W4 - Confidence Intervals & Hypothesis Testing Flashcards
Do we want a higher or lower SE?
Lower SE.
How is SE calculated?
SD / (square root of sample size)
What are confidence intervals (CI)?
Range of values between which you would expect the pop mean to sit.
95% likely to include the REAL pop mean.
What does the width of the confident interval (CI) indicate?
Uncertainty about the unknown pop mean.
What might a very wide CI indicate?
More data should be collected before anything can be determined.
What type of width (bigger or smaller) would you want the CI for increased certainty?
Smaller width
How is the lower boundary of 95% CI calculated?
Mean of sample - (1.96 x SE)
How is the upper boundary of 95% CI calculated?
Mean of sample + (1.96 x SE)
What are the 2 types of research Q?
Are the 2 variables related?
Are the 2 means different?
TYPES OF RESEARCH Q
Are the 2 variables related?
What are the 2 ways of showing this?
Correlation (r)
Regression
TYPES OF RESEARCH Q
What test would you use for the following type of research Q:
Are the 2 means different?
T-test
What is the null hypothesis?
States there will be NO difference between means or NO relationship between variables
H(little 0)
What does the alternative hypothesis (Ha or H1) state?
That there WILL be a difference between means or there WILL be a relationship between variables.
H(little 1)
Can you prove that the alternative hypothesis is true?
no
Instead, can demonstrate that its more likely than the null hypothesis.
What determines whether the null hypothesis is rejected in favour of the alternative hypothesis or if we fail to reject the null hypothesis?
Significance level + the probability values
What are the types of alternative hypothesis?
Directional
Non-directional
What is the alpha level?
(a.k.a significance level)
Probability of rejecting null hypothesis when it’s actually true.
i.e a significance level of 0.05 indicates a 5% risk of concluding there’s a difference when there’s no actually difference.
How is a type 1 error (a.k.a false +ive) created in regards to the null hypothesis?
You conclude there’s a difference, when in reality there isn’t.
What is the probability of making a type 1 error represented by?
Alpha level
How is a type 2 error created in regards to the null hypothesis?
Researcher concludes there’s NO difference when there actually is.
Could happen if their sample size is too small.
What does the p-value provide a measure of?
Strength of evidence vs null hypothesis.
What does a smaller p-value mean?
Smaller probability that the observed difference was due to chance (unrepresentative samples)
What happens when p=0.03?
REJECT null hypothesis + interpret difference as ‘real’.
Yet there is a 3% chance that the diff has occurred by chance (due to sampling variation).
What does a smaller P value result in?
Stronger evidence vs the null hypothesis
