1. AP Biology Intro to Statistics

2. Statistics
Statistical analysis is used to collect a sample size of data which can infer what is occurring in the general population
More practical for most biological studies
Requires math and graphing data
How much variation do I expect in my data?

3. Measures of Central Tendencies
Mean
Average of data set
Median
Middle value of data set
Mode
Most common value of data set

4. Typical data will show a normal distribution (bell shaped curve).
Range of data

5. AP Biology Calculations: Standard Deviation and Standard Error
Boseman videos on standard deviation and standard error linked below.

6. Standard Deviation:
A measure of how spread out the data is from the mean

7. Lower standard deviation:
Data is closer to the mean
Greater likelihood that the independent variable is causing the changes in the dependent variable
Higher standard deviation:
Data is more spread out from the mean
More likely factors, other than the independent variable, are influencing the dependent variable

8. 68% of data fall within ±1s of mean
σ = standard deviation
68% of data fall within ±1s of mean
95% of data fall within ±2s of mean
99% of data fall within ±3s of mean

9. The magnitude of the standard deviation depends on the spread of the data set
Two data sets: same mean; different standard deviation

10. Actual data sets aren’t always so pretty...

11. Calculating standard deviation, s
Calculate the mean (x)
Determine the difference between each data point, and the mean
Square the differences
Sum the squares
Divide by sample size (n) minus 1
Take the square root
Xi is a data point.

12. Standard Error
Indication of how well the mean of a sample estimates the true mean of a population
Measure of accuracy, if the true mean is known
Measure of precision, if true mean is not known

13. Accuracy – How close a measured value is to the actual (true) value
Precision – How close the measured values are to each other.

14. Calculating Standard Error, SE
Calculate standard deviation
Divide standard deviation by square root of sample size
If this is really confusing, the SEx basically gives you smaller error bars than using standard deviation.

15. How do we use Standard Error?
Create bar graph
mean on Y-axis
sample(s) on the X-axis
chemical 1 mean = 30 cm
chemical 2 mean = 50 cm

16. Typically the graph will
Add error bars!
± SE
Indicate in figure caption that error bars represent standard error (SE)
Typically the graph will
indicate how many standard errors of the mean are used.
For example in this graph, if
the bars are for one SE, then
we can assume basically that
68% of the data falls between 20 and 30 cm root length for chemical 1, etc.
You may not even need to figure that out, depends on the question.

17. Analyze! Look for overlap of error lines:
If they overlap: The difference is not significant
If they don’t overlap: The difference may be significant

18. SEM SEM – overlapping - sample means are not significantly different
With respect to SEM, overlapping bars can be used to infer that the sample means are not significantly different. However, the absence of overlapping bars (Figure 4A) cannot be used to infer that the sample means are different.

19.   Which is a valid statement?
Fish2Whale food caused the most fish growth
Fish2Whale food caused more fish growth than did Budget Fude
LOOK FOR OVERLAP OF ERROR BARS.  

20. Statements:
In all four regions, more males exhibited the trait measured than did females.
More males in region 3 exhibited the measured trait than did females  

21. Statistics can also be used to test the validity of our data in supporting our hypotheses.

22. Chi-Square Statistical Analysis
First “chi” is pronounced as “ki”!
Used to determine if experimental data are a good approximation to the expected data
This test can determine if deviations from the expected values are due to chance alone (like errors in technique or sampling) or the effect of the independent variable.
A “goodness of fit” statistic

23. Null Hypothesis
The hypothesis in a chi-square statistical analysis is stated as a null hypothesis.
This states that there is no statistically significant difference between the observed and expected data.
An alternate hypothesis may be generated that implies there is a difference between the observed and expected data.

24. Example of a null hypothesis
Placement in study groups will result in no improvement in student test scores.
An alternate hypothesis would be:
Placement in study groups will result in
improvement in student test scores.

25. Formula for Chi-Square

26. What does the Chi-square value mean?
Refer to the table for chi-square values.
Look under the degrees of freedom row.
Degrees of freedom are “one less than the number of categories”

27. Chi-Square Table (is available on all tests and AP exam)
At the 0.05 row are the critical values for acceptance/rejection of your chi-square value in biology.

28. What does the “0.05 P” mean?
If your null hypothesis is rejected, this means that less than 5% of the time would you expect to collect the observed data if the null hypothesis is correct.
You would be 95% sure that the data do NOT fit the expected 1:1 ratio!

29. If your data does not fit your null hypothesis…..
The consider reasons for this variation.
In other words, the data support the alternate hypothesis.

30. If you need more explanation, watch the Boseman video linked below