TOPIC 1: STATISTICAL ANALYSIS

1.1.1 ERROR BARS•G

raphical representation of the variability of data.

1.1.1 Error bars

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.

1.1.1 Error bars

•Can be used to show either:•The range of the data, OR•The standard deviation.

1.1.2 Calculate the mean

1.1.2

1.1.2 Calculate the standard deviation of a sample (s):

S =

1.1.2 Standard deviation (s )

•Is a number which expresses the difference from the mean.

1.1.2

(X-mean)X

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: ?

1.1.2 Error bars – can show the range of data point OR the S.D

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.

1.1.3

1.1.3 normal distributed data -

refer to pg 17-18, h/book.

1.1.3

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.

1.1.4

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).

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:

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.

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.

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.

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.

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.

THANK YOU…