STATS lec 3-hypothesis and probability Flashcards
1
Q
Simplified objective
A
- To know that if p is smaller than 0.05 (p<0.05) you have a significant result and can reject the null hypothesis
- But how confident can you be that you are RIGHT
- To realise that inferential statistics are all about probability and the likelihood of replicating the result that you have found
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2
Q
principles of probability
A
- Number of times the event of interest could happen divided by the total number of possible event
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3
Q
Principles of probability
A
-
Addition rule: for a number of mutually exclusive outcomes
- (i.e. one thing or the other, not both)
- All probabilities will sum to= 1
- e.g. probability baby will be male= 0.5
- So probability baby will be female = 1-0.5 = 0.5
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4
Q
Golden rule for significance
A
- Values of p smaller than 0.05 are accepted as ‘statistically significant’
- If p<0.01 then it is also true that p <0.05
- p <0.001 is also smaller than p <0.05 and so this result would also be accepted as significant
- What do we mean by significant
- Mean that we can reject the null hypothesis
- With a certain degree of confidence
- Mean that we can reject the null hypothesis
5
Q
Hypothesis
A
- A researcher wants to know whether attending lectures improves a student exam performance
- His hypothesis is
- Attending lectures will be associated with increase examination scores
- The null hypothesis (HO)
- Attending lectures will have no effect on exam scores
6
Q
What is the null hypothesis
A
- John is investigating whether there is a difference in the number of cups of coffee drunk in a day between group A and group B
- John states that “there is no difference in the number of cups of coffee drunk by group A and B”
- H0
7
Q
What is the alternate hypothesis
A
- John is investigating whether there is a difference in the number of cups of coffee drunk in a day between group A and group B
- John states that “there is a difference in the number of cups of coffee drunk by a group A and B”
- Or saying it another way
- The observed difference in the number of cups of coffee drunk by group A and B did not happen by chance
8
Q
Nota Bene
A
- We are assessing the PROBABILITY that the results we see are due to chance
- We are calculating the confidence we have in REJECTING the null hypothesis
- That is saying, saying how confident we are that the results are NOT due to chance
9
Q
Experiments
A
- Designed to test a hypothesis
- Calculate a statistic to help decide if you can reject the null hypothesis
- Statistical tests to help decide if any changes were seen are real or due to chance
- BUT there is always a chance (probability) that some change that seems to be real could actually be due to chance
- CAN come to the wrong conclusion- and how likely this is
10
Q
2 types of error
A
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Type 1: Incorrectly rejecting the null hypothesis
- Saying there is a significant difference when there is not
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Type 2: Incorrectly accepting the null hypothesis
- Saying there is NO difference when there is
11
Q
The “p” values
A
- Is the probability that you have rejected the null hypothesis when it was in fact true
- The probability of making a Type 1 error
- Therefore how could you calculate the probability of having come to the correct conclusion = addition rule
12
Q
Various P values (p=1 is a certainty)
A
- P = 0.05
- 5 in 100 ( 1 in 20) chance of making a type 1 error
- P <0.05
- Less than 5 in 100 chance
- P = 0.02
- 1 in 50 chance
- P <0.001
- 1 in 1000 chance
13
Q
Pause for thought
A
- These are probabilities of making a type 1 error STATISTICALLY
- How does this statistical certainty correlate with the actual results of the experiment
- Clinical significance
- Importance of outcome
- Would you accept
- A probability of missing a bus = 0.05
- A probability of a new helping you = 0.05
- A probability of a new drug killing you= 0.05
