Measurement and sampling theory

Question 1

What are inferential statistics?

Answer 1

“Allows one to draw conclusions or inferences from data. This
means coming to conclusions (such as estimates, generalisations,
decisions, or predictions) about a population on the basis of data
describing a sample.”

Question 2

What is a population?

Answer 2

A group of experimental data, persons, etc. A population is built up of elementary units, which cannot be further decomposed.

Question 3

What is a population total?

Answer 3

Is the sum of all the elements in the sample frame.

Question 4

What is a population mean?

Answer 4

Is the average of all elements in a sample frame or population

Question 5

What is a sample?

Answer 5

Is segment of the population

Question 6

What is a sampling frame?

Answer 6

is a list of all the units in the population from which the sample is selected

Question 7

What is a representative sample?

Answer 7

A sample that accurately reflect the population

Question 8

What is a probability sample?

Answer 8

Random selection procedure, each unit equal chance of selection

Question 9

What is a non-probability sample?

Answer 9

Sample not selected using random selection method

Question 10

What is a normal distribution?

Answer 10

A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Question 11

What are standard deviations?

Answer 11

A measure of the amount of variation or dispersion of a set of values.
• ~68% within 1 SD
• ~95% within 2 SD
• ~99% within 3 SD

Question 12

Explain the process of inferences in quantitative research

Answer 12

• Sample taken from the population
• Produces random sample
• Inference is then made from random sample about the population

Question 13

What is the definition of inferential statistics?

Answer 13

“Allows one to draw conclusions or inferences from data. This means coming to conclusions (such as estimates, generalisations, decisions, or predictions) about a population on the basis of data describing a sample.”

Question 14

How and why do we select participants for a study?

Answer 14

• Select to reduce bias
• Select to cover all relevant groups adequately
• Select to be logistically feasible
• Select to have enough statistical power to test hypotheses

Question 15

Why do we need to sample?

Answer 15

• Human Variability
• Sample likely to differ from population
• Confidence in generalisation?
• Want to make claims about general population

Question 16

What is an example of selection bias?

Answer 16

• Women have been excluded from sport research

* Less than 40 per cent included women

Question 17

What is a sampling error?

Answer 17

• The error that occurs when you analyse a sample instead of a population
• Best designed research is assumed to be affected by sampling error, also known as random error

Question 18

What do you need to do when selecting a sample?

Answer 18

• Population characteristics must be clearly defined

* A poorly defined population or its parameters leads to weak sample data

Question 19

What does being representative of a sample involve?

Answer 19

It is important that the sample is representative of the

population

Question 20

What three types of errors are involved in sampling?

Answer 20

1. Sampling variability
2. Sampling error
3. Non‐sampling error

Question 21

What is a sampling variability error?

Answer 21

Different samples from the same population do not always produce the same mean & SD e.g. class heights

Question 22

What is sampling error?

Answer 22

The mean of a sample will not be the same as the mean of a population; can be minimised but not eliminated using good selection criteria

Question 23

What is a non-sampling error?

Answer 23

Errors not connected with the sampling method e.g.
• Questions asked in a bad or leading way
• Measurement error
• Errors made in coding or recording data

Question 24

What is a random sample? and key aspects

Answer 24

• Everybody in the population has the same chance of being selected
• Allocate everybody or every location a number
• Use a random number generator to generate numbers
• Pull out of a hat (need a good way of mixing numbers to avoid bias)
• SPSS can generate random samples

Question 25

What are stratified random samples?

Answer 25

A method of sampling that involves the division of a population into smaller groups known as strat

Question 26

What needs to be considered when deciding how large a sample should be?

Answer 26

• Populations with greater variability need a larger
sample size
• Greater precision requires larger sample size BUT not
a proportional increase in precision with sample size though!
• Needs to fit with study budget & resources
• Use Gpower and speak with supervisor

Question 27

What are sample means?

Answer 27

• Means of different samples
• The distribution of sample means from a population will be approximately normally distributed
• A reasonable number of sample means the mean of the sample means will approximately equal the population mean
• Narrower normal distribution than the whole population

Question 28

What is the distribution of sample means?

Answer 28

• Sample means form a normal distribution
• It looks the same as the normal distribution for individuals within a group
• Different in one crucial respect
• Each sample has a mix of scores and high scores tend to be cancelled out by low ones
• The standard deviation (SD) of sample means around the mean of the sample means is therefore smaller than the
SD of the actual scores around the population mean

Question 29

When does an infinite number of sample means form a normal distribution?

Answer 29

• If the sample size is large or

* if the population is normally distributed

Question 30

What is central limit theorem?

Answer 30

• Samples of size n selected from a population will have:
• Approximately normally distributed means
• Mean of sample means = population mean

Question 31

How can samples be made more reliable?

Answer 31

• Use an appropriate, accurate and up‐to‐date sampling frame
• Randomise samples
• Adequately powered ( a priori sample size calculation)
• Recruit a sufficient number of participants/subject