RM5 - Sampling

p-value

probability

0-1

p-value: statistically significant

less than or equal to 0.05

Type 1 vs Type 2 error

Type 1: thinking there is a difference when there isnt one

Type 2: thinking there was no difference when there actually was one

Statistical Power

The power of any test is the ability to detect a difference when one exists

bigger sample size = find smaller differences with greater confidence.

Parametric tests

Tests with data that have normal distributions/can be assumed to be normally distributed

More normal distribution are more likely with…

increasing sample size

Sampling Frame

a list of all members of a population

used as a basis from which to select a sample from

Representative Sampling

Reflects the population.

If a sample is representative, we can make generalisations about it to the population.

a random sample, estimates produced by the sample will be close to the true population figure.

Sampling Error

The chance difference between the sample and the population

Sampling Methods

Probability sampling methods

• each member of a population has an equal chance of being selected

Non-probability sampling methods

• each member of the population does not have an equal chance of being selected.

Types of Probability Sampling

• Simple random sampling

  • “Lottery”  

• Systematic sampling

  • Use of sampling interval e.g. every 10th subject

• Stratified random sampling

  • Structure population into known sub-sets (eg. male and female) and random sample from each group

• Cluster sampling

  • Divide population into clusters (e.g. 1st 100, 2nd 100 etc.) and sub-sample from each cluster

Types of Non-Probability Sampling

• Incidental (coincidence) sampling, e.g. Pharmacy customers.

• Quota sampling, e.g. Opinion polls,

  • Quotas set on gender, age, socio-economic group etc.

• Purposeful sampling, e.g. the “typical” GP surgery.

• Snowball sampling

  • used for inaccessible groups, e.g. drug misusers, where contact with one client can lead to contact with another

What does the type of sampling chosen depend on?

• cost

• required accuracy

• the nature of the research and what is possible.

Central Tendency measures

mean, mode and median

Measures of dispersion

refer to how closely the data cluster around the measure of central tendency:

• the variation ratio

• the inter-quartile range

• the standard deviation

Levels of Measurement

• Categorical (Nominal)

• Ordinal (Ranked)

• Interval / ratio

Nominal Data

• Based on being a member (or not) of a category e.g. bipolar or schizophrenic, eye colour

• All measurements within group are equivalent

Ordinal Data

• Based on ranks or order

• Only know that one is more than another but not the differences between them

• e.g. scale of pain +++ > ++ > +

Interval Data

• Equal intervals between values (e.g., the difference between 10°C and 20°C is the same as between 30°C and 40°C).

• No absolute zero – zero does not mean "none" (e.g., 0°C doesn't mean "no temperature")

Ratio Data

• Equal intervals like interval data

• Has a true zero – zero means "none" (e.g., 0 kg = no weight)

Types of Statistics

• Descriptive Statistics

• Measures of Association

• Inferential Statistics

Descriptive Statistics

concerned with the presentation, organization and summarization of data

Measures of Association

How strong is the relationship between two variables

Inferential Statistics

• Allow us to generalise from our sample of data to a larger group of subjects:

• Used to test and examine relationships between data parameters

Standard Error of Mean

shows how close mean scores from repeated samples will be to the true population mean (assume random sampling)

What is Fisher’s Exact Test used for?

Small sample sizes (n < 20) with nominal data.

When is the Wilcoxon Test appropriate?

For ordinal data or small sample sizes (n < 25); especially with paired or matched samples when normality cannot be assumed.

When do you use the Mann–Whitney U Test?

For ordinal data in unmatched or unpaired groups; similar purpose to Wilcoxon but for independent samples

What is the Kruskal–Wallis test used for

Comparing more than two independent (unmatched) groups with ordinal or non-parametric data

What is the Friedman test used for?

Comparing more than two matched groups with ordinal or non-parametric data

What type of data is needed for a t-test?

Interval (or ratio) data that is normally distributed.

What's the difference between a paired and unpaired t-test?

• Paired t-test: Same subjects under two conditions (matched data)

• Unpaired t-test: Different subjects in two groups (independent samples)

When is ANOVA used?

To compare means from more than two groups with normally distributed interval data.

What are post-hoc tests used for in ANOVA?

To control for Type I error when making multiple pairwise comparisons.