comparing two means: one-sample & paired-sample t-tests lesson 12
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 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 known t test if unknown ~
t statistic
Xs
Xt
1ndf
Example: One-sample t-test Survey: college students study 21 hr/wk
Do Coe students study 21 hrs/week? Select sample (n = 16)
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
And standard deviation of D ~
N
DD
1
2
n
DDsD
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 H0: D = 0
H1: D 0 Directional
H0: D > 0
H1: D < 0 Remember: it depends on the direction of
the prediction ~
Sample Statistics
Mean difference
Mean for single sample
N
XX
DN
D
Standard Deviation: Related-samples Single sample
1
2
N
DDsD
1
2
N
XXs
1NdfD 1Ndf
Estimated Standard Error
Calculate same as single sample use standard deviation of
difference scores
Ds
N
sD
Test Statistic
Related-samples t test
Since D= 0
D
Dobs s
Dt
D
obs s
Dt
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