum effect of interest N = # of PAIRS = rMEI(N-1)1/2 WHERE is related to ? power rMEI = minimum effect of interest N = # of PAIRS #5 Visual Cliff Example N = (/rMEI)2 + 1 ( WHERE is related to 0.80 power rMEI = minimum effect of interest N = # of PAIRS #5 Visual Cliff Example N = (/rMEI)2 + 1 ( WHERE is related to 0.80 power rMEI = minimum effect of interest N = # of PAIRS N = (2.80/0.25)2 + 1 (2.80/0.25) WHERE is related to 0.80 power rMEI = minimum effect of interest N = # of PAIRS N = 126.44 N = 126 pairs of numbers 4 Final Steps... Step 6: Collect Data Step 7: Run appropriate statistical tests find p-values & compare to alpha refer to handout #6, 7 Visual Cliff Example WHERE r = Pearson's correlation coefficient Pearson' N = # of PAIRS t(124) = [-0.407131(124)1/2]/ [[1-(-0.407131)2]1/2 [1= -4.963622 t = -4.96 #6, 7 Visual Cliff Example Do we have statistical significance? #6, 7 Visual Cliff Example Do we have statistical significance? -4.96 tOBS Critical t Value (CV) -1.984 tCRIT 0 +1.984 tCRIT 5 Decision Time IF [tOBS] > [tCRIT] then reject H0 IF [tOBS] < [tCRIT] then retain H0 = 0.05 2.5% (0.025) 95% (0.95) 2.5% (0.025) Difference! Null is true critical value critical value Difference! p = proportion under the curve #6, 7 Visual Cliff Example Do we have statistical significance? YES! t(124) = -4.96, p < 0.05 What does "p < 0.05" really 0.05" mean? p : The probability of getting a value more extreme given that the null is true -4.96 tOBS -1.984 tCRIT 0 +1.984 tCRIT 6 Final Steps... Step 8: Calculate your observed effect sizes Now need to see if have practical significance find observed effect sizes and compare to MEI #8 Visual Cliff Example No need to calculate observed effect size Already did, rOBS = -0.407 Compare to rMEI = 0.25 IF [rOBS] > [rMEI], then have practical significance [-0.407] > [0.25] We have practical significance! Step 9: Decision Making Statistical Significance (related to p-values) YES p< Practical Significance (related to effect sizes) Visual Cliff: Decision As the mothers' expressions became more negative, infants were less likely to move forward across the visual cliff ( t (124) = -4.96, p < 0.05, r = -.407). NO p> power too low YES ES > MEI SIGNIFICANT! power too high ? Type I error too many subjects # subjects NO ES < MEI NOT SIGNIFICANT 7 #2 Visual Cliff Example DV#1: Ratings of mother's negative expression on a scale of 0 - 6 Directionality? How do we know that infants were less likely to move across the cliff when the mom's expression was more negative? 1200 r = -0.407 1000 800 600 Movement (cm) 0 3 6 400 200 Interval! 0 0 1 2 3 4 5 6 Mom Rating One last note... r-to-t approximation follows the same assumptions as correlations 8 ...
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