Statistics
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The following mathematical and
statistical knowledge will be
assumed:
arithmetic mean
variance
standard deviation
standard deviation (error) of
the mean
Statistics
• fit confidence limits to means
at a stated level of probability
• frame null hypotheses;
interpret probability values
• test significance of difference
between means of two samples
from normal distributions using
Student’s t-test
Statistics
• use Chi squared test for
goodness of fit between observed
and expected frequencies in one
way classification
Confidence limits
• comment on the size of the 95%
confidence limits:
narrow limits are more reliable
than broad limits
reliability is improved with large
sample sizes
• comment on the differences
between sample means using the
confidence limits:
no overlap suggests that there is
a significant difference between
the sample means;
overlap suggests that there is no
significant difference between
the two sample means
• you may be asked to complete
the calculation of upper and
lower confidence limits using the
information provided in a table of
statistical parameters
• Remember that the term 95%
confidence limits refers to the range
or interval within which there is a
95% chance or probability that the
population mean is found:
do not confuse this with the sample
mean; by definition it must have a
100% chance of being in this range
Table of Rf values of known and unknown amino acids
Ph
Ala
Met
Tyr
U 1
U 2
0.70
0.39
0.58
0.53
0.69
0.54
0.66
0.42
0.53
0.48
0.64
0.47
0.66
0.38
0.54
0.44
0.65
0.51
0.71
0.40
0.60
0.55
0.69
0.55
0.69
0.33
0.57
0.43
0.63
0.43
0.65
0.34
0.49
0.46
0.70
0.46
0.66
0.35
0.62
0.43
0.66
0.43
1.
2.
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4.
Calculations
go to statistics mode
clear memory
enter data: value, followed by M+
Record mean:
5. Record:
σ
n-1
6. Square this value
7. Divide this value by 7
8. Take the square root of this value
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Use the table for t tests to find
the t value:
read across at d.f. = 6
(sample size – 1), at p = 0.05 (5%)
t = 2.447
Multiply this by your calculated
value
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Add this value to the mean: this
gives the upper 95% confidence
limit
Subtract this value from the
mean: this gives the lower 95%
confidence limit
Repeat for each set of results
Table of mean Rf values (with upper and lower 95%
confidence limits) of known and unknown amino acids
Ph
Ala
Tyr
Met
U 1
U 2
Mean 0.676 0.373 0.474 0.561 0.666 0.484
UL
0.698 0.404 0.519 0.602 0.692 0.530
LL
0.654 0.342 0.429 0.520 0.640 0.438