Lecture 2 What is p?

Question 1

Try to draw a conclusion about a population as you cant measure everyone form the population - how should you draw a conclusion?

Answer 1

Measure a sample then get to conclusions about the population using the samples

Question 2

null hypothesis

Answer 2

A null hypothesis is a type of hypothesis used in statistics that proposes that there is no difference between certain characteristics of a population (or data-generating process).

For example, a gambler may be interested in whether a game of chance is fair. If it is fair, then the expected earnings per play come to 0 for both players

If the average earnings from the sample data are sufficiently far from zero, then the gambler will reject the null hypothesis and conclude the alternative hypothesis

opposite to alternate hypothesis

Question 3

what is the p-value?

Answer 3

The probability value (p-value)

the p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct

Question 4

Normally we reject the null hypothesis if the p-value is less than what?

Answer 4

0.05 (i.e. 5%)

Such a result is called statistically significant

Question 5

If 3 people preferred A and 11 B …? - would we reject the null hypothesis?

Answer 5

The probability value is 0.0576 (>0.05)

This is still quite an unlikely finding to happen by chance – it’s borderline

But by convention this would not be regarded as statistically significant and we would not reject the null hypothesis

Conclusion: there is no evidence that the two drugs have different effects in the population

Question 6

• We don’t often know about a whole population
• We can ‘guess’ what the population looks like if we have a _______
• But different samples will give different ______

Answer 6

sample

results

Question 7

•The standard deviation of the sampling distribution of the sample mean is known as what?

Answer 7

the standard error of the mean

Question 8

what is SE?

Answer 8

• The SE provides a measure of how far from the true population value ANY estimate is likely to be (the precision). We’ve just considered the SE for the mean
• We can see this is related to sample size. The larger the sample the more precise this estimate

Question 9

• The standard deviation and the standard error of the mean are NOT the same
• SD measures the variation _______ a sample and should be quoted with its sample mean
• SE measures the _______ of the sample mean with respect to the population mean (or can be compared to another sample mean)

How precise is that sample mean in respect to the population mean, larger the sample then closer it will be to the true population mean

Answer 9

within

precision

Question 10

what is CI?

Answer 10

• Using this variability in the sample data we can calculate a range of values (interval) in which we would expect the true population value to lie
• This will vary in width depending on how confident we want to be that we have included the true population parameter value
• Generally we use the 95% CI

Question 11

•Area under the curve represents probabilities

Easier to work with Z-scores - wat are they?

Answer 11

how many standard deviations a particular value is from the mean value

•The probability between any Z-scores points is calculated as the area under the curve