This is a detailed summary of the Correlational Research Methods course. It includes notes from the slides together with extra explanations from the book and tutorials.
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introduction to
Correlational Research Methods
This summary is based on lecture slides, knowledge clips, additional explanations from tutorials and
recommended literature
Laura C. Correlational Research Methods/ Tilburg University/’23-‘24 ~1~
, Introduction to correlational research
Aspects of empirical research
Sampling designs
- simple random sampling: every member in the population has an equal chance to
be sampled
-stratified sampling: the population is
divided based on certain criteria (=strata);
then, from each stratum a random sample
is selected
-convenience sampling: the sample is
made of people who are readily available
(family/friends of the researchers,
students at X university, etc)
Descriptives
- descriptives= ways we use to describe the data we have
e.g: to summarize the data we can look into:
measures of central tendency:
mean
median (the score that separated the higher half of data from the lower half)
mode (the score that is observed most frequently)
measures of dispersion (highlight the differences):
∑(𝑋−𝑀)2
variance; 𝑠 2 = 𝑛−1
∑(𝑋−𝑀)2
standard deviation; 𝑠 = √𝑠 2 = √ 𝑛−1
Inferential statistics
- inferential statistics is used to draw conclusion about a population based on the
information from a sample
- two procedures are popular when it comes to inferential statistics:
null hypothesis testing (H0 testing)
confidence interval estimation
null hypothesis testing (H0 testing) step by step:
1. formulate the null and alternative hypothesis (H0 and H1)
2. set a decision rule
3. obtain the t-value and the p-value from the output
(p-value= the probability under the assumption of no effect or no difference (null hypothesis), of
obtaining a result equal to or more extreme than what was actually observed)
Laura C. Correlational Research Methods/ Tilburg University/’23-‘24 ~2~
, 4. make the decision: reject or keep the null hypothesis
example: does the average exam grade in the population (μ) equals 6.0?
1. H0: μ=6.0 and H1≠6.0
2. the decision rule:
if the p-value < α we reject H0
e.g., if p<.05, we reject H0
output:
3. we have the t-value and the p-value from the output
t(29)=1.815, p=0.074
4. decision: because p>0.05 we keep the null hypothesis = the average exam score is not
statistically different from 6.0
Measurement levels
classical measurements levels:
o nominal scale
o ordinal scale
o interval scale
o ration scale
• nominal scale- consists of a set of categories that have different names; measurements on
a nominal scale label and categorise observations but do not make any quantitative
distinctions between observations
Laura C. Correlational Research Methods/ Tilburg University/’23-‘24 ~3~
, examples of nominal scales include classifying people by race, gender, or
occupation
the measurements from a nominal scale allow us to determine whether two
individuals are different, but they do not identify either the direction or the
size of the difference
• ordinal scale- consists of a set of categories that are organised in an ordered sequence;
measurements on an ordinal scale rank observations in terms of size or magnitude
e.g., an ordinal scale consists of a series of ranks (first, second, third, and so on)
like the order of finish in a car race
with measurements from an ordinal scale, you can determine whether two
individuals are different, and you can determine the direction of difference;
however, ordinal measurements do not allow you to determine the size of the
difference between two individuals
e.g.,: in a NASCAR race, the first-place car finished faster than the second-
place car, but the ranks don’t tell you how much faster
• interval scale- a scale that consists of ordered categories that are all intervals of precisely
the same size; equal differences between numbers on the scale reflect equal differences in
magnitude; the zero point on a scale is arbitrary and does not indicate a zero amount of
the variable being measured
e.g., temperature and IQ scores (a temperature of 0º Fahrenheit does not mean that
there is no temperature, and it does not prohibit the temperature from going even
lower; an IQ score of 0 does not mean one has no intelligence)
• ratio scale- it is an interval scale with the additional feature of an absolute zero point; the
existence of an absolute, non-arbitrary zero point means that we can measure the absolute
amount of the variable; that is, we can measure the distance from 0
e.g., weight, income
-in the context of CRM, we distinguish between categorical (discrete) and
quantitative variables (continuous):
a discrete variable consists of separate, indivisible categories, often whole numbers that vary
in countable steps; no values can exist between two neighbouring categories
o e.g., the number of children a family has, how many students attend a class
each day, classifying people by gender or occupation, etc.
for a continuous variable, there are an infinite number of possible values that fall between
any two observed values; a continuous variable can be divisible into an infinite number of
fractional parts
Laura C. Correlational Research Methods/ Tilburg University/’23-‘24 ~4~
Correlational research- investigating the relationship between variables
e.g., heights+ shoe size, amount of hrs studies + exam grade
Pearson’s correlation coefficient
- Pearson’s correlation coefficient describes a linear association
- ρ (rho)= correlation in the population
r= correlation in the sample
- -1 ≤ r ≤ 1 (r can take any values between -1 and 1)
- if r =o => there’s no linear association (but a non-linear association cannot be
excluded!)
Laura C. Correlational Research Methods/ Tilburg University/’23-‘24 ~5~
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