topic 1 stat. analysis
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TOPIC 1: STATISTICAL ANALYSIS
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1.1.1 ERROR BARS•G
raphical representation of the variability of data.
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1.1.1 Error bars
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1.1.1 Error bars = range of data•"
error bars" - the graphical display of a data point including its errors (uncertainties / range of data).
•We illustrate for a data point where (x, y) = (0.6 ± 0.1, 0.5 ± 0.2).
•The value of the data point, (0.6, 0.5), is shown by the dot, and the lines show the values of the errors.
•The lines are called error bars.
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1.1.1 Error bars
•Can be used to show either:•The range of the data, OR•The standard deviation.
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1.1.2 Calculate the mean
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1.1.2
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1.1.2 Calculate the standard deviation of a sample (s):
S =
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1.1.2 Standard deviation (s )
•Is a number which expresses the difference from the mean.
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1.1.2
(X-mean)X
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1.1.2 calculation
Raw data (height in cm): 63.4, 56.5, 84.0, 81.5, 73.4, 56.0, 95.9, 82.4, 83.5, 70.9
Mean: ?S.D: ?
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1.1.2 Error bars – can show the range of data point OR the S.D
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1.1.3 Standard deviation (s )•I
s used to summarize the spread of values around the mean.
•For normally distributed data 68% of the values fall within one standard deviation.
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1.1.3
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1.1.3 normal distributed data -
refer to pg 17-18, h/book.
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1.1.3
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1.1.4•A
large value for S.D indicates that there is a large spread of values / the data are widely spread.
•Whereas, a small value for S.D indicates that there is a small spread of values / the data are clustered closely around the mean.
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1.1.4
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1.1.5 The significance of the difference between two sets of dataHand Mean length (mm) S.D (mm)Left 188.6 11.0Right 188.4 10.9
Difference : 0.2 Interpretation of calculated data:SD much greater than the difference in mean length.Therefore, the difference in mean length between left and right hand is NOT significant. Conclusion:The length of right and left hands are almost the same.(The SD can be used to help decide whether the difference between 2 means is likely to be significant).
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1.1.5 another example…Hand / foot mean length (mm) S.D (mm)Right foot 262.5 14.3Right hand 188.4 10.0
Difference: 74.1Interpretation of calculated data:S.D is much less than the difference in mean length.Therefore, the difference in mean length between right hands and right feet is significant.
Conclusion:
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1.1.5 t-test•C
an be used to find out whether there is a significant difference between the two means of two samples.
•Use GDC or computer to get the calculated value for t.
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1.1.5 t-testStages in using t-test and a sample Table of critical values of t Please refer page 2, Biology for IB Diploma, Andrew Allot.
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1.1.5 t-test•E
.g of the use of the t-test:Hand
Mean length t critical value for t (P=0.05)
Left188.6mm 0.082 2.002
Right188.4mm
Interpretation of calculated data:
The calculated value for t is much smaller than the critical value.
So, the difference between the mean lengths of left and right hands is NOT significant at 95% confidence level.
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1.1.5 t-test (another example….)
•E.g of the use of the t-test:
HandMean length t critical value for t (P=0.05)
R hand188.4mm 23.32.005
R feet262.5mm
Interpretation of calculated data:
The calculated value for t is much larger than the critical value.
So, the difference between the mean lengths of R hand and R feet is SIGNIFICANT at 95% confidence level.
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1.1.6 Correlation (pg 23, h/book)
•Correlation is a measure of the association between two factors (variables)
•Correlation does not imply causation.
•Finding a linear correlation between two sets of variables does not necessarily mean that there is a cause and effect relationship between them.
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THANK YOU…