Variance & Power

Question 1

Define the range of sample

Answer 1

The distance from the smallest data point from the largest

Question 2

What is another name for the normal distribution

Answer 2

Bell curve or Gaussian distribution

Question 3

Consider the plot of the results from the experiment to determine if either two genetic manipulations effected growth. Did a or b have a statistically significant effect. The mean effect of both A and B group are clearly larger then C can we make conclusions based on this

Answer 3

• A is different but not B because it overlaps
• no because the mean average falls within the confidence interval of 95% and if there is a lot of variation in the data the confidence might be wide, the mean value is an estimate only and does not reflect variation in the data

Question 4

Two types of error

Answer 4

Type I: false pos (rejecting a null hypothesis when there is no real difference)

Type II: false negative (failing you reject a null hypothesis when the alternative hypothesis is the true state)

Question 5

The 95% confidence interval bars around the means tells us what

Answer 5

This means that there is a 95% confidence that the real mean falls within within the interval bars

Therefore if the confidence interval overlaps we can not say that there is a difference because it is possible that the real mean in both groups is the same value

Question 6

What is the relationship between statistical power and replication

Answer 6

The more replication (is coin flips) the greater the power

Question 7

If the trial to test of a coin was fair involved 10 tests. The 95% confidence interval was 0.19 to 0.81. What does this mean

Answer 7

It means that we can not reject the Ho that the coin is fair as long as we get between 2(0.19) and 8(0.81)

Question 8

What are the three main factors affecting statistical power

Answer 8

Sampling size
Effect size
Variation in the data

Question 9

Draw the power curve and explain what it is

Answer 9

Illustrates the relationship between sampling effort and the inferential power of those samples for a given size. It shows the min number is samples necessary to provide sufficient power and when the addition of more samples will yield little improvement in power

A bad
B good
C bad

Question 10

Define p-value

Answer 10

The prob that we would collect data with the observed level of difference if in reality the Ho is true. In other words if we see a very large difference the prob of this magnitude being observed given Ho is true is less than 5%

Question 11

If confidence increases two the interval increase or decrease

Answer 11

Increases

Question 12

Measures of variability

Answer 12

Describes the dispersion of the values

Range 
Variance 
Standard deviation 
Confidence interval
Standard error of mean

Question 13

Normal distribution

Answer 13

If a set of normally distributed about its mean, variation is distributed evenly around the mean

With SD we can estimate how dispersed the data are without actually sampling all individuals

Question 14

If estimator varied widely under repeated sampling what happens to CI

Answer 14

Confidence in results will be lower as it is a less precise estimator or the pop param

Question 15

Which of the following increase power? 
Increasing variation 
Increasing sample size 
Increasing acceptable error
Increasing the mag of difference between means

Answer 15

No
Yes
No
Yes

Question 16

When is a difference big enough to be considered scientifically valid

Answer 16

Has more to do with the variation around the mean than the mean itself

A difference can be exceedingly small, so long as the variance around those means is also small we can call them different

Question 17

Two misconceptions

Answer 17

-the prob value is the prob that null hypothesis false
Prob of an observed result or more so would be observed if the null hyp is true

-a non sig outcome means that the null hyp is probably true
Means data do not conclusively demonstrate the null hyp is false

Question 18

Three testing hyp for rockfish

Answer 18

RCA eff: fish abundance inside and outside RCAs is equivalent

Methodology: SCUBA and BUWV yield similar estimates of rockfish abundance

Poaching: RCA efficacy is independent of a angler non-compliance

Question 19

Results

Answer 19

Methodology: 0.04 so they are different

RCA eff: 0.01 so they are different

Poaching: 0.12 no difference

Question 20

Greater/ smaller SD
Greater / smaller CI
Greater / smaller sample size

Answer 20

Larger / smaller

Larger / smaller

Smaller / larger

Question 21

Statistical power

Answer 21

Prob that test will correctly reject the null hyp if false