PYC3704/201/1/2021
Tutorial Letter 201/1/2021
PYC3704
Psychological Research: Early Completion
Programme (ECP).
Semester 1
Department of Psychology
• How to cope with formulas
• Feedback for assignment 01
BARCODE
,Dear Student
This tutorial letter contains:
• How to cope with formulas
• Answers and feedback for Assignment 01
1. How to cope with formulas
This is a relatively elementary introduction for those of you who find the formulas
intimidating. Other students can skip this section.
First, don’t panic. These formulas may seem scary, but they can usually be solved with a bit of careful
work. It takes concentration and attention to detail and becomes easier with practise.
A ‘formula’ is more properly referred to as an equation. This term implies that what is on the left hand side
of the formula must be set equal to what is written on the right hand side. It represents a concise description
of a calculation which you need to perform, displaying the variables you need to consider and the
relationships among them. Think of it as a system which tells you how to calculate something in a very
precise way. You have to learn how to use it, and this is something you learn by doing, not just by looking
at it.
Each symbol in such an equation represents a variable, and you need to find the current value of that
variable based on the data which you have. First you substitute the symbol with that number. Then you
have to perform the calculation, which is an arithmetic procedure, making use of operations like adding,
subtracting, division, multiplication, calculating square roots and so on (see Appendix E in the PYC3704
Guide).
Let us first consider a simple example. Look for at the formula for the mean of a sample of data (given in
Appendix C in the Guide):
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𝑥̅ = ∑𝑥
𝑛
The symbol x̄ is a conventional way to indicate a mean (some books use the symbol M for this). Each of
the symbols on the right hand side of the equation is to be replaced by a number. Σx is a conventional way
of writing ‘the sum of all the x-values’ (see Appendix E in the Guide). To do the calculation you would need
to have a set of data representing various measurements of the variable indicated by ‘x’.
So what this formula tells you is that the mean of the x-values is calculated by adding them up and dividing
the result with n (which is equivalent to multiplying the result with 1/n).
Let us test this on a small set of data (which can be regarded as different measurements of a variable ‘x’).
X 14 12 11 22 15 10 15 17 13 15
Here the sum of x would be: Σx = 14 + 12 + 11 + 22 + 15 + 10 + 15 + 17 + 13 + 15 = 144.
Because there are 10 values for x, we know that n = 10. So if we substitute this in the formula:
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, PYC3704/201
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𝑥̅ = ∑𝑥 = × 144 = 14.4
𝑛 10
For a more advanced example, let us calculate the value of the sample standard deviation, usually
indicated by s. The formula for s (given in Appendix C in the Guide) is as follows:
∑(𝑥 − 𝑥̅ )2
𝑠= √
𝑛−1
This formula describes the calculation process which you need to perform to get the standard deviation of
the sample of data above. It tells you that you have to subtract the mean (x̄) from each value of x, square
the result, and add these together. This total you divide by n-1. The square root (√) of this result then gives
you the value of s. If you do not take the square root here, you will in fact end up with s2, which is referred
to as the sample variance.
A good way to calculate a somewhat complicated sum like Σ(x - x̄)2 by hand is to first arrange the data in
a table, like below:
Measurement
x x - x̄ (x - x̄)2
no.
1 14 -0.4 0.16
2 12 -2.4 5.76
3 11 -3.4 11.56
4 22 7.6 57.76
5 15 0.6 0.36
6 10 -4.4 19.36
7 15 0.6 0.36
8 17 2.6 6.76
9 13 -1.4 1.96
10 15 0.6 0.36
Sum Σ 144 0.0 104.4
The second column presents the values of x, and the third column shows the values of each x with the
mean (which we calculated above as x̄ = 144.4) subtracted from that value of x. The fourth column gives
the squares of each of these new values (that is, the column 3 values multiplied with themselves). We are
interested in the sum of these (usually referred to as the sum of squares), which adds to 104.4, indicated
in the bottom row of the table. This result therefore indicates that Σ(x - x̄)2 = 104.4.
When you use tables like this, make sure you understand how to use this notation. For example, you have
to know that if you were working with two variables x and y, Σxy and ΣxΣy will not produce the same result
(see Appendix E in the PYC3704 Guide, especially p. 176).
To determine the standard deviation, we should substitute the sum of squares we calculated above in the
formula for s, as follows:
∑(𝑥−𝑥̅ )2 104.4 104.4
𝑠= √ =√ =√ = √11.6 = 3.406 (rounded off).
𝑛−1 10−1 9
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, Note how it takes many words to explain this process, and that it can be difficult to express it in a very
exact way in words. The formula is a very concise and exact expression of the process, which is why we
need to use it.
2. Feedback for Assignment 01 of the first semester of 2021
For your convenience, each question is given followed by the appropriate answer and an explanation
of the correct response. Work your way systematically through these, comparing it with your own
answer. Even if you chose the correct alternative, you may find that the explanations we give are useful.
Try to understand the explanations. Many of the items require insight, not just factual knowledge. You
will not pass this course if you try and memorise the questions and answers!
Assignment 01
Semester 1 Closing date: 17/05/2021 798359 (Semester 1)
Question 1
The goal of quantitative research in psychology is best described as aiming to - - - - -.
1. develop appropriate statistical tests which can be used to determine the relationships among
psychological variables that occur at a level greater than chance
2. develop theories that helps us to explain human experience and behaviour
3. formulate clear hypotheses based on insights about human experience and behaviour
4. convert theoretical constructs into measurable variables through operationalisation
➔ Answer: Option 2 gives the correct answer.
The goal of research is to develop theories which can explain aspects of human behaviour and experience.
Options 3 and 4 refer to stages in the process of doing quantitative research but these are not the goals
of the research. The goal of the research is also not to develop statistical tests, as implied in option 1.
These tests are developed by statisticians and are used by researchers in social and other scientific
research, but developing the tests is not part of the goal of the research.
Question 2
The aim of psychological research is to - - - - -
a) establish relationships among constructs for the purpose of developing a theory.
b) draw definite conclusions about a population of interest based on sample statistics.
c) test an existing theory.
d) predict how constructs are likely to interact in general using relevant theoretical underpinnings.
1. (a)(b) and (c)
2. (a)(c) and (d)
3. (b)(c) and (d)
4. All of the above
➔Answer: The correct choice would be Option 2.
We can only draw inferences about a population from sample statistics and not definite conclusions.
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