1. Modify—use bio. IB book  IB Biology Topic 1: Statistical Analysis

2. An investigation of shell length variation in a mollusc species
A marine gastropod (Thersites bipartita) has been sampled from two different locations:
Sample A: Shells found in full marine conditions
Sample B: Shells found in brackish water conditions.
sample size = 10 shells
length of the shell measured as shown
Experimental DESIGN

3. Analysis of Gastropod Data
measured height of shells (ruler)
Units: mm + / - 1 mm (ERROR)
Significant digits
Uncertainty
all measuring devices!
reflects the precision of the measurement
There should be no variation in the precision of raw data
must be consistent.

4. 1.1.1 Error bars and the representation of variability in data.
Biological systems are subject to a genetic program and environmental variation
collect a set of data  it shows variation
Graphs: show variation using error bars
show range of the data or
standard deviation

5. Mean & Range for each group
Marine
Brackish

6. Graph Mean & Range for each group
Quick comparison of the 2 data sets

7. 1.1.2 Calculation of Mean and Std Dev
3 classes of data
Mean
arithmetic mean (avg): measure of the central tendency (middle value)
Std Dev
Measures spread around the mean
Measure of variation or accuracy of measurement

8. 1.1.2 Calculation of Mean and Std Dev
Std Dev of sample = s
is for the sample not the total population
Pop 1. Mean = 31.4
s = 5.7
Pop 2. Mean = s = 4.3

9. Graphing Mean and Std Dev: Error Bars
Mean +/- 1 std dev
no overlap between these two populations
The question being considered is:
Is there a significant difference between the two samples from different locations? or
Are the differences in the two samples just due to chance selection?

10. Graphing Mean and Std Dev: Error Bars
StdDev graph compares 68% of the population % begins to show that they look different.
Range graph :
misleads us to think the data may be similar

11. 1.1.3 Standard deviation and the spread of values around the mean.
StdDev is a measure of how spread out the data values are from the mean.
Assume:
normal distribution of values around the mean
data not skewed to either end
68% of all the data values in a sample can be found between the mean +/- 1 standard deviation

12.
Animation of mean and standard deviation

13. 1.1.3 Standard deviation and the spread of values around the mean.
4. 95% of all the data values in a sample can be found between the mean + 2s and the mean -2s.

14. 1.1.4 Comparing means and standard deviations of 2 or more samples.
Sample w/ small StdDev suggests narrow variation
Sample w/ larger StdDev suggests wider variation
Example: molluscs
Pop 1. Mean = 31.4 Standard deviation(s)= 5.7
Pop 2. Mean =41.6 Standard deviation(s) = 4.3

15. 1.1.4 Comparing means and standard deviations of 2 or more samples.
Pop 2 has a greater mean shell length but slightly narrower variation.
Why this is the case would require further observation and experiment on environmental and genetic factors.

16. 1.1.5 Comparing 2 samples with t-Test
Null Hypothesis:
There is no significant difference between the two samples except as caused by chance selection of data. OR
Alternative hypothesis:
There is a significant difference between the height of shells in sample A and sample B.

17. 1.1.5 Comparing 2 samples with t-Test
For the examples you'll use in biology, tails is always 2 , and type can be:
1, paired 2,Two samples equal variance 3, Two samples unequal variance

18. Good idea to graph it
Bar chart
Error bars
Stats

19. T-test: Are the mollusc shells from the two locations significantly different?
T-test tells you the probability (P) that the 2 sets are basically the same. (null hypothesis)
P varies from 0 (not likely) to 1 (certain).
higher P = more likely that the two sets are the same, and that any differences are just due to random chance.
lower P = more likely that that the two sets are significantly different, and that any differences are real.

20. T-test: Are the mollusc shells from the two locations significantly different?
In biology the critical P is usually 0.05 (5%) (biology experiments are expected to produce quite varied results)
If P > 5% then the two sets are the same
(i.e. accept the null hypothesis).
If P < 5% then the two sets are different
(i.e. reject the null hypothesis).
For t test, # replicates as large as possible
At least > 5

21. Drawing Conclusions
1. State null hypothesis & alternative hypothesis (based on research ?)
2. Set critical P level at P=0.05 (5%)
3. Write the decision rule—
If P > 5% then the two sets are the same (i.e. accept the null hypothesis).
If P < 5% then the two sets are different (i.e. reject the null hypothesis).
4. Write a summary statement based on the decision.
The null hypothesis is rejected since calculated P = (< 0.05; two-tailed test).
5. Write a statement of results in standard English.
There is a significant difference between the height of shells in sample A and sample B.

22. 1.1.6 Correlation & Causation
Sometimes you’re looking for an association between variables.
Correlations see if 2 variables vary together
+1 = perfect positive correlation
0 = no correlation
-1 = perfect negative correlation
Relations see how 1 variable affects another

23. Pearson correlation (r)
Data are continuous & normally distributed

24. Spearman’s rank-order correlation (r s)
Data are not continuous & normally distributed
Usually scatterplot for either type of correlation
both correlation coefficients indicate a strong + corr.
large females pair with large males
Don’t know why, but it shows there is a correlation to investigate further.

25. Causative: Use linear regression
Fits a straight line to data
Gives slope & intercept
m and c in the equation y = mx + c
Doesn’t PROVE causation, but suggests it...need further investigation!