Introductory Statistics for
Laboratorians dealing with High
Throughput Data sets
Centers for Disease Control
Evaluation of a Laboratory Diagnostic
Procedure for Mycoplasma pneumoniae
• We believe that serum levels of the
immunoglobulin M antibody may have
diagnostic significance for identification of
Mycoplasma pneumoniae.
• First thing we need to know is if people who
have the pneumonia show higher serum levels
of the antibody.
Experimental Design
• We will select two groups of subjects
– Experimental Group: Persons with clinically
defined pneumonia
– Control Group: Asymptomatic cases
• We will draw serum samples from each
person and evaluate the serum level of
immunoglobulin M antibody in each sample.
Step 1: State the Null and Alternative
Hypotheses
• H0: The mean serum level for the
experimental group will not be different from
the mean serum level for the control group
(no difference/ nothing is happening)
• Ha: The mean serum level for the
experimental group will be different from the
mean serum level for the control group (there
is a real difference/ something is happening)
Select Statistical Test and Specify the
Region of Rejection
• We will use a t-test for two independent
samples
• We will have 20 people in each group (degrees
of freedom = 38)
• We will reject the null hypothesis if the
probability of it being true is less that 5
chances in 100 (alpha = .05)
Conduct Experiment and Collect Data
Serum Levels of IgM
Data Table
Subject
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Mean
SD
Control Group
Experimental Group
59
57
69
30
34
68
64
27
77
62
60
47
61
83
82
62
57
57
56
56
97
75
78
85
60
75
87
87
78
93
63
76
49
80
51
76
65
66
66
65
58.67
75.60
17.50
14.28
Compute the Test Statistic
Group Statistics
Group
IgM Serum Level Control Group
Experimental Group
N
Mean
Std. Deviation
Std. Error Mean
20
58.4
15.06966
3.369679
20
73.6
12.94685
2.895005
Compute the Test Statistic
Independent Samples Test for IgM Serum Level
Levene's Test for Equality
of Variances
t-test for Equality of Means
95% Confidence Interval
of the Difference
F
Equal variances
assumed
Equal variances not
assumed
Sig.
0.00077
0.978001
t
Sig. (2tailed)
df
Mean
Difference
Std. Error
Difference
Lower
Upper
-3.4215
38
0.001503
-15.2
4.442498
-24.1934
-6.20663
-3.4215
37.15644
0.001529
-15.2
4.442498
-24.2001
-6.19992
Accept or Reject H0:
• As seen in the previous table, the probability
that these two means are samples from the
same population (that the difference is zero) is
• p = .001503
• That is less than our chosen alpha = .05
• Reject the Null hypothesis.
• Conclude that the experimental group has
significantly higher serum levels of IgM
Effectiveness of a Program to Increase
Seatbelt Use Among High School Seniors
• We have developed a program for use with
High School seniors to increase seatbelt use
and wish to determine if the program is
effective.
Experimental Design
• The school has a separate parking lot of
seniors. There is only one entrance and the
students must swipe their ID to enter or leave
the lot. A security camera positioned at the
entrance photographs every driver as they
enter and exit. This system has been in place
for a couple of years.
• Students and their parents will sign a release
granting permission to participate in the study.
• Two weeks later, unannounced, we will begin
reviewing the security camera data and recording
the drivers ID and if he/she was wearing a
seatbelt.
• We will record for 2 weeks before the program is
presented. (Pretest)
• All seniors will then complete the course and
accompanying workbook.
• Then we will record for another two weeks.
(Posttest)
• Each student who regularly drives to school
during the period (must drive at least 3 days a
week during both pretest and posttest) will
become subjects in the experiment.
• Subjects score will be the percent of time they
were wearing a seatbelt when they exited the
gate
– Number of times wearing seatbelt/number of
times exiting * 100
• We will have a pretest score and a posttest
score for each person.
Step 1: State the Null and Alternative
Hypotheses
• H0: The mean percent seatbelt usage on the
posttest will not be different from the mean
percent seatbelt usage on the pretest. (The
program did nothing, nothing happened).
• Ha: The mean percent seatbelt usage on the
posttest will be different from the mean
percent seatbelt usage on the pretest. (The
program changed the seatbelt usage, it did
something.)
Select Statistical Test and Specify the
Region of Rejection
• We will use a t-test for paired samples
– Paired samples = repeated measures = matched
samples = pretest posttest
• We will reject the null hypothesis if the
probability that it could be true is less than 5
chances in 100, ie:
• Alpha = .05
• In this case we don’t know in advance how many
subjects we will get so we can’t specify the
degrees of freedom until after we finish data
collection. That’s OK as long as you specify alpha.
Conduct Experiment and Collect Data
Percent Seatbelt Use
Data Table
Subject
Pretest
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Mean
SD
Posttest
100
11
0
100
41
0
0
40
8
55
100
0
71
39
54
43
24
23
21
14
100
0
28
82
8
100
100
50
100
86
100
35
0
38
100
66
50
48
47
48
37.20
59.30
33.94
35.15
Compute the Test Statistic
Paired Samples Statistics
Mean
N
Std. Deviation Std. Error Mean
Pretest
37.2
20
33.9374
7.588634
Posttest
59.3
20
35.15395
7.860662
Compute the Test Statistic
Paired Samples Test
95% Confidence
Interval of the
Difference
Paired Differences
Std.
Std. Error
Mean
Deviation Mean
Lower
Pair 1
Pretest Posttest
-22.1
42.37663
9.475703
-41.9329
Upper
-2.26713
t- test
t
Sig.(2tailed)
df
-2.33228
19
0.030838
Accept or Reject H0:
• As seen in the previous table, the probability that
these two means are samples from the same
population (that the difference is zero) is
• p = .030838
• That is less than our chosen alpha = .05
• Reject the Null hypothesis.
• Conclude that the Posttest mean is significantly
higher than the Pretest mean. The program
significantly increased seatbelt usage among our
Highschool Seniors.