This document discusses various statistical analysis concepts including error bars, mean, standard deviation, t-tests, and correlation. It provides definitions and formulas for calculating these values. For example, it defines error bars as showing the range or standard deviation of a data point, and standard deviation as a measure of how spread out values are from the mean. It also gives an example of using a t-test to determine if differences between two means are statistically significant or not. In the last section, it defines correlation as a measure of association between two variables but notes it does not imply one causes the other.

1. TOPIC 1:
STATISTICAL
ANALYSIS

2. 1.1.1 ERROR BARS
raphical representation of the
variability of data.

3. 1.1.1 Error bars

4. 1.1.1 Error bars = range of
data
error bars" - the graphical
display of a data point
including its errors
(uncertainties / range of
data).
e illustrate for a data point
where (x, y) = (0.6 ± 0.1, 0.5
± 0.2).
he value of the data point,
(0.6, 0.5), is shown by the
dot, and the lines show the
values of the errors.

5. 1.1.1 Error bars
an be used to show
either:
•The range of the
data, OR
•The standard
deviation.

6. 1.1.2 Calculate the mean

7. 1.1.2

8. 1.1.2 Calculate the standard
deviation of a sample (s):
S
=

9. 1.1.2 Standard deviation (s )
s a number
which
expresses the
difference from

10. 1.1.2
(X-mean)
X

11. 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: ?

12. 1.1.2 Error bars – can show the
range of data point OR the S.D

13. 1.1.3 Standard deviation (s )
s used to summarize
the spread of values
around the mean.
or normally distributed
data 68% of the values
fall within one

14. 1.1.3

15. 1.1.3 normal distributed data
- refer to pg 17-18, h/book.

16. 1.1.3

17. 1.1.4
large value for S.D
indicates that there is a
large spread of values / the
data are widely spread.
hereas, a small value for S.D
indicates that there is a
small spread of values / the
data are clustered closely
around the mean.

18. 1.1.4

19. 1.1.5 The significance of the
difference between two sets of
data
Hand Mean length (mm) S.D (mm)
Left 188.6 11.0
Right 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).

20. 1.1.5 another example…
Hand / foot mean length (mm) S.D
(mm)
Right foot 262.5 14.3
Right hand 188.4 10.0
Difference: 74.1
Interpretation 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:

21. 1.1.5 t-test
an be used to find out
whether there is a
significant difference
between the two
means of two samples.
se GDC or computer to

22. 1.1.5 t-test
Stages in using t-test
and a sample Table
of critical values of t
Please refer page 2,
Biology for IB
Diploma, Andrew
Allot.

23. 1.1.5 t-test
.g of the use of the t-test:
and Mean length t critical value
for t
(P=0.05)
eft 188.6mm 0.082
2.002
ight 188.4mm

24. 1.1.5 t-test (another
example….)
.g of the use of the t-test:
and Mean length t critical value
for t
(P=0.05)
hand 188.4mm 23.3
2.005
feet 262.5mm

25. 1.1.6 Correlation (pg 23,
h/book)
orrelation is a measure of the
association between two
factors (variables)
orrelation does not imply
causation.
inding a linear correlation
between two sets of variables
does not necessarily mean that
there is a cause and effect

26. THANK YOU…