1. Statistics for IB-SL Biology
Making meaning out of data
Maria Garling – Hilton High School
12/4/2018

2. Quantitative – measured using a naturally occurring numerical scale
Quantitative data
Quantitative – measured using a naturally occurring numerical scale
Examples
Chemical concentration
Temperature
Length
Weight…etc.
Maria Garling – Hilton High School
12/4/2018

3. Qualitative Data
Information that relates to characteristics or description (observable qualities)
Information is often grouped by descriptive category
Examples
Species of plant
Type of insect
Shades of color
Rank of flavor in taste testing
Remember: qualitative data can be “scored” and evaluated numerically
Maria Garling – Hilton High School
12/4/2018

4. How many can you measure?
Sampling Data
Don’t have enough time or resources to measure every individual in a population.
Choose and measure a representative sample from a population.
Need to have a good SAMPLE SIZE in order to “believe” your data. (statistically significant)
Sample Size –
How many can you measure?
Maria Garling – Hilton High School
12/4/2018

5. Can you count EVERY ONE?!?! Maria Garling – Hilton High School
12/4/2018

6. Statistical analysis of a sample
Mean: is the average of data points
Range: range is the measure of the spread of data
Standard Deviation: is a measure of how the individual observation of data set are dispersed or spread out around the mean
Maria Garling – Hilton High School
12/4/2018

7. Standard Deviation
The standard deviation tells us how tightly the data points are clustered together
When standard deviation is small—data points are clustered very close
When standard deviation is large—data points are spread out
Maria Garling – Hilton High School
12/4/2018

8. We will use standard deviation to summarize the spread of values around the mean and to compare the means and spread of data between two or more sample
In a normal distribution, about 68% of all values lie within ±1 standard deviation of the mean
This rises to about 95% for ±2 standard deviation from the mean
Standard Deviation
Maria Garling – Hilton High School

9. Confidence Interval (CI)
95% certain the mean will be found within the interval
Maria Garling – Hilton High School
12/4/2018

10. Confidence Interval (CI)
We will use a CI of 95% (2 SD away from the mean) to measure “significance”.
Scenario:
You are trying to find the average height of a 5th grade student. You measure 15 students present in one 5th grade class.
You calculate the mean to be 1.6 m and the confidence interval to be +/- 0.5m.
You measure a second class of 5th grade students, and then a third class of 5th graders, etc. 95% of the time the mean should be between….
Maria Garling – Hilton High School

11. To clarify….
95% of the times you sample this population (ex: 5th graders), the mean you calculate will be within your CI.
Therefore, only 5% of the time, the mean of your population will lie outside this range.
Maria Garling – Hilton High School
12/4/2018

12. New Question: Are 6th graders the same height as 5th graders?
You use the same procedure to measure the height of 6th graders.
How will you know if there is enough of a difference between the average heights of the two groups to truly be different?
Statistical significance: 95% of the data should not overlap
So, CI’s should not overlap. If they do, it is not statistically significant (not different).
12/4/2018
Maria Garling – Hilton High School

13. We will use Excel Error Bars
To graphically display data, you will use the CI to generate error bars.
Error bars represent the spread around the mean.
We will use Excel
Maria Garling – Hilton High School
12/4/2018

14. Are 5th graders shorter than 6th graders?
Maria Garling – Hilton High School
12/4/2018

15. Comparing Means
What can you conclude when error bars do overlap? No surprises here. When error bars overlap, you can be sure the difference between the two means is not statistically significant. (Due to chance variations)
What can you conclude when error bars do not overlap? When error bars do not overlap, you cannot be sure that the difference between two means is statistically significant. T-test is commonly used to compare these groups.
What if you are comparing more than two groups? ANOVA is commonly used for comparing multiple groups; we will not be using ANOVA.
Maria Garling – Hilton High School
12/4/2018

16. T-test
The t-test determines whether the difference observed between the means of two samples is significant
The test works by considering the following:
The size of the difference between the means of the samples.
The number of items in each sample.
The amount of variation between the individual values inside of each sample (the standard deviation).
Maria Garling – Hilton High School
12/4/2018

17. T-test significance level
When a t-test is performed in Excel, it returns the p value
We want p< 0.05
When p < 0.05 than less than 5% of the time the CIs of the two groups will overlap.
(Two groups ARE statistically different)
When p > 0.05, there is a greater chance the CIs of the two groups will overlap.
(Two groups ARE NOT statistically different; difference is due to natural randomness).

18. Are 5th graders shorter than 6th graders?
Excel T-test returned this value:
p =
Are the heights significantly different?
Maria Garling – Hilton High School
12/4/2018

19. Correlation r = 0 no correlation
Correlation is a measure of the association between two factors.
The strength of the association between two factors can be measured.
An association in which all the values closely follow the trend is described as being a strong correlation.
An association in which there is much variation, with many values being far from the trend, is described as being a weak correlation.
A value can be given to the strength of the correlation, r.
r = +1 a complete positive correlation
r = 0 no correlation
r = -1 a complete negative correlation
12/4/2018
Maria Garling – Hilton High School

20. Is there a correlation between sunlight intensity and temperature?
If so, what kind?