One sample t tests

Question 1

One-sample hypotheses

Answer 1

-Tests whether the mean of a sample is different to a pre specified comparison value
e.g. attendance in class is more than 80%.

Question 2

T test equation

Answer 2

t value = mean of observed data - comparison value/ SEM

Question 3

When does t test value grow

Answer 3

t-value grows as difference between observed and comparison gets bigger - top of fraction gets larger whilst bottom stays the same

Question 4

When does t test value shrink

Answer 4

t-value shrinks as variance of observed data gets bigger - bottom of fraction gets larger, top remains the same

Question 5

What did we do before t tests

Answer 5

Estimate of SD is more unreliable than estimate of mean so original answer was to restrict analyses to very large samples where we can be confident in SD

Question 6

Student t test

Answer 6

camping distribution of t-values is t-distributed - not normally distributed
accounts for additional uncertainty in smaller samples with wider tails