1. STATISTICS
Topic 1
IB Biology
Miss Werba

2. TYPES OF STATISTICAL DATA
1.1
TYPES OF STATISTICAL DATA
DATA TYPE
EXAMPLE
CENTRAL TENDENCY
NOMINAL
Named categories
Mode
ORDINAL
Ranked or relative data
Median
INTERVAL
On a scale (normally distributed)
Mean
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3. CALCULATING THE ARITHMETIC MEAN
1.1
CALCULATING THE ARITHMETIC MEAN
Find the average of the individual conditions
Measure of central tendency
The formula for the arithmetic mean is:
where,
= arithmetic mean
= sum of all measurements
= total no. of measurements
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4. 1.1
ERROR BARS
Variability: differences in various traits that exist between members of a population
All data has some degree of associated error.
This error is presented by error bars on a graph.
Error bars also allow us to record the degree of variability in the readings.
Error bars typically show either:
range
standard deviation
95% confidence intervals (CI)
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5. CALCULATING THE STANDARD DEVIATION
1.1
CALCULATING THE STANDARD DEVIATION
The standard deviation of the mean tells us how spread out the readings are.
A small S.D. indicates a small range of data
A large S.D. indicates a large range of data
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6. SPREAD OF DATA Large standard deviation Small standard deviation 1.3
1.4
SPREAD OF DATA
Large standard deviation
Small standard deviation
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7. SPREAD OF DATA The standard deviation is used to show data spread
1.3
1.4
SPREAD OF DATA
The standard deviation is used to show data spread
68% of data falls within one S.D. of the mean
95% of data falls within two S.D. of the mean
99% of data falls within three S.D. of the mean
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8. SPREAD OF DATA Standard deviation is useful for :
1.3
1.4
SPREAD OF DATA
Standard deviation is useful for :
comparing means
comparing the spread of data between two or more samples
When considering multiple samples, the closer the means and S.Ds, the more likely that the samples have been drawn from similar (or the same) populations.
If the S.D. is greater than the difference between two means, then the difference is not statistically significant
Remember: small samples are unreliable!!!!!!!!!!!!!!
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9. STUDENT t-TEST Used to compare 2 populations
1.5
STUDENT t-TEST
Used to compare 2 populations
The size of sample determines the reliability of the results.
The t-test shows the significance of the difference between two sets of data:
Large t-values indicate a significant difference between the two sets of data.
Small t-values indicate little to no difference between the populations.
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10. 1.5
STUDENT t-TEST
Need to either prove or disprove your experimental hypothesis :
H0 = null hypothesis
H1 = experimental hypothesis  that the IV affects the DV
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11. STUDENT t-TEST Choose a one-tailed or two-tailed t-test:
1.5
STUDENT t-TEST
Choose a one-tailed or two-tailed t-test:
1-tailed = there is an effect (one of +ve or –ve)
2-tailed = there is an effect (either +ve or –ve)
Choose a paired or unpaired:
paired = same organisms measured in difft conditions
unpaired = difft organisms measured in difft conditions
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12. STUDENT t-TEST Select your degrees of freedom: Select your p-value:
1.5
STUDENT t-TEST
Select your degrees of freedom:
Degrees of freedom = sample size (n) - 1
This occurs for each group - ie. two groups = (n1 +n2) - 2
Select your p-value:
Generally use p = 0.05
If H1 is supported, it will indicate that you are 99.95% confident that the IV had a significant effect on the DV
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13. STUDENT t-TEST Calculate the t-value:
1.5
STUDENT t-TEST
Calculate the t-value:
Use formula, calculator or Excel
Compare t-value to t-test data table:
If t-value exceed p=0.05 value, then data is significant
Reject the null hypothesis and accept the experimental hypothesis
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14. CORRELATION vs CAUSATION
1.6
CORRELATION vs CAUSATION
Correlation means that there is a relationship between two (or more) things.
This DOES NOT MEAN that one has caused the other to occur.
There might be a common event that causes bother events to occur.
t-tests show a correlation between the two sets of data but does not prove a causal relationship….
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15. CORRELATION vs CAUSATION
1.6
CORRELATION vs CAUSATION
Correlation describes the strength and direction of a linear relationship between two variables
Use the Pearson correlation coefficient (r):
+1  strong, positive correlation
0  no correlation
–1  strong, negative correlation
Used if data is continuous and normally distributed
A line of best fit is obtained from a scatter plot of the data points and the gradient is obtained.
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16. CORRELATION vs CAUSATION
1.6
CORRELATION vs CAUSATION
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