Unformatted text preview: Introduction
Rare that you know the population mean
1 Sample tTest t Dependent tTest More likely comparing samples:
1. Dependent tTest tWithinSubjects tTest WithintRepeated Measures tTest t 2. Independent tTest tBetween Subjects tTest t Dependent tTest
A dependent ttest is the test statistic for two types tof research designs:
1. Dependent tTest
We've seen this type of design before...where? We' before...
Sign test! RepeatedMeasures Design Repeated What's different? What'
For the dependent tTest you keep the magnitude. tNot changing to nominal data. Test Retest 1 Dependent tTest
2. Dependent tTest
Based on the difference scores rather than the raw scores
Difference Scores: For each person, subtract one score from the other MatchedSubjects MatchedDesign Assumptions
1. When to use:
Dependent tTest 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
tTests 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 tTest
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 tTest
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 tTest
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 selfregard. 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 selfregard? Should the researcher continue testing? Complete all steps to hypothesis testing. 3 Steps to Hypothesis Testing: Dependent tTest
Step 1: State the Hypotheses:
H0 : MD = 0 H1 : MD 0
Note. keeping in mind that D = 0 Steps to Hypothesis Testing: Dependent tTest
Step 3: Choose the appropriate test statistic (determines H0 distribution):
Dependent tTest: 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 tTest
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 tTest
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 tTest
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 tTest
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 tobserved? What' t No Statistical Significance, p > 0.05 Retain Ho 5 Steps to Hypothesis Testing: Dependent tTest
Step 8: Calculate observed effect size Steps to Hypothesis Testing: Dependent tTest
Step 9: Final Decision
Does cognitive therapy affect one's positive selfregard? 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 selfregard, 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' selfregard. 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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 Spring '08
 Dicorcia
 Statistics, Normal Distribution, Statistical hypothesis testing, researcher, Statistical significance

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