Repeated Measures_Sp08_BB

Repeated Measures_Sp08_BB - Introduction Rare that you know...

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Unformatted text preview: Introduction Rare that you know the population mean 1 Sample t-Test t- Dependent t-Test More likely comparing samples: 1. Dependent t-Test tWithin-Subjects t-Test WithintRepeated Measures t-Test t- 2. Independent t-Test tBetween Subjects t-Test t- Dependent t-Test A dependent t-test is the test statistic for two types tof research designs: 1. Dependent t-Test We've seen this type of design before...where? We' before... Sign test! Repeated-Measures Design Repeated- What's different? What' For the dependent t-Test you keep the magnitude. tNot changing to nominal data. Test Retest 1 Dependent t-Test 2. Dependent t-Test Based on the difference scores rather than the raw scores Difference Scores: For each person, subtract one score from the other Matched-Subjects MatchedDesign Assumptions 1. When to use: Dependent t-Test tInterval/ratio data No information on population parameters (, ) ( Comparing mean differences (MD) based on (M difference scores Same (or matched) subjects tested twice Normality of the population t-Tests are robust to moderate violations of the normality assumption No Independence Assumption between conditions! Only one IV Only two levels 2 When to use Dependent t-Test Same procedure as t test for single sample, except Use difference scores Assume that the population mean is 0 1. Steps to Hypothesis Testing: Dependent t-Test Hypotheses: H0: MD = 0 (keeping in mind that D = 0) H1: MD 0 Why 0? We are interested in a population of difference scores Zero implies no difference between the scores (i.e., the scores are the same, your manipulation had no effect) Difference scores For each person, subtract one score from the other Carry out hypothesis testing with the difference scores Dependent t-Test Quick note for w/in t, `n' = `N' Example As part of a pilot study, a researcher examines the effect of cognitive therapy on positive self-regard. The number of positive selfstatements made about oneself is recorded for each participant during the first meeting. After 8 weekly therapy sessions, the measures are repeated for each person. Here are the data: Participant A B C D Before tx 3 5 7 1 After tx 12 10 8 14 t (n 1) = MD SED Does cognitive therapy affect one's positive self-regard? Should the researcher continue testing? Complete all steps to hypothesis testing. 3 Steps to Hypothesis Testing: Dependent t-Test Step 1: State the Hypotheses: H0 : MD = 0 H1 : MD 0 Note. keeping in mind that D = 0 Steps to Hypothesis Testing: Dependent t-Test Step 3: Choose the appropriate test statistic (determines H0 distribution): Dependent t-Test: tDo not know population parameters Interested in the mean difference (i.e., change scores) Same (or matched) subjects tested twice Step 2: Determine the nature of the DV: Number of positive statements: RATIO! Steps to Hypothesis Testing: Dependent t-Test Step 4: Set Type I & Type II Error Rates: = 0.05 = ?? Either 0.20 and then power is 0.80 OR if you already know your sample size you need to find power first Steps to Hypothesis Testing: Dependent t-Test Step 5: Determine the size of your sample: = d MEI n = 0.50 4 = 1.00 Power = 0.17 Participant A B C D Before tx 3 5 7 1 After tx 12 10 8 14 4 Steps to Hypothesis Testing: Dependent t-Test Step 4: Set Type I & Type II Error Rates: = 0.05 = 0.83 Either 0.20 and then power is 0.80 OR if you already know your sample size you need to find power first Steps to Hypothesis Testing: Dependent t-Test Step 6: Collect Data Done! Step 7: Run appropriate statistical test (find probability values for your statistic) t (n - 1) = MD SED Participant A B C D Before tx 3 5 7 1 After tx 12 10 8 14 Difference 9 5 1 13 MD = 7.000 SDD=5.16398 t (n - 1) = = MD SED 7.000 5.163978 ( ) 4 = 2.7111 0 M t (n - 1) = D SED What's our t-observed? What' t- No Statistical Significance, p > 0.05 Retain Ho 5 Steps to Hypothesis Testing: Dependent t-Test Step 8: Calculate observed effect size Steps to Hypothesis Testing: Dependent t-Test Step 9: Final Decision Does cognitive therapy affect one's positive self-regard? Should the researcher continue testing? Complete all steps to hypothesis testing. dOBS = = MD SDD 7.000 5.163978 = 1.3555 We have practical significance! We have practical but not statistical significance, t(3) = 2.7111, p > 0.05, dOBS=1.3555. This is a very large effect size. Power is very low (0.17), so the researcher should continue with their study by collecting more participants. It looks as though cognitive therapy does affect one's one' positive self-regard, we just don't have enough power to selfdon' show the statistical effect yet. Now let's try it with CIs... MD +/- (tCRIT)(SED) Confidence Interval 7.0000 0.0000 -8.2159 8.2159 Given: tCRIT = +/- 3.182 SED = 2.58199 6 Confidence Interval Decision: Constructing the 95% confidence interval around the expected mean (i.e., 0) gives us upper and lower limits of +/- 8.2159. +/Our observed mean difference of 7.00 falls within these limits. Consequently, cognitive therapy does not affect one's positive one' self-regard. But due to our small sample size and due to our selfobserved mean difference being close to the confidence limit, we may want to continue collecting data to see if the mean difference increases or decreases. 7 ...
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