Foundations of Statistical Inference

Question 1

Probability

Answer 1

The likelihood that any one event will occur, given all the possible outcomes
Implies uncertainty - what is likely to happen
Essential to understand inferential statistics

Question 2

Sampling Error

Answer 2

The sample mean won’t equal the population mean
Measured by the standard error of the mean
- If you repeat the study using new samples from the SAME population, how much will the sample mean vary?

Question 3

Standard Error of the Mean

Answer 3

Basis for statistical inference
Allows us to estimate population parameters

Question 4

Point Estimate

Answer 4

A single value that represents the best estimate of the population value
Many times it is the mean

Question 5

Confidence Interval

Answer 5

A range of values that we are confident contains the population parameter
Width concerns the precision of the estimate

Question 6

Correct Interpretation of Confidence Intervals

Answer 6

95% CI = if we were to repeat sampling many times, 85% of the time out confidence interval would contain the true population mean

Question 7

Incorrect Interpretation of Confidence Intervals

Answer 7

There is a 95% probability that the population mean falls within an obtained confidence interval
The population mean is a fixed unknown value

Question 8

Hypothesis Testing

Answer 8

Estimation of population parameters is only one part of statistical inference. Also used to make inferences about observed difference or apparent relationships from sample data

Question 9

Alpha

Answer 9

Maximum probability of type 1 error
Set by researcher before running statistics
Usually set to 0.05 (max chance of type 1 error = 5%)

Question 10

P-Value

Answer 10

Probability of type 1 error if the null hypothesis is true
Probability of observing a value more extreme than an actual value observed, if the null hypothesis is true

Question 11

Type 1 Error and Significance

Answer 11

Mistakenly finding a difference (false positive)
Interpreting probability values - the p value is the probability of finding an effect as big as the one observed when the null hypothesis is true

Question 12

Type 2 Error and Power

Answer 12

Mistakenly finding no difference (False-negative)
Probability of making a type 2 error
Statistical power - power is the probability that a test will lead to rejection of the null hypothesis, or the probability of attaining statistical significance

Question 13

Two-tailed Test

Answer 13

Allows for possibility that difference may be positive or negative

Question 14

One-tailed Test

Answer 14

More power = more likely to find significance when there is significance
Should only be used when the relevant difference is only in one direction

Question 15

Statistical Power

Answer 15

The probability of finding a statistically significant difference exists in the real world
The probability that the test correctly rejects the null hypothesis
Only matters when the null is false

Question 16

The Four Pillars of Power

Answer 16

Alpha, Effect Size, Variance, and Sample Size

Question 17

Increased Power

Answer 17

To ______ the power, you decrease the variance

Question 18

Decreased Power

Answer 18

To _______ the power, you decrease the alpha, effect size, and the sample size

Question 19

Determinants of Statistical Power

Answer 19

P = power
A = Alpha levels of significance
N = Sample size
E = Effect size
Knowing three of these four will allow for determination of the fourth

Question 20

Power Analysis

Answer 20

Estimating one of the four pillars of power based on the other three pillars

Question 21

A priori

Answer 21

Used to figure out how many subjects to use before a study is started
Minimum sample required

Question 22

Post Hoc

Answer 22

After data collection
Only an issue if you fail to reject the null hypothesis