Hypothesis testing

Question 1

Sampling variability and standard errors

Answer 1

Standard deviation of the sampling distribution of the mean, measures the typical size of error between the sample mean and the (whole) population mean

This quantifying the accuracy of our sample as an estimate of the (whole) population mean, and is known as the standard error (SE) of the mean

Question 2

What is standard deviation

Answer 2

Standard deviation of a sample of observations measures how a typical observation in the sample differs from the sample mean

Question 3

What is standard error

Answer 3

The standard error quantities the typical error or difference between the mean measured in the sample and the theoretical mean in the population from which the sample was drawn
The SE indicates how accurately the sample mean estimates the population

Question 4

What is the importance of normal distribution in medical research

Answer 4

Central tendency
- crucial for interpreting and summarising large data sets e.g blood pressure readings

Statistical inference
- many statistical tests and confidence intervals assume normality

Predictive modelling
- normal distribution often used in predictive modelling and risk assessment e.g probability of disease occurrence based on various risk factors)

Quality control and standardisation
- normal distribution used in quality control process to monitor and maintain the consistency of medical tests and procedures

Question 5

Hypothesis testing

Answer 5

Null or alternative hypothesis depends on type of investigations as follows:

Types of investigation

To see whether there is a difference between two procedures
NULL
- the hypothesis says no difference

ALTERNATIVE
- the hypothesis says that there is a difference

To find out if a bold claim is true
NULL
- there is no difference
ALTERNATIVE
- drug is better or worse

Question 6

Assumptions for hypothesis testing

Answer 6

My sample is:
1. is representative
2. Is independent
3. Has homogeneous variance
4. Is normal

3/4 need to test with appropriate tools and techniques.

Question 7

Error types

Answer 7

Type 1 - if the null hypothesis is rejected when it is true and its probability is denoted by a

Type 2 - if the null hypothesis is not rejected when it is false and is probably denoted by b

The decision to reject or not to reject is based on a test statistic computed from the values of a random sample.

Question 8

P value

Answer 8

P value gives us the measurement of strength of evidence against the null hypothesis

0.05 value means that there is a 5% or 1 in 20 chance that is sample result does not represent the reality

Small p value means the null hypothesis is unlikely to be true

Question 9

Confidence interval

Answer 9

The confidence interval is the range of values, estimated from a sample whiting which the true population value is likely to be found.

95%
- draw and repeat sample 100 times
- calculate for each sample
- 95/100 intervals will contain the true population parameter