L9 - Hypothesis testing

What is the null hypothesis?

• Fall back option

• Usually no difference, relationship or interest.

• Boring option

What is the alternative hypothesis?

is the opposite:

the one we are hoping to get evidence to support

‘more interesting option’

What are two contrasting hypothesis for an accusation in court?

Null Hypothesis (H0 ) – the defendant is innocent

Alternative Hypothesis (H1 ) – the defendant is guilty

Will continue to believe the H0 until sufficient evidence against it

‘Sufficient evidence’ means a probability of less than 5% that you can continue to believe H0 .

What is a type 1 error?

When you get false positive results

e.g You conclude that the drug intervention improved symptoms when it actually didn’t These improvements could have arisen from other random factors or measurement errors

What is a type 2 error?

When you get false negative results

e.g You conclude that the drug intervention didn’t improve symptoms when it actually did Your study may have missed key indicators of improvements or attributed any improvements to other factors instead

What is a t-test?

• used to compare the means of sets of data

• see if they are statistically significant

What is the degrees of freedom?

is the number of independent pieces of information used to calculate a statistic.

It’s calculated as the sample size minus the number of restrictions.

V = n₁ + n₂ - 2

n₁ = group 1

n₂ = group 2

for unpaired : n-1

What is the standard error?

indicates how different the population mean is likely to be from a sample mean. I

t tells you how much the sample mean would vary if you were to repeat a study using new samples from within a single population

Why is the standard error important?

can estimate how representative your sample is of your population and make valid conclusions

What is the difference between standard error and standard deviation?

standard deviation = variability within a single sample

Standard error = estimates the variability across multiple samples of a population