Biomeasurement
www.biomeasurement.net
Continued from last week:
t- and Mann-Whitney U tests
Background reading: Chapter 7
Lecture Content
• Comparing t- & MWU tests
• t-test
• Mann Whitney U test
Mann-Whitney U Test
•
•
•
•
•
Comparison to t-Test
When to use
Example data
Four steps
Example from literature
Similarities
Bone
Density
(g/cm2)
Females
0.972
0.732
0.874
0.943
1.024
0.755
0.779
1.007
0.816
0.755
0.871
0.721
0.727
0.796
0.612
0.775
0.849
0.773
0.649
0.865
Males
0.905
1.016
0.873
0.74
0.861
0.817
0.897
0.962
0.851
0.821
0.763
0.876
0.944
0.993
0.774
0.785
0.892
1.076
0.888
0.865
Brine Shrimp
Length
(mm)
Medium
Salinity
5.5
6.0
5.0
7.0
5.5
6.0
7.0
8.0
6.0
8.0
6.0
7.0
6.0
7.0
6.0
8.0
6.0
7.0
7.5
6.0
7.5
High
Salinity
6.0
7.0
7.5
6.0
7.5
8.0
11.0
9.0
8.0
11.0
8.0
8.0
7.0
7.0
7.0
9.0
.
.
.
.
.
Birth weight (kg) of babies born to
Non smokers
Heavy smokers
3.99
3.18
3.79
2.84
3.60
2.90
3.73
3.27
3.21
3.85
3.60
3.52
4.08
3.23
3.61
2.76
3.83
3.60
3.31
3.75
4.13
3.59
3.26
3.63
3.54
2.38
3.51
2.34
2.71
• Difference
• Two samples
• Unrelated
Differences
t-test
• Parametric
• Scale data only
Mann-Whitney U test
• Nonparametric
• Scale or ordinal data
Speed of swimming
Medium Salinity
High
Salinity
Slow
Fast
Fast
Medium
Slow
Very slow
Very Fast
Very Slow
Slow
Fast
Medium
Slow
Fast
Slow
Very Fast
Fast
Medium
Very slow
Slow
Very Fast
Very Fast
Very Fast
Fast
VerySlow
Time spent
Playing
(hours/day)
Enrichment
Control
4.5
4.3
5.3
6.4
4.9
3.7
5.2
3.5
6.3
7.8
4.3
4.6
5.1
When to use
•
•
•
•
Difference.
Two samples.
Unrelated data.
Dependent variable: Scale level
Do not use if...
• Comparing frequency distributions.
Example Data
Bone
Density
(g/cm2)
Females
0.972
0.732
0.874
0.943
1.024
0.755
0.779
1.007
0.816
0.755
0.871
0.721
0.727
0.796
0.612
0.775
0.849
0.773
0.649
0.865
Males
0.905
1.016
0.873
0.74
0.861
0.817
0.897
0.962
0.851
0.821
0.763
0.876
0.944
0.993
0.774
0.785
0.892
1.076
0.888
0.865
Choosing
Chart
for Graphs
Tests on counts/frequencies
For counts/frequencies in categories
Tests of Relationship
For scale/ordinal data from two variables
Pie Charts
Scatterplots
1 set of Categories
2 sets of Categories
Regression
Correlation
One
Pie Chart
Two
Pie Charts
Scatterplot
Scatterplot
Tests of Difference
For scale/ordinal dependent variable data in categories distinguished by the independent variable
Errorplots or Boxplot
©Hawkins & Carter 2004
Parametric
Nonparametric
Errorplots
Boxplots
The Four Steps
1. Construct a Null Hypothesis (Ho).
2. Decide Critical Significance Level (a).
3. Calculate Statistic.
4. Reject or Accept the Null Hypothesis.
1. Construct Ho
In general no difference between
the samples.
Ho: There is no difference between the
bone density of males and females
over 50 years old.
2. Decide a.
a = 5% = 0.05.
3. Calculate Statistic.
U
Size of
sample 1
Sum of
ranks of
sample 2
Check:
U1 + U2 =
n1 n 2
U is the the lower value of U1 or U2.
More
about R
R1
R2
U
U = 120.5
n1 = 20
n2 = 20
Using SPSS
Dependent Variable
Independent Variable
4. Reject or Accept.
Using Critical Values.
Reject if your t is bigger than tcritical.
Where do you get
these from?
Using P Values
Reject if P is less than or equal to a.
Using Critical Values.
If U </= Ucritical  REJECT H0  significant result.
From...
Step 2: a = 0.05
120.5< 273  Reject
Bone density between males &
Step 3: U=120.5, n1=20, n2=20 females over 50 is different
Using P Values.
If P </= a  reject the null hypothesis.
If P > a  accept the null hypothesis.
0.032< 0.05  Reject
Bone density between males
& females over 50 is different
Example from Literature
Drews (1995),
BEHAVIOUR 133
The pattern and context of
injuries was studied in a
troop of yellow baboons in
Mikumi National Park
(Tanzania).
TABLE 7. Median and range of healing
times in days for baboon injuries.
N Median
Total sample*
35
23.0
Small injuries (<5cm) 15
14.0
Large injuries (>5cm) 11
24.0
Min
8
8
10
Max
120
114
120
* The sample is composed of 24 cuts, 4 punctures, 1 tear, 1 case of
limping, 1 bruise, and 3 injuries of unspecified shape.
Quote from results:
The difference between small and large
wounds (Table 7) was not statistically
significant (Mann-Whitney test, Z= -1.461,
N1=15, N2=11, p=0.14).
What is Z? - bone example
revisted.
Back to baboons….
QUESTIONS:
• What were the two samples? Sample
sizes?
• What might the raw data have looked
like?
• Why might he have used a MannWhitney U test instead of a t-test?
Lecture Content
• Comparing t- & MWU tests
• t-test
• Mann Whitney U test