Week 2 - Statistical testing and Type 1 Error

Question 2

What are the three types of probability

Answer 2

1. propensity
2. frequentist
3. subjective

Question 3

What is propensity probability

Answer 3

Things just have a tendency. 1/6 on a dice because of its nature

Question 4

what is subjective probability

Answer 4

How likely think we think its going to happen? we express our belifs

Question 5

what is frequentist probability

Answer 5

The relative frequence over time. The proportion of times we roll 1if we keep rolling

Question 6

Where can propensity be used in statistics

Answer 6

With the Law of Large Numbers

Question 7

Where does Subjective probability come from

Answer 7

The basis of Bayesian statistics
Uses prior and posterior probabilities

Question 8

What is frequentist probability used for?

Answer 8

The truth is fixed but unknown. Sampling is random so sample statistics are random variables.

Question 9

What are the 5 frequentist testing steps

Answer 9

1. Make hypotheses
2. Collect data
3. Calculate statistics
4. Inference
5. Draw Conclusions

Question 10

What are the two types of hypothesis

Answer 10

Null hypothesis, Alternate hypothesis
H0:d=0 Ha:dbigger0

where d is the mean difference in speed in the population. d=mean-mean^

Question 11

What are the hypothesis in a two sided

Answer 11

H0: d=0 Ha: d!=0

Question 12

1. Proof for a hypothesis is ____
2. Evidence against a hypothesis is ____

Answer 12

impossible
possible

Question 13

Take into account randomness of sampling

Answer 13

• size of effect
• Variation in statistic

Question 14

what is test statistic for

Answer 14

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.

Question 15

What are the three distributinos

Answer 15

1. Population distribution
2. Sample distribution
3. Sampling distribution

Question 16

What is the central limit theorem

Answer 16

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)

Question 17

what is the p-value

Answer 17

The probability of finding this test statistic, or a more extereme one, if the null-hypothesis is true

Question 18

What to do if the hypothesis is two sided

Answer 18

add the p-values from both sides

Question 19

I

Idea of a frequentist inference:

Answer 19

1. Assume nothing going on H0
2. Look at data, calculate a statistic and a test statistic
3. what is p-value: chance of oberving this data
4. if low: H0 wasnt true
5. if not low: H0 could be true

Question 20

What is type 1 error and type 2 error

Answer 20

Type 1 error: rejecting the null-hypothesis while it is true
Type 2 error: failing to reject the null-hypothsis that is not true

Question 21

what is p-value really mean

Answer 21

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

Question 22

P(Data | Hyp)=

Answer 22

P(Data AND Hyp)/P(Hyp)