Inferential Statistics Flashcards
Inferential Statisitcs
Techniques that allow us to study samples and then make generalizations about the populations from which they are selected.
Chance
Could affect results when inferences about populations are made from samples
Hypothesis Testing
Statistical method that uses sample data to evaluate a research hypothesis about a population parameter
Hypothesis-Driven Research Steps
- State a research hypothesis about a population
- Set criteria for a description
- Obtain a random sample from a population and compute sample statistics
- Make a decision (accept/reject null hypothesis)
Null Hypothesis
- No change, effect, difference, or relationship
- Cannot reject if weak evidence or insufficient power
Alternative Hypothesis
- 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
Non-Directional
- 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
Setting Criteria
- Define level of significance (alpha) for hypothesis test
- Probability of erroneously rejecting Ho when it is true
- Usually set to 0.05 (5%)
Collecting Data/Computing Statistics
- 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
Decision Making
- Reject Null: there is an association between independent and dependent variables
- Failure to reject null: appears to have no effect
P-Value
- 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
Alpha Level
- 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)
Statistically Significant
Happens when….
- Null hypothesis is rejected
- Result is unlikely due to chance
- *Gives no information about magnitude of association or clinical significance**
P-Value Influencers
- Magnitude of association (how big of a difference)
- Sample size
- Variation in observed outcome
No p-value excludes or mandates chance
P-Value Misconceptions
- 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
Type of Errors
- 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
Factors Impacting Power
- Sample size: power increases with its increase
- Level of significance (alpha): power decreases as it decreases
- Beta (type II error)
- Choice of statistical test used
- Variability (precision) of outcome variable: power increases as it decreases
- Effect size: increases power as it increases (large difference between groups)
Confidence Interval
- 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%
95% CI
- 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
Difference in Means
- 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
Width of CI
- Indication of precision
- Wider the interval, the less precise
Precision Affectors
- Level of confidence - larger level of confidence makes the CI larger
- Sample size: larger n causes smaller CI (more precise)
MORE CONFIDENT = LESS PRECISE