**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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- Psychology, Statistics, Normal Distribution, Statistical hypothesis testing, Student's t-distribution, Thomas E. Heinzen, Susan A. Nolan