Inferential Statistics

Question 1

Inferential Statisitcs

Answer 1

Techniques that allow us to study samples and then make generalizations about the populations from which they are selected.

Question 2

Chance

Answer 2

Could affect results when inferences about populations are made from samples

Question 3

Hypothesis Testing

Answer 3

Statistical method that uses sample data to evaluate a research hypothesis about a population parameter

Question 4

Hypothesis-Driven Research Steps

Answer 4

1. State a research hypothesis about a population
2. Set criteria for a description
3. Obtain a random sample from a population and compute sample statistics
4. Make a decision (accept/reject null hypothesis)

Question 5

Null Hypothesis

Answer 5

• No change, effect, difference, or relationship

- Cannot reject if weak evidence or insufficient power

Question 6

Alternative Hypothesis

Answer 6

• Change, effect, difference, relationship from the general population
• Non-directional: doesn’t specify direction of effect, more common and conservative
• Directional/one-tailed: direction of association, rarer

Question 7

Non-Directional

Answer 7

• Two-tailed test
• More common, conservative, and convential
• No need to “guess” direction of association
• Even if association occurred in direction opposite from expected, it will be tested

Question 8

Setting Criteria

Answer 8

• Define level of significance (alpha) for hypothesis test
• Probability of erroneously rejecting Ho when it is true
• Usually set to 0.05 (5%)

Question 9

Collecting Data/Computing Statistics

Answer 9

• Check assumptions (random, independent, observations, homogeneity of variance, normality)
• Decide whether parametric or non-parametric test should be used
• Compute the appropriate test statistics: Z-score, T-score, Chi-square, r statistic

Question 10

Decision Making

Answer 10

• Reject Null: there is an association between independent and dependent variables
• Failure to reject null: appears to have no effect

Question 11

P-Value

Answer 11

• Probability of result occuring by chance
• Smaller = less likely to be due to chance
• If p < alpha = reject Ho
• Since alpha usually set to 0.05, p < 0.05 to have statistically significant results

Question 12

Alpha Level

Answer 12

• Level of statistical significance (max probability of making a Type I error)
• Test statistic compared to predefined “significance” level
• Allow 5% chance usually
• Arbitrary, but customary
• Can be 0.01 or 0.1 too (more/less conservative respectively
• Low alpha can be chosen in some situations (EX: multiple comparisons)

Question 13

Statistically Significant

Answer 13

Happens when….

• Null hypothesis is rejected
• Result is unlikely due to chance
• *Gives no information about magnitude of association or clinical significance**

Question 14

P-Value Influencers

Answer 14

1. Magnitude of association (how big of a difference)
2. Sample size
3. Variation in observed outcome

No p-value excludes or mandates chance

Question 15

P-Value Misconceptions

Answer 15

• Calculates probability, not a clear yes or no
• 0.05 is ARBITRARY
• Does not imply causality
• Statistically significant is NOT the same as clinically significant

Question 16

Type of Errors

Answer 16

• Type 1 Error (alpha): rejecting Ho when it’s true, significance level
• Type 2 Error (beta): failure to reject a false Ho
• Power: probability of rejecting Ho when it is false

Question 17

Factors Impacting Power

Answer 17

1. Sample size: power increases with its increase
2. Level of significance (alpha): power decreases as it decreases
3. Beta (type II error)
4. Choice of statistical test used
5. Variability (precision) of outcome variable: power increases as it decreases
6. Effect size: increases power as it increases (large difference between groups)

Question 18

Confidence Interval

Answer 18

• CI: range of values likely to cover true parameter
• Built around point estimate
• Point estimates +/- margin or error
• 90%, 95%, 99% usually (arbitrary), 95% most common since alpha is usually 5%

Question 19

95% CI

Answer 19

• Addresses precision of point estimates: range of values that lies within 95% confidence
• Can be used for hypothesis testing
• Can indicate is results are statistically significant

Question 20

Difference in Means

Answer 20

• Provides index of variability in group mean differences that would be expected by chance
• Difference between means = 0, no association (Ho = true)
• If “0” isn’t included within the interval, we can conclude that the means are different

Question 21

Width of CI

Answer 21

• Indication of precision

- Wider the interval, the less precise

Question 22

Precision Affectors

Answer 22

1. Level of confidence - larger level of confidence makes the CI larger
2. Sample size: larger n causes smaller CI (more precise)

MORE CONFIDENT = LESS PRECISE