Using statistics to infer

Question 1

Typical structure of a research report in quantitative educational research

Answer 1

Example Headings and Sub-headings:
Introduction
Literature review
Methods
- Research design
- Participants/ sample
- Measures
- Analytic approach
Results
- Answering research questions
Discussion and conclusion
- Making inferences about the broader population
References

Question 2

what is the aim of quantitative research?

Answer 2

Quantitative research aims to find out new knowledge about a group (population) by only considering some of them (sample)
Infer something about the broader group (population) based on research obtained from the limited numbers that have been investigated (sample)
From the sample, we must calculate statistics to give us information about the broader population

Question 3

what must researchers think about when dealing with a sample of a population?

Answer 3

Researchers must think about how they are going to collect data from their sample and think about whether their sample is representative of their population

Question 4

why choose samples?

Answer 4

Samples are more feasible and less costly and less time-consuming

Question 5

statistical symbols for samples:

Answer 5

frequency: n
mean: M or x̅
standard deviation: SD or s

Question 6

statistical symbols for population:

Answer 6

frequency: N
mean: μ
standard deviation: σ

Question 7

what does inferential statistics do?

Answer 7

gathers information from a sample and makes inferences about the wider population

Question 8

why can we never be 100% sure about the conclusions we make when taking a sample?

Answer 8

When we have information from a sample, we can never be 100% sure that the conclusions we draw from this information will also be true in the broader population
There will always be a chance that our sample may not represent our population
How sure can we be that the statistics we generate from a sample also tell us something about the population?

Question 9

what are the two ways that researchers typically represent uncertainty in their data?

Answer 9

point estimates and interval estimates

Question 10

what are point estimates?

Answer 10

A ‘best guess’ of the value in a population that comes with an estimate of how certain this estimate is

Question 11

what are interval estimates?

Answer 11

An estimate of the range of likely values within the population

Question 12

standard error and point estimates

Answer 12

This is an estimate of uncertainty that links the statistics we get from samples to the ‘best guesses’ that we make as regards the same statistic in the broader population. It is used with Point Estimates.
A ‘standard error’ (SE) estimates how accurate a statistic is when we generate it from a sample, but want to use it as an estimate of the same statistic in the broader population.
Smaller standard errors mean that our sample statistic is more likely to be accurate estimate of the population as there is less error
The most frequent standard error we will see is the ‘Standard Error of the Mean’ (SEM)
We can present standard errors alongside our ‘sample statistics’ when we want to make claims about the broader population when we want to make ‘inferences’.

Question 13

confidence intervals and interval estimates

Answer 13

Confidence Intervals (Cis) are examples of Interval Estimates.
They use the Standard Error to calculate a range of values that might be true in a population
In research, we commonly estimate a range of values that will give us 95% confidence
A 95% CI around a population mean = the sample Mean +/- 1.96 X the SEM