1. Statistical Tests
P Values

2. The Impact of Sampling We are sampling
We don’t expect every sample to look exactly like the population.
There is going to be variability because of chance

3. Simulation – 20 trials Simulation – 10000 trials 1 2 3 4 5 6 7 8 9 10
Number Heads 1 2 3 4 5 6 7 8 9 10
Total Times occurred
Probability of Occurring
0.0
0.05
 0.15
0.15
0.25
0.2
0.1   0
Simulation – trials
Number Heads 1 2 3 4 5 6 7 8 9 10
Total Times occurred 92
461
1154
1981
2537
2063
1117
479
101
Probability of Occurring
0.0005
0.009
0.046
 0.115
0.198
0.245
0.206
0.117
0.048
0.010
 0.0006

4. The Big Question… My simulation – 10000 trials
What is the likelihood (probability) of having AT LEAST 8 heads in our sample (getting 8, 9, or 10 heads)?
My simulation – trials
Number Heads 1 2 3 4 5 6 7 8 9 10
Total Times occurred 92
461
1154
1981
2537
2063
1117
479
101
Probability of Occurring
0.0005
0.009
0.046
 0.115
0.198
0.245
0.206
0.117
0.048
0.010
 0.0006

5. The Big Question… My simulation – 10000 trials
What is the likelihood (probability) of having AT LEAST 8 heads in our sample?
p= so p=0.0586
(8) (9) (10)
My simulation – trials
Number Heads 1 2 3 4 5 6 7 8 9 10
Total Times occurred 92
461
1154
1981
2537
2063
1117
479
101
Probability of Occurring
0.0005
0.009
0.046
 0.115
0.198
0.245
0.206
0.117
0.048
0.010
 0.0006

6. Logic of Statistical Testing
Inferring from samples – INFERENTIAL STATISTICS
Scientists collect data from a sample and determine whether or not that sample provides EVIDENCE AGAINST the null hypothesis.
If the null hypothesis is true, what is the probability we would have randomly chosen a sample with the values we observed?
Analysis:
By looking at our probability of obtaining 80% or 8 heads in a sample of 10 flips, we can make a decision.
PROBABILITY IS OFTEN CALLED THE P value

7. Our Example
Likelihood of getting 8 heads out of ten in our sample if the null hypothesis were actually true is p= meaning it would occur roughly 6 times out of 100.
Do you consider this value low or high?
Do you think it provides enough evidence against the null hypothesis?

8. Statistical Significance
Need a cut point for the p-value
Common “cut points”: 0.05, 0.01, .001
If P value < 0.05,
you say the result is “statistically significant” and you reject the null hypothesis (Ho).
If the null hypothesis is true, the probability of randomly getting the observed sample is unlikely.
This provides evidence against the null hypothesis and we would REJECT the null hypothesis, suggesting one of the alternative hypotheses were correct.

9. Statistical Significance
If P value > 0.05,
You say the results were “not statically significant”
If the null hypothesis is true, the probability of randomly getting the observed sample is likely.
This does not provides evidence against the null hypothesis and we would FAIL TO REJECT OR ACCEPT the null hypothesis, allowing us to reject the alternative hypotheses.

10. Statistical Tests/Hypothesis Testing/Inferential Test:
All statistical tests provide a P value that is the probability that your results would have occurred if the null hypothesis were true.
They use information from your data (mean, standard deviation, etc.) to figure out a probability based upon a population that meets the null hypothesis (much like our card simulation).
You use the p-value to make a data-driven decision

11. Example Hypotheses and P value
Null Hypothesis
P-Value
Decision
Interpretation
The mean life-span is 15 years.
0.078
The correlation between amount of nutrient and growth is 0.
The mean height of plants exposed to sunlight equals the mean height of plants not exposed to light.
Cut-off value is 0.05

12. Example Hypotheses and p-value
Null Hypothesis
P-Value
Decision
Interpretation
The mean life-span is 15 years.
0.078
Do not reject the null hypothesis
There is no evidence to suggest the mean life-span is not 15 years.
The correlation between amount of nutrient and growth is 0.
The mean height of plants exposed to sunlight equals the mean height of plants not exposed to light.
Cut-off value is 0.05

13. Example Hypotheses and p-value
Null Hypothesis
P-Value
Decision
Interpretation
The mean life-span is 15 years.
0.078
Do not reject the null hypothesis
There is no evidence to suggest the mean life-span is not 15 years.
The correlation between amount of nutrient and growth is 0.
0.010
The mean height of plants exposed to sunlight equals the mean height of plants not exposed to light.
Cut-off value is 0.05

14. Example Hypotheses and p-value
Null Hypothesis
P-Value
Decision
Interpretation
The mean life-span is 15 years.
0.078
Do not reject the null hypothesis
There is no evidence to suggest the mean life-span is not 15 years.
The correlation between amount of nutrient and growth is 0.
0.010
Reject the null hypothesis
(P < 0.05)
There is evidence to suggest the correlation is not zero.
The mean height of plants exposed to sunlight equals the mean height of plants not exposed to light.
Cut-off value is 0.05

15. Example Hypotheses and p-value
Null Hypothesis
P-Value
Decision
Interpretation
The mean life-span is 15 years.
0.078
Do not reject the null hypothesis
There is no evidence to suggest the mean life-span is not 15 years.
The correlation between amount of nutrient and growth is 0.
0.010
Reject the null hypothesis (at sig level of 0.05)
There is evidence to suggest the correlation is not zero.
The mean height of plants exposed to sunlight equals the mean height of plants not exposed to light.
0.0001
Cut-off value is 0.05

16. Example Hypotheses and p-value
Null Hypothesis
P-Value
Decision
Interpretation
The mean life-span is 15 years.
0.078
Do not reject the null hypothesis
There is no evidence to suggest the mean life-span is not 15 years.
The correlation between amount of nutrient and growth is 0.
0.010
Reject the null hypothesis (at sig level of 0.05)
There is evidence to suggest the correlation is not zero.
The mean height of plants exposed to sunlight equals the mean height of plants not exposed to light.
0.0001
Reject the null hypothesis
There is evidence to suggest light makes a difference on plan growth.
Cut-off value is 0.05