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Chapter 2

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University of Toronto St. George

Psychology

PSY201H1

Kristie Dukewich

Fall

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PSY201H1: Chapter 2 Review Notes
Key Symbols to remember:
X/Y= Terms used for variable to be measured
N= Total number of subjects or scores
X(i)= is the (i)th score, which can vary from 1 to N.
Summation
- One of the most frequent operations utilized in statistics in psychology.
- Usually the summation of all or part of the scores relevant to the distribution.
- Represented by the Greek symbol entitled sigma or “”
- The algebraic phrase typically employed is read as “sum of the X variable
from i=1 to N”, represented algebraically below:
Note: The algebraic symbol represents the summation of the X variable scores, from
1 to N. It is also important to note that the summation of the X/Y variable scores
may not always be from 1 to N. Instead they may be represented from 2 to 4, which
then must be solved accordingly.
- It is also important to note there are also two types of summation: “X^”
and “(^2)”
- Each of which have a different meaning and must be carefully differentiated
in order to carry out the operations appropriately.
“X^”: Sum of the squared X scores; indicates we first square the relevant scores
then sum them.
“(^2)”: Sum of the X scores, quantity squared; indicates we first sum the scores
then square the final resulting number.
Order of Mathematical Operations
- Always remember to do operations in parentheses first.
- Summation should always be done last, unless present within the
parentheses.
- In cases where multiplication, addition and division are concerned – always
perform the multiplication first (only exception: if parentheses are present)
- In cases where division, addition and subtraction are concerned – always
perform the division first (again, only exception: if parentheses are present) Measurement Scales
- Four major scales in the behavioral sciences: ordinal, nominal, interval and
ratio.
- Each scale differs in the mathematical attributes they possess.
Nominal Scales
- Considered the lowest scale of measurement
- Used with variables which are typically qualitative in nature, rather than
quantitative.
- Examples of qualitative variables: brands of trainers, eye color, nationality,
religious preference, kinds of fruit, types of music.
- In nominal scales, the variable is divided into several distinctive categories.
- These categories are known as “units” of the scale, objects are “measured” by
determining what category they come from.
- Measurement within this scale therefore refers to the classification of
objects and naming them.
- Hence the term ‘nominal scale’
- Fundamental property associated with nominal scales – ‘equivalence’
basically means that all members from a given class are the same from the
standpoint of a classification variable.
- Nominal scale allows for the categorization of objects into mutually exclusive
categories.
Example: variable chosen: ‘brand of jogging shoes’ ; categories/units: ‘Nike’, ‘New
Balance’, ‘Adidas’.
Note: During nominal scales, mathematical operations including addition,
subtraction, multiplication, division or ratios cannot be implemented.
Ordinal Scales
- Relatively low level on the property of magnitude.
- Rank based on the objects being measured according to whether they
possess more, less or the same amount of the variable being measured.
- It is important to note that due to the ranking nature of this scale, it does not
allow for the measurement of whether there is equal interval between the
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