Transcript Comparing Two Means: One-sample & Paired-sample t-tests Lesson 12 Inferential Statistics Hypothesis testing  Drawing conclusions about differences between groups  Are differences likely due to chance?  Comparing.

Comparing Two Means:
One-sample &
Paired-sample
t-tests
Lesson 12
Inferential Statistics
Hypothesis testing
 Drawing conclusions about differences
between groups
 Are differences likely due to chance?
 Comparing means
 t-test: 2 means
 Analysis of variance: 2 or more means ~

Comparing 2 means: t-tests
One-sample t-test
 Is sample likely from particular
population?
 Paired-Sample t-test
 2 dependent (related) samples
 Independent-samples t-test
 2 unrelated samples ~

The One-sample t-test
Evaluating hypothesis about population
 taking a single sample
 Does it likely come from population?
 Test statistics
 z test if s known
 t test if s unknown ~

t statistic
X 
t
sX
df  n  1
Example: One-sample t-test
Survey: college students study 21 hr/wk
 Do Coe students study 21 hrs/week?
 Select sample (n = 16)
 s unknown
 Nondirectional hypothesis:
 H0 :  = 21;
H1 :   21
 reject H0 if increase or decrease
 PASW/SPSS: Test value = 21
 Assumed from H0 ~

PASW One Sample T Test


Menu
 Analyze
 Compare Means
 One-Sample T Test
Dialog box
 Test Variable(s) (DV)
 Test Value (value of  testing against)

Options (to change confidence intervals) ~
PASW Output
*1-tailed probability: divide Sig. 2-tailed by 2
Paired-Samples t-tests
2 samples are statistically related
 Less affected by individual differences
 reduces variance due to error
 Repeated-measures
 2 measurements on same individual
 Matched-subjects
 Match pairs on some variable(s)
 Split pairs into 2 groups ~

Difference Scores
Find difference between each score
 D = X2 - X1
 Requires n1 scores equal n2 scores
 Calculate mean D

D

D
N
 And standard deviation of D
2

~
DD

sD 


n 1
Repeated-measures
2 measurements of same individual
 Pretest-posttest design
 measure each individual twice
 pretest  treatment  posttest
 compare scores ~

Matched-subjects
Match individuals on important
characteristic
 individuals that are related
 IQ, GPA, married, etc
 Assign to different treatment groups
 each group receives different
levels of independent variable ~

Assumptions: Related Samples
 Population
of difference scores
is normal
 Observations within each
treatment independent
 scores for each subject in a
group is independent of other
subjects scores ~
Related-samples Hypotheses
Nondirectional
 H 0:  D = 0
 H 1:  D  0
 Directional
 H 0:  D > 0
 H 1:  D < 0
 Remember: it depends on the
direction of the prediction ~

Sample Statistics

Mean difference
D
D 
N

Mean for single sample
X
X 
N
Standard Deviation:
Related-samples
Single sample
dfD  N 1
D  D 
df  N  1
sD 
N 1
X  X 
2
2
s
N 1
Estimated Standard Error

Calculate same as single sample
 use standard deviation of
difference scores
sD
sD 
N
Test Statistic

Related-samples t test
tobs

D  D

sD
Since D= 0
tobs
D

sD
Example
Does exercising longer have greater
health benefits?
 Participants
 7 pairs of people matched on age,
sex, & weight
 Manipulation (IV)
 1 of each pair exercised 2 hrs/week
 1 of each pair exercised 5 hrs/week
 Outcome (DV): Health rating ~

PASW Paired-Sample T Test



Data entry
 1 column each DV
Menu
 Analyze
 Compare Means
 Paired-Sample T Test
Dialog box
 Paired Variable(s) (DV)

Options (to change confidence intervals) ~
PASW Output