Lecture 9 Flashcards
Stat Significance, Standard Error, Effect Size, CIs
Three common tools/indices to find ‘meaningfulness’ of statistical analysis?
- Statistical Significance (p-value)
- Confidence Intervals (95% or 99%)
- Magnitude of the effect (effect size)
Tools/indices for meaningfulness also tell us:
How well SAMPLE statistics generalize to the larger TARGET population
Inferential stats
Making inferences about larger population based on sample–we should see the same results with a different sample
Statistical significance definition
The probability that a statistic from the sample represents a genuine phenomenon in the population–what we see in the sample we should see in the population
Statistical significance elements
- Null Hypothesis Significance Testing
- Systematic and Unsystematic Variation
- Comparing signal to noise
Null Hypothesis Significance Testing
We test null hypotheses… they are simpler. (H0) The question of interest is simplified into two competing claims (or hypotheses) between which we have a choice (between the null hypothesis and the alternative hypothesis). Special consideration is given to the null hypothesis. (e.g., H0 : there is no difference in symptoms for those receiving the new drug (Tx) compared to the current drug)
Systematic Variation
Variation that is explained by the model (SIGNAL)
Unsystematic Variation
Variation that cannot be explained by the model (NOISE)
Comparing Signal:Noise
We want the Effect(signal)>Error(noise)
What are the two possible conclusions of a hypothesis test with regard to the null hypothesis?
Reject
Fail to reject
What are the four possible outcomes of a hypothesis test?
- REJECT NULL THAT IS TRUE (Type 1 error, Incorrect Decision)
- REJECT NULL THAT IS FALSE (Correct Decision)
*ACCEPT NULL THAT IS TRUE
(Correct Decision)
*ACCEPT NULL THAT IS FALSE
(Type 2 error, Incorrect Decision)
Null Hypothesis
- H-0
- “Simpler” and given priority over a more “complicated” theory
- We either REJECT or FAIL TO REJECT
Alternative Hypothesis
- H-1
* A statement of what a statistical hypothesis test is set up to establish
Type I error
Rejecting the Null when it is true
- *Group differences were found when no actual differences exist
- *Alpha
Which is the more serious error: Type I or Type II?
A Type I error is more serious and therefore more important to avoid.
*The test procedure is therefore adjusted so there is a guaranteed “low” probability of making a Type I error
The probability of a Type I error can be precisely computed:
Probability of a Type I error = alpha = p-value
The Probability Value (p-value)
The probability of getting a value of the test statistic as extreme as or more extreme than that observed by chance alone, if the null is true
What do small p-values suggest?
The null is unlikely to be true