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
rtot 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 2tailed 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 tdistribution 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(N1)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 pvalues & 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 pvalues) 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... rtot approximation follows the same assumptions as correlations 8 ...
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 Spring '08
 Dicorcia
 Statistics, #, Statistical hypothesis testing, Statistical significance, Statistical power

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