Practical 2
Practical 2
Biostatistics
Context 1 : Grip Strength
INTERVAL ESTIMATION for NORMAL DATA
In all the examples of this and the next practical you must proceed in the analysis of each
data set by carrying out the following steps:
i)
Identify the key question of interest;
ii)
Ensure the data are appropriate to answering this question;
iii)
Plot the data in a reasonable fashion;
iv)
Provide a subjective answer to the question on the basis of your plot;
v)
Analyse the data by means of a suitable model;
vi)
Summarise your conclusions on the basis of the plot and analyse;
vii)
Present a clear report of all of the above stages.
In this practical illustration two sample Normal Confidence Intervals for
POPULATION
MEANS
will be considered and the appropriate data plotted and analysed in Minitab.
The specific contexts dealt with in this practical are
1:
Grip Strength;
2:
Shellfish contamination.
The Practical Taker will go through these contexts with you and you should record all
relevant material in the worksheets provided. You will be expected to analyse Context 2
yourself and to write up a report on one of the questions.
Source:
Val Hynes (Dept. of P.E. and Sports Science).
Context:
Rock climbing is an arduous and demanding pastime. Representative samples
of regular climbers and non-climbers were taken and had various aspects of
their strength - in particular their arm and hand strength - measured in a Sports
Science laboratory.
Question:
Is the grip strength (of the dominant hand) of regular climbers on average
greater than that of non-climbers.
Data:
This is held in a Minitab Worksheet CLIMBER and loaded from the Q-drive
It contains the grip strength in a column labelled ‘GRIPSTR’ and the type of
climber in ‘TYPE’ where 1 denotes a regular climber and 2 denotes a nonclimber
Practical 2
Practical 2
SKILLS ACHIEVED in this PRACTICAL
Context 2 : Shellfish Contamination
Source:
Marine Institute, Ireland
Context:
Data from regular monitoring of shellfish sites in Ireland with details on
location, type of shellfish (mussel, oysters), method of cultivation, and levels
of various metals.
Question:
How large a difference is there on average between the cadmium level of
mussels and oysters?
What are the typical values of cadmium for the three different species
(Mussels and two type of Oysters) respectively?
How large a difference is there on average between the cadmium level of
mussels grown on ropes and those grown on the bottom?
Data:
i)
How to use the one and two sample t-test commands to produce one and two
sample 95% Confidence Intervals.
ii)
How to UNSTACK data and hence make summaries on individual groups.
How to SPLIT worksheets to facilitate the analysis of specific subgroups.
REPORT WRITING
For ONE of the questions in the SHELLFISH context (to be announced at the practical) you
should write a report containing the following:-
This is held in a Minitab Worksheet SHELLFISH and loaded from the Qdrive
i)
a plot of the data;
ii)
a subjective answer to the key question;
iii)
the appropriate Minitab output
iv)
a simple summary of how you would use the plot and analysis to answer the
key question.
Note
To separate out the species into different columns use UNSTACK
COLUMNS command from the data menu and save them at the end of
the worksheet.
An alternative way is to SPLIT the worksheet
and
Practical 2
WORKSHEET FOR GRIP STRENGTH PROBLEM - 1
Aim:
A popular pastime in Scotland is the sport of rock climbing. It is reasonably common
knowledge that rock climbing is an arduous and demanding pastime. It has been
suggested that in Scotland male rock climbers are therefore likely to be stronger than
male non-rock climbers. In order to investigate this hypothesis representative
samples of regular male climbers and male non-climbers from around Scotland were
taken and various aspects of their strength - in particular their arm and hand strength were measured in a Sports Science laboratory.
The key question of interest was to investigate if the grip strength (of the dominant
hand) of regular male climbers (TYPE = 1) was on average greater than that of male
non-climbers (TYPE = 2).
Subjective Impression:
Practical 2
strength of about 56 kg whereas non-climbers only have a mean grip strength of about
48 kg. These figures perhaps suggest that the regular climbers are slightly stronger on
average than non-climbers. Notice also that if we compare the standard deviations for
the two groups it appears that there is more variability in the grip strength of the
climbers compared to the non-climbers.
However before any conclusions can be drawn a formal and objective analysis of the
data must be carried out.
Formal Analysis:
To carry out a formal analysis of the question we need to produce a two sample 95%
confidence interval for the difference in the population mean grip strength between
the two groups. If the confidence interval does not contain 0 then there is significant
evidence of a difference between the population means of the two groups and if it
does contain 0 then there is no evidence of a difference.
To do this use the command
TWOT ‘GRIPSTR’ ‘TYPE’
In order to get a feel for the data and a subjective answer to the question let us look at
a descriptive statistics and boxplots of the data for each type separately by means of
the commands
DESC ‘GRIPSTR’ ;
BY ‘TYPE’ .
(or in this instance
TWOT
C2 C1 )
to obtain the following output:
TWOSAMPLE T FOR GRIPSTR
TYPE
N
MEAN
STDEV
1
10
55.6
11.3
2
20
47.85
8.68
and
BOXP ‘GRIPSTR’ ;
BY ‘TYPE’ .
SE MEAN
3.6
1.9
95 PCT CI FOR MU 1 - MU 2: ( -1.0,
16.5)
TTEST MU 1 = MU 2 (VS NE): T= 1.91
P=0.077
DF=
14
respectively to obtain
GRIPSTR
TYPE
1
2
N
10
20
GRIPSTR
TYPE
1
2
MIN
37.50
35.50
MEAN
55.60
47.85
MAX
67.50
69.00
MEDIAN
61.75
48.00
Q1
42.13
39.63
TRMEAN
56.37
47.36
STDEV
11.27
8.68
SEMEAN
3.57
1.94
Q3
63.62
53.37
TYPE
1
2
-------------------------------------I
+ I-----------------------------------------------------------I
+
I--------------------------------------------+---------+---------+---------+---------+----GRIPSTR
35.0
42.0
49.0
56.0
63.0
The shape of the boxplots suggest that the data for both the regular climbers and the
non-climbers arose from Normal distributions. There appears to be a difference of
about 8 kg in average strength between the two groups, climbers having a mean grip
Note: This confidence interval is for the mean grip strength of the population of
regular climbers minus that for non-climbers.
Conclusion:
The confidence interval for the difference (i.e. average for regular climbers minus
non-climbers) is (-1, 16.5) kg. Therefore it is just conceivable that among males in
Scotland there is no significant difference between the grip strength of regular
climbers and non-climbers since 0 lies inside this interval.
However as most of the interval is positive it is possible that with an increased
sample size (e.g. 20 in each group) it might be found that on average the climbers are
stronger in terms of grip strength.