Measurement and sampling theory Flashcards
What are inferential statistics?
“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.”
What is a population?
A group of experimental data, persons, etc. A population is built up of elementary units, which cannot be further decomposed.
What is a population total?
Is the sum of all the elements in the sample frame.
What is a population mean?
Is the average of all elements in a sample frame or population
What is a sample?
Is segment of the population
What is a sampling frame?
is a list of all the units in the population from which the sample is selected
What is a representative sample?
A sample that accurately reflect the population
What is a probability sample?
Random selection procedure, each unit equal chance of selection
What is a non-probability sample?
Sample not selected using random selection method
What is a normal distribution?
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.
What are standard deviations?
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
Explain the process of inferences in quantitative research
- Sample taken from the population
- Produces random sample
- Inference is then made from random sample about the population
What is the definition of inferential statistics?
“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.”
How and why do we select participants for a study?
- 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
Why do we need to sample?
- Human Variability
- Sample likely to differ from population
- Confidence in generalisation?
- Want to make claims about general population
What is an example of selection bias?
- Women have been excluded from sport research
* Less than 40 per cent included women
What is a sampling error?
- 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
What do you need to do when selecting a sample?
- Population characteristics must be clearly defined
* A poorly defined population or its parameters leads to weak sample data
What does being representative of a sample involve?
It is important that the sample is representative of the
population
What three types of errors are involved in sampling?
- Sampling variability
- Sampling error
- Non‐sampling error
What is a sampling variability error?
Different samples from the same population do not always produce the same mean & SD e.g. class heights
What is sampling error?
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
What is a non-sampling error?
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
What is a random sample? and key aspects
- 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
What are stratified random samples?
A method of sampling that involves the division of a population into smaller groups known as strat
What needs to be considered when deciding how large a sample should be?
• 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
What are sample means?
- 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
What is the distribution of sample means?
• 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
When does an infinite number of sample means form a normal distribution?
- If the sample size is large or
* if the population is normally distributed
What is central limit theorem?
- Samples of size n selected from a population will have:
- Approximately normally distributed means
- Mean of sample means = population mean
How can samples be made more reliable?
- 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
