Summary Part B Statistics 1 (Applying Statistics in Behavioural Research)
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Course
Statistics 1 (SOWPSB1RS10N)
Institution
Radboud Universiteit Nijmegen (RU)
Book
Applying statistics in behavioural research
This document contains the summary of part B of the statistics 1 course of B1 psychology. It was written in 2023 and based on the book Applying Statistics in Behavioural Research by Jules L. Ellis.
Summary Part C Statistics 1 (Applying Statistics in Behavioural Research)
Summary Part A Statistics 1 (Applying Statistics in Behavioural Research)
Summary Statistics 2 Part B
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Statistics 1 (SOWPSB1RS10N)
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Statistics 1 Summary Part B
(applying statistics in behavioural research)
Basic report of association between two quantitative variables:
- Design, degree of control, and name of the analysis
- Scatter plot with regression line
- Regression coefficients (slope and intercept) and correlation
- List of influential observations
- Indication of linearity
Design
The design specifies the variables that you report about and their (hypothetical causal) role.
Independent variable (x) = the variable that is supposed to be the cause
Dependent variable (y) = the variable that is supposed to be the consequence
The design contains (for both variables):
- the role of the variable (independent or dependent)
- the name of the variable
- the measurement level of the variable (qualitative or quantitative)
- the possible outcomes or levels of the variable
Example:
Dependent variable = grade after studying summary (quantitative, 1-10)
Independent variable = grade before studying summary (quantitative, 1-10)
Degree of control
For the independent variable, state whether it is experimental or not. It is experimental if it is
actively manipulated and randomised.
Name of the analysis
The analysis that is done in this basic report is a simple linear regression analysis. It is called simple
because there is only one independent variable.
Scatterplot
In a scatterplot, each subject is represented by a dot. The score of the independent variable is used
as the horizontal coordinate (x) of this dot. The score on the dependent variable is used as the
vertical coordinate (y) of a dot.
Regression coefficients and correlation
The (linear) regression line is a straight line through the dots in the scatterplot. The line can be
described by the equation:
Y = a + bX
Where:
a and b are regression coefficients
a is the intercept, which is the height at X = 0
b is the slope, which tells you how much the line increases if X increases by 1 unit (1 to the left, ?
upwards)
, The correlation (r) indicates the direction and the strength of the association between the variables.
The correlation is a number between -1 and 1.
You can compute the regression coefficients with the statistical functions of a calculator during the
exam.
Regression line
Now that you have a and b, you can use Xmin and Xmax to calculate the coordinates of the two ends
of the regression line.
Example:
a = 2.75
b = 0.55
so then the formula is
Y = 2.75 + 0.55X
Then you fill in the formula with Xmin (3) and Xmax (7)
Y = 2.75 + 0.55*3 = 4.4
Y = 2.75 + 0.55*7 = 6.6
So, the coordinates that you use to draw the regression line are
(3, 4.4) and (7, 6.6)
Find the coordinates in the graph and draw a line between them.
Influential observations = observations that have a large impact on the correlation
When in doubt whether a certain point is influential, compute r 2 with, and without that point. If the
difference is larger than .20, the point is influential.
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