What are the 3 types of quantitative psychological research?
What is the goal of psychological research?
When we conduct a psychological research project, our aim is to make inferences (in other words, suggestions or claims) about a population. Put simply, we want to say something about a population.
What is a population?
What are mean scores indicators of?
In quantitative terms, mean scores will be our indicator of what is typical. We know the population mean in this example. We could compare our sample mean to this value to assess evidence for a difference.
Based on the results of this comparison, we will make an inference about the population of psychology students and whether or not it is likely to differ from the general population in intelligence.
Summarise inference
Describe distributions of data
When measured, constructs takes on different values for different people in a sample.
Collectively, those different values form a distribution of data, which can be described in terms of central tendency and variability.
What are mean and standard deviation measuring in this subject?
Mean = measure of central tendency
Standard Deviation = measure of variability
What is a normal shape?
Most of the people are in the middle. The peak of the graph.
Relatively fewer people are on the outsides. The tails of the graph.
What is the 2s rule of thumb?
In a distribution with a normal shape, 95% of scores fall within approximately 2 standard deviations (s) of the mean.
We can think of those scores inside 2 standard deviations (s) of the mean as being typical. They are expected as they occur frequently in this distribution.
We can think of those scores outside 2 standard deviations (s) of the mean as being extreme. They are not expected as they occur infrequently in this distribution.
How is the 2s rule of thumb applied?
Double Standard deviation, then add and subtract it from the mean to get critical limits for determining what is typical or extreme
To apply our rule of thumb:
m = 46.87
s = 4.84 × 2 = 9.68
Lower limit
46.87 - 9.68 = 37.19
Upper limit
46.87 + 9.68 = 56.55
What is a z score?
A z-score, also known as a standard score, measures how many standard deviations a data point is from the mean of a dataset
How can we convernt a raw score to z score?
We can also convert raw scores into z scores to get a better idea of where in the distribution those scores fall. Let’s say we get a score of 68 on an exam. We may be disappointed to have scored so low, but perhaps it was just a very hard exam. Having information about the distribution of all scores in the class would be helpful to put some perspective on ours. We find out that the class got an average score of 54 with a standard deviation of 8. To find out our relative location within this distribution, we simply convert our test score into a z score.
z= X−μ/σ = 68−54/8 =1.75
What is the formula for converting a z score to x score for a population?
x=zσ+μ
What is the formula for converting a z score to x score for a sample?
x=zs+M
Example of turning raw scores into z scores
Notice that these are just simple rearrangements of the original formulas for calculating z from raw scores.
Let’s say we create a new measure of intelligence, and initial calibration finds that our scores have a mean of 40 and standard deviation of 7. Three people who have scores of 52, 43, and 34 want to know how well they did on the measure. We can convert their raw scores into z scores:
z = 52-40/7 = 1.71, z = 43-40/7 = 0.43, z = 34-40/7 = -0.80