Normal Distribution & Inferential statistics

Question 1

Why is normal distribution important?

Answer 1

basis for statistical inference

good description of distribution for commonly studied quantitate variables

determines choice of statistical method for data

Question 2

Normal distribution characterisations

Answer 2

mathematically defined theoretical distribution

symmetrical bell-shaped curve

approx. describes many quantitative variables eg height, birthweight

Question 3

What does knowing the data is normally distributed & having the mean & SD give us the ability to do?

Answer 3

Calculate the percentage of people that score below/above any value or within a range

Question 4

Normal distribution common characteristic values

Answer 4

68% of scores with 1 SD

95% within 1.96 SD

99.7% within 3 SD

Question 5

How is 95% range for normally distributed data calculated?

Answer 5

lower bound of range = mean - 1.96 x SD

upper bound = mean + 1.96 x SD

Question 6

Population, Sample & data definitions

Answer 6

Population - total number of people with a certain characteristic

Sample - the people from population taking part in study

Data - information from the sample population

Question 7

Parameters & estimates explained

Answer 7

data from sample is used to obtain estimates of the true values of parameters (true mean/values)

eg % of people with type II diabetes

Question 8

Why do we need statistical methods?

Answer 8

the answer provided by sample data is rarely the correct answer in the population

uncertainty due to - variability & the sample being a subset of the pop

Question 9

What are descriptive statistics?

Answer 9

describing & summarising data from a sample

Question 10

What are inferential statistics?

Answer 10

using sample data to make inferences about characteristics & relationships in the wider population

Question 11

What are standard errors working out?

Answer 11

How close the estimate from the sample data is to the parameter value (truth) if the study was repeated with different samples

Question 12

How can standard error be decreased?

Answer 12

using a larger sample sizes as this gives us more confident estimate

Question 13

Why are inferential statistics required?

Answer 13

we cant draw conclusions about the population using just the mean difference from a sample

Question 14

What does a 95% Confidence interval show?

Answer 14

95% certain that something in the population is true (giving a range of data from sample study)

Question 15

Why is a range of data from sample study given when using 95% confidence interval?

Answer 15

Because we don’t know the true population parameter value but can be 95% sure the parameter value will be within the given range

Question 16

95% confidence interval definition

Answer 16

the range of values within which we are 95% certain the true parameter (mean) lies)

Question 17

Is a narrow or wider Confidence interval (CI) better

Answer 17

narrower because we are then more certain about what the truth is

Question 18

What does p-value show?

Answer 18

values between 0-1, the lower the value the greater the chance of evidence contradicting the null hypothesis

Question 19

What is hypothesis testing

Answer 19

Concerned with what the true answer isn’t

assessing the extent to which the sample estimate disproves the null hypothesis

Question 20

What is a null hypothesis

Answer 20

The most boring truth - that nothing is different between control & intervention groups in a test

eg Mean systolic blood pressure in diabetics is the same as in the healthy population

Question 21

What is a alternative hypothesis

Answer 21

the opposite of the null hypothesis

That there is a significant difference between the two sample groups

Question 22

Why is a 0.05 p-value significant?

Answer 22

is used as a threshold to reject the null hypothesis

below = reject
above = not enough data to reject

Question 23

P-value examples

> 0.001 = ?

0.05 = ?

> 0.1 = ?

Answer 23

< 0.001 = strong evidence against null hypothesis

0.05 = moderate

> 0.1 = little

Question 24

What does a small p-value not prove?

Answer 24

That there is a large difference between the groups just shows that there is some difference

Question 25

Why are CI’s better than P-values (hypothesis testing)

Answer 25

because they tell you something about what the true answer in the population is

However CI can not always be calculated

Question 26

95% CI to 0.05 P-value link?

Answer 26

If 0 (null hypothesis value) is within 95% CI = P-value > 0.05

if it is excluded = < 0.05 p-value

if it is either the upper or lower boundary = 0.05 p-value