Experiments
 We
wish to conduct an
experiment to see the effect of
alcohol (explanatory variable)
on reaction time (response
variable).
1
Factors and Treatments
 The
manipulated factor will be the
amount of alcohol consumed.
 There will be two treatments
– No alcohol (Control group – drink
grape punch)
– Alcohol (Treatment group – drink
grape punch spiked with grain
alcohol)
2
Experimental Design
 The
twelve participants will be split,
at random, into two groups of 6.
Each participant will drink two 8
ounce glasses of grape punch in
half an hour. Reaction time of each
participant will be measured after
drinking the punch.
3
Experimental Design
 Control
of outside variables.
–Each participant drinks grape
punch.
–Each participant has reaction
time measured in the same way.
4
Experimental Design
 Randomization
–Participants are randomly
assigned to treatment groups.
 Replication
–There are 6 participants in each
treatment group.
5
Natural Variation
 Participants
will vary in terms of
their natural reaction time.
 Randomization spreads this
variation evenly across the
treatment groups.
6
Data

1. Control Group

2. Treatment Group
n1  6
n2  6
y1
y2
s1
s2
7
Analysis of Results
 The
data gathered from this
experiment can be analyzed
using the methods presented in
Chapter 24 (Lectures 33 and
34).
 Two independent samples.
8
Natural Variation
 We
cannot control the natural
variation in reaction time, i.e. make
each participant have the same
reaction time to begin with.
 We can account for this natural
variation by introducing a blocking
variable.
9
Block Design
 Have
each participant serve as
a block.
 Each participant will experience
both treatments (no alcohol,
alcohol) in a random order.
10
Block Design
 There
is no variation in the
natural reaction time within a
block (it is the same person
within a block).
 Therefore we can better assess
the effect of alcohol on each
person’s reaction time.
11
Data
 With
this block design we will
get a pair of observations
(reaction time after grape punch
and reaction time after grape
punch with alcohol) for each
participant.
12
Two Independent Samples
 Two
separate sets of
individuals.
 One value of the response
variable for each individual.
13
Paired Samples
 One
set of individuals.
 Two values of the response
variable (a pair of values) for
each individual.
14
Know the Difference
 It
is important to know the
difference between data arising
from two independent samples
and data arising from paired
samples.
15
Example
 Alcohol
and Reaction Time
 Experiment run as a block
design with participants as
blocks.
 A pair of reaction times
(seconds) for each participant.
16
Participant
No Alcohol
Alcohol
1
2
3
6.7
7.0
7.0
7.4
7.0
7.7
4
5
6
7
7.3
7.2
7.4
6.2
7.5
7.0
7.6
7.4
8
9
10
6.4
6.6
7.7
7.5
7.2
7.4
11
12
7.7
6.5
7.7
7.4
Difference
Alc – No Alc
0.7
0.0
0.7
0.2
–0.2
0.2
1.2
1.1
0.6
–0.3
0.0
0.9
17
Summary of Differences
n  12

d  5.1

d

 0.425
n
12
sd  0.5083
sd
0.5083
SEd  

 0.1467
n
12
18
Conditions & Assumptions
 Randomization
Condition
–Paired data
 Nearly
Normal Condition
–The differences could have come
from a population whose
distribution is a normal model.
19
.99
2
.95
.90
.75
.50
1
0
.25
.10
.05
.01
Normal Quantile Plot
3
-1
-2
-3
4
2
Count
3
1
-0.5
.0
.5
Difference
1.0
1.5
20
Confidence Interval for  d
d  t SEd 
sd
SEd  
n
*
t from Table T;
*
df  n  1
21
Table T
df
1
2
3
4

2.201
11
Confidence Levels 80%
90%
95%
98%
99%
22
Confidence Interval for  d
d  t SEd 
0.425  2.2010.1467 
0.425  0.323
0.102 to 0.748
*
23
Interpretation
 We
are 95% confident that the
population mean difference in
reaction time is between 0.102 and
0.748 seconds.
 On average, a person’s reaction
time increases from 0.102 to 0.748
seconds after drinking this amount
of alcohol.
24
Test of Hypothesis for  d
 Step
1: Null and Alternative
Hypotheses.
H 0 : d  0
H A : d  0
 Step
2: Check Conditions
–See earlier slides.
25
Test of Hypothesis for  d
 Step
3: Test Statistic and P-value
d 0
0.425
t

 2.897
SEd  0.1467
P  value is between 0.005 and 0.01
26
Test of Hypothesis for  d
 Step
4: Use the P-value to make
a decision.
–Because the P-value is small,
reject the null hypothesis.
27
Test of Hypothesis for  d
 Step
5: State a conclusion within
the context of the problem.
–The population mean difference in
reaction time, with and without
alcohol, is not zero.
28
Comment
 This
agrees with the confidence
interval. Zero was not in the
confidence interval and so zero
is not a plausible value for the
population mean difference.
29
JMP
 Data
in two columns
–Reaction time with no alcohol.
–Reaction time with alcohol.
 Create
a new column of
differences
–Cols – Formula
30
JMP
 Analysis
– Distribution
–Differences
 JMP
Starter – Basic
–Matched Pairs
31
Analysis - Distribution
Distributions
Difference
M ome nts
Test M ean=value
Mean
0.425 Hypothesized Value
0
Std Dev
0.5083395 Actual Estimate
0.425
Std Err Mean
0.146745 df
11
upper 95% Mean 0.7479835 Std Dev
0.50834
lower 95% Mean 0.1020165
t Test
N
12 Test Statistic
2.8962
Prob > |t|
0.0145
Prob > t
0.0073
Prob < t
0.9927
32
Matched Pairs
Matched Pairs
Difference : Alcohol-No Alcohol
Alcohol
No Alcohol
Mean Difference
Std Error
Upper95%
Lower95%
N
Correlation
7.4
6.975
0.425
0.14674
0.74798
0.10202
12
0.20195
t-Ratio
DF
Prob > |t|
Prob > t
Prob < t
2.896181
11
0.0145
0.0073
0.9927
33