RMA: WEEK 11

Question 1

Probability

Answer 1

• Measure of how likely it is that some event will occur
• E.G: Probability of getting a heart card out of suits > p = 1/4 = 0.25 so 25% of the time you will get a heart
• p can vary from 0 (never) to 1 (always) > e.g: if we remove the heart card from deck then p=0 as we cannot get a heart. If we take out all other suits and keep hearts then p=1 because we know we will get it

Question 2

Statistical use of probability

Answer 2

• Can use probability in things like case studies
• What is the probability that one particular score (case study score) belongs to a distribution (normal distribution of typical people)
• e.g: what is the probability that the reading score of stroke patients matches that of controls?

Question 3

Competing hypotheses (Alt and null)

Answer 3

• Null hypothesis: suggests there is no difference (e.g: there will be no difference in patients reading ability and reading ability of control group)
• Alternative hypothesis: suggests there is a meaningful difference. (e.g: there will be a difference in patients reading ability and reading ability of control group)

Question 4

How do we find out if there is a meaningful difference and accept alternative hypothesis?

Answer 4

• Firstly, assume the null hypothesis (H0) is true, so assume there is no difference between scores, the score is inside the normal distribution and any difference is due to individual differences
• Under this assumption, calculate how probable it is to get the score as extreme as the patient or observed score or more extreme than this
• If the probability is very low then reject null hyp and accept alternative
• If the probability is not that low then keep the null hyp

Question 5

How to workout probability of getting a certain score

Answer 5

• Work out Z score first so Z = (x - mean)/SD
• The Z score show how far the given score deviates from the mean
• Create distribution of Z scores on SPSS and find P value or significance value > x by 100 and this is the percentage of the probability of getting that score
• E.G: Z=(28-50)=22/10= -2.2 (2.2 SD’s lower than mean)
• Table entry shows percentage of results to the left of the Z score (less than -2.2)
• P value on table entry shows 0.0139 > x100 = 1.39% > 1.39% of people got 28 or less

Question 6

Significance threshold for hypothesis testing

Answer 6

• Alpha level for significance or p is 5% or 0.05
• If p value is less than 5% or 0.05, we reject the null hyp and accept alternative hyp
• p<0.05

Question 7

What are critical values?

Answer 7

• Critical values are real life scores which are at a threshold or cut off point for statistical significance. so if you score less than a certain cut off point that is significantly less than the pop or if you score higher than cut off point that is significantly higher

Question 8

Working out critical values

Answer 8

• Work backwards from Z score table
• We are working from 0.05 because this is the point of significance > where is this boundary + what Z score would give a probability of 0.05?
• Table entry on SPSS will show the Z score at 5% which is a critical z-score so any less/more depending on the question will be significant
• use - or + depending on if we are interested in a critical value for what is significantly less (-) or more (+)
• Find critical value of real score (not z) by going backwards so Z=(critical value-mean)/SD > backwards to find critical value so Z score x SD and then mean - z score = critical value.
• e.g: z score associated with 5%= -1.645 > -1.645 (Z) = critical v-50(mean)/10(SD) > -1.645x10= -16.45 > 50–16.45= 33.55 (critical v) > 33.55 is 5% score

Question 9

Type I error

Answer 9

• Accepting our alternative hyp when we should accept our null hypothesis > we say there is a significant difference from the distribution when there isn’t
• Happens more when alpha level is higher like 0.10 or 10% because that means we are only 90% sure we are correct.
• If alpha level is 5% we are 95% sure we are correct
• But making alpha level smaller increases likelihood of type II error

Question 10

Type II error

Answer 10

• Accepting our null hyp when we should accept or alternative hyp
• Saying there is no significance when there actually is
• Happens more if alpha level is 0.01 or 1% because it is difficult to be correct 99% of the time.
• Type I and II errors are intrinsically linked > as one increases (greater likeliness of type I) the other decreases (lower likeliness of type II) + vice versa

Question 11

Directional/one tailed hypothesis

Answer 11

• Suggests there will be a direction in the difference in results + is used when prior research indicates this.
• One tailed because it should go in one way
• Alternative directional hyp e.g: “The patient’s score will be lower than the scores of healthy controls.”
• Null hyp e.g: “The patient’s score does not differ from the scores of healthy controls.”
• Null hyp doesn’t differ regardless of direction

Question 12

Non-directional/two tailed hypothesis

Answer 12

• There is no direction in research and can go either way which is why its called two tailed
• Non directional alternative hyp: “The patient’s score is different from the scores of healthy controls.”
• Null hyp: “The patient’s score does not differ from the scores of healthy controls.”
• Null hyp doesn’t differ regardless of direction

Question 13

Statistical inference

Answer 13

• When we do research we don’t refer to pop as a whole as it is almost impossible but we gather a sample from target pop (e.g: target pop is UoB students + take data about this pop from a sample of 20 ppl)
• Can take mean and SD from sample and try generalise it to the wider population
• We make inferences about the sample to apply to the wider pop > bigger the sample the better the inference as its more representative > can see how similar the sample is to population
• Cannot be 100% sure the mean + SD from sample resemble the population but can find probability of being correct