Psych 100A - Lecture 9 - Essentials of Statistics for the...

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Unformatted text preview: Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen The Paired-Samples t-Test Chapter 9 Revised by Jeffrey B. Henriques, Ph.D. University of Wisconsin-Madison Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan An Example • Naltrexone and alcohol within groups Thomas E. Heinzen Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen Paired-Samples t Test • Two sample means and a withingroups design • Same steps as other test, except for calculation: Text examples: test performance with or without caffeine/Adderall/shots - happiness before and after a child - depression levels with and without antidepressants t= M difference - mudifference s M df = N - 1 where N = number of difference scores Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen Another Example • Weight Loss • Freshman 15 weigh before attend school; weigh again after first quarter • Exercise and diet programs Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen Distribution of Differences Between Post Holiday Weight – Pre Holiday Weight Means Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen The Paired-Samples t Test • The six steps of hypothesis testing 1. Identify populations, distributions, assumptions 2. State the null and research hypotheses null: difference should = 0 or the mean of group 1 H0 : m1 = m2 H1 : m1 ≠ m2 = mean of group 2 3. Characteristics of the comparison distribution 4. Identify critical values: df = N - 1 5. Calculate 6. Decide example: differences in age, IQ, etc. between husbands and wives - would use paired-samples t Test; too similar groups to be considered random people - comparing 2 separate groups of people but match them between something relevant: study whether people can lift more on/off steroids: 2 separate groups lifting = match weight Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen Buy me a big monitor please!!! does size of monitor matter? Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen Example: Paired-Samples t Test -11 ((X - Y) – M(X-Y)) D - µD 0 ((X - Y) – M(X-Y))2 (D - µD)2 0 116 -15 -4 16 127 113 -14 -3 9 4 123 119 -4 7 49 5 132 121 -11 0 0 Subject X Y (X - Y) 1 122 111 2 131 3 Mdifference = -11.000 sdifference = 4.301 1. give set of tasks: time how M s fast they can complete the task on different size monitors 2. calculate difference 3. treat it like a single sample t Text test Text = 4.301 5 = 1.923 Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen Step 4 • Determine the critical values, or cutoffs use 2 tailed alpha=0.05 t test if no information is given Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen Step 5 • Calculate the test statistic t= ( M difference - mu sM difference ) ( - 11 - 0) = = 5.72 1.923 expected to be no difference because you are testing the NULL hypothesis Why? expected average difference = 0; there is suppose to be no difference between groups Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Step 6 • Make a decision t(4) = -5.72, p < 0.05 Thomas E. Heinzen Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen Steps for Calculating Confidence Intervals • Step 1: Draw a normal curve with the sample difference between means in the center • Step 2: Indicate the bounds of the CI on either end, writing the percentages under each segment of the curve Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen A 95% Confidence Interval for Differences Between Means, Part I Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen Steps for Calculating Confidence Intervals • Step 1: Draw a normal curve with the sample difference between means in the center • Step 2: Indicate the bounds of the confidence interval on either end of the distribution • Step 3: Look up the t values for lower and upper ends of the confidence interval in the t table Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen A 95% Confidence Interval for Differences Between Means, Part II 95% of time you perform the study, the mean will fall in this range Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen Steps for Calculating Confidence Intervals • Step 1: Draw a normal curve with the sample difference between means in the center • Step 2: Indicate the bounds of the confidence interval on either end of the distribution • Step 3: Look up the t values for lower and upper ends of the confidence interval in the t table • Step 4: Convert the t values to raw differences • Step 5: Check the answer Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen A 95% Confidence Interval for Differences Between Means, Part III The confidence interval is [-16.34, -5.66]. Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen Calculating Effect size (M - mu ) d= s ( - 11 - 0) d= = 2.56 4.301 Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan Thomas E. Heinzen Stop and Think • When would you use a z test over a t SD is given; or all tools needed test? when population to get population z test = use z test when there are 2 samples but they are • When would you use an notindependentrelated at all . take a class and split it into two groups: smoking group and sample t test? Think of a upspecific study. non-smoking group • When would you use a paired-samples t test? Think of a specific study. do prep classes actually improve test scores? Essentials of Statistics for the Behavioral Sciences, 2nd Edition Susan A. Nolan An Example • Injectable Naltrexone (Vivitrol) Thomas E. Heinzen ...
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