biostats exam part 3

1. what is statistical significance? 

1. decision threshold to accept that a relationship between two variables is not caused by random chance

1. what does statistical significance really mean? 

1. we have evidence that the effect that we see in the sample also exists in the population

2. probability of rejection of the null hypothesis

1. what do we use to decide if a sample is statistically significant? 

1. p-value

1. what is the p-value? 

1. probability of obtaining the data if the null hypothesis is true

what does it mean for a sample to be statistically significant?

likelihood of getting those results purely by random chance is very small

1. what is the p-value NOT? 

1. NOT the probability that the null hypothesis is true

1. how big / small is the p-value for central values and extreme values? 

1. central values → high p-value → higher probability of occurring under the null

2. extreme values → smaller p-value → smaller probability of occurring under the null

1. if probability is high, what does the p-value look like and is the null likely true? 

1. p-value is high

2. H₀ is likely true 

3. difference is due to chance

1. if probability is low, what does the p-value look like and is the null likely true? 

1. p-value is low

2. H₀ is likely false

3. difference is statistically significant

1. what is the symbol we use for significance level? 

1. alpha (𝜶)

1. what is significance level? 

1. predetermined probability threshold that tells you when to reject a null hypothesis

2. represents maximum risk you are willing to take of committing a Type I error

1. what is the “equation” for 𝜶? what do we define 𝜶 based on? 

1. 𝜶 = 1 - CI

2. how much risk we are willing to take

1. what have we arbitrarily decided to be comfortable with for the CI and significance level? 

1. CI = 95%

2. 𝜶 = 0.05 (5%)

1. difference between two-sided and one-sided 𝜶? 

1. two-sided → 2.5% on both tails

2. one-sided → 5% on one tail

if the confidence interval is 95%, what is the significance level?

=1 - 0.95

= 0.05

1. how do you interpret p < 𝜶? 

1. there is sufficient evidence to reject H₀ and accept H_A

1. how do you interpret p > 𝜶?

1. there is insufficient evidence to reject H₀

1. what is a Type I error? 

1. false positive

2. we reach the conclusion that something is true / exists / works, when in fact it is / does not

1. what is a Type II error? 

1. false negative

2. we reach teh conclusion that something is not true / doesn’t exist / work, when it is / does

1. what is the reality if H₀ is true but you rejected H₀? what about if you did not reject H₀? 

1. reject H₀ → Type I error (false positive) 

2. do not reject H₀ → correct conclusion

1. what is the reality if H₀ is false and you rejected H₀? what about if you did not reject H₀? 

1. reject H₀ → correct conclusion

2. do not reject H₀ → Type II error (false negative)

1. the probability of a Type I error is the ___________ _________. 

1. significance level

1. when conducting clinical studies (or other potentially life-threatening studies), what should you do to your 𝜶? consequence of this?

1. decrease your 𝜶 to reduce the chance of Type I error

2. harder to reject the null hypothesis

1. what kind of study is said to have high power? 

1. study that has low probability of Type II error 

1. what is power? 

1. probability that a random sample will lead to rejection of a false null hypothesis 

1. to increase power, what should you do to 𝜶 and sample size? 

1. increase 𝜶

2. increase sample size (narrower distribution, less variation / overlap)