Week 2 - Statistical testing and Type 1 Error Flashcards
What are the three types of probability
- propensity
- frequentist
- subjective
What is propensity probability
Things just have a tendency. 1/6 on a dice because of its nature
what is subjective probability
How likely think we think its going to happen? we express our belifs
what is frequentist probability
The relative frequence over time. The proportion of times we roll 1if we keep rolling
Where can propensity be used in statistics
With the Law of Large Numbers
Where does Subjective probability come from
The basis of Bayesian statistics
Uses prior and posterior probabilities
What is frequentist probability used for?
The truth is fixed but unknown. Sampling is random so sample statistics are random variables.
What are the 5 frequentist testing steps
- Make hypotheses
- Collect data
- Calculate statistics
- Inference
- Draw Conclusions
What are the two types of hypothesis
Null hypothesis, Alternate hypothesis
H0:d=0 Ha:dbigger0
where d is the mean difference in speed in the population. d=mean-mean^
What are the hypothesis in a two sided
H0: d=0 Ha: d!=0
- Proof for a hypothesis is ____
- Evidence against a hypothesis is ____
impossible
possible
Take into account randomness of sampling
- size of effect
- Variation in statistic
what is test statistic for
Test statistics are often a measure for how different our data is from what we would expect if H0 were true, taking into account the variation due to sampling.
What are the three distributinos
- Population distribution
- Sample distribution
- Sampling distribution
What is the central limit theorem
For a random sample size of size n from a population with mean u and standart deviation o, the sampling distribution of ites mean x tends towards a normal distribution, with mean ux=u and standard deviation o=o/sqrt(n)
what is the p-value
The probability of finding this test statistic, or a more extereme one, if the null-hypothesis is true
What to do if the hypothesis is two sided
add the p-values from both sides
I
Idea of a frequentist inference:
- Assume nothing going on H0
- Look at data, calculate a statistic and a test statistic
- what is p-value: chance of oberving this data
- if low: H0 wasnt true
- if not low: H0 could be true
What is type 1 error and type 2 error
Type 1 error: rejecting the null-hypothesis while it is true
Type 2 error: failing to reject the null-hypothsis that is not true
what is p-value really mean
What is the probability if observing this or more extreme data, if the null hypothsis is true. NOT: what is the proability that the null-hypothesis is true
P(Data | Hyp)=
P(Data AND Hyp)/P(Hyp)
