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Chapter 2

# Chapter Two PSY201

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University of Toronto St. George

Psychology

PSY201H1

Kristie Dukewich

Fall

Description

Chapter Two: Basic Mathematical and Measurement Concepts
– X(bar) → the mean of the sample
Mathematical Notation:
– deal with group data that result from measuring one/more variables
+ data often derived from samples, occasionally from populations
– N represents the number of scores in the distribution
– X/Y stands for the variable measured
+ N stands for the total number of subjects/scores
+ Xi is the ith score, where i can vary from 1 to N
Summation:
– sum all or part of the scores in the distribution
– Σ indicates the operation of summation
– read as “sum of the X variable from i = 1 to N”
+ the term below summation sign tells us the first score in the summation, and the term above the
summation sign designates the last score
+ we are to add the X scores, beginning with the first score and ending with the Nth score
– when summation is over all the scores (from 1 to N), the summation phrase itself is often abbreviated by
omitting the notations above and below the summation sign and by omitting the subscript i
→
– Σ X^2 → sum of the squared X scores
+ first square the X scores and then sum them
– (Σ X)^2 = sum of the X scores, quantity squared)
+ we first sum the X scores and then square the resulting sum
Order of Mathematical Operations:
– the order in which one perform mathematical operations can make a great difference in the result
+ should follow the order indicated by the symbols in the mathematical phrase or equation
Measurement Scales:
– a measuring scale can have one or more of the following mathematical attributes: magnitude, an equal
interval between adjacent units, and an absolute zero point
– four types of scales are commonly encountered in the behavioral science: nominal, ordinal, interval, and
ratio
+ they differ in number of mathematical attributes that they possess
Nominal Scales:
– lowest level of measurement and is most often used with variables that are qualitative in nature rather
than quantitative
+ the variable is divided into its several categories
+ comrpise the “units” of the scale, and objects are “measured” by determining the category to which they
belong
– qualitative variable measured on a nominal scale
– because the units are categories, there's no magnitude relationship between the units of a nominal scale →
no quantitative relationship between the categories of two variables – fundamental property of nominal scales is that of equivalence
+ all variables are from the standpoint of the classification variable – same, despite that there may be
different types
+ ie: different types of Nike jogging shoes
– does not possess any of the mathematical attributes of magnitude, equal interval or absolute zero point →
allows categorization of objects into mutually exclusive categories
Ordinal Scales:
– represents the next higher level of measurement
+ possess a relatively low level of the property of magnitude
+ rank-order the objects being measured according to whether they possess more, less, or the same
amount of the variable being measured
+ allows determination of whether A>B, A=B, or A 18 → 15
Ratio Scales:
– has all the properties of an interval scale and has an absolute zero point
+ without an absolute zero point, it's not legitimate to compute ratios with the scale readings
+ are permissible
– ie: compare difference between interval and ratio scales → Celsius scale with Kelvin scale
+ Zero on Kelvin scale is absolute zero (complete absence of heat)
+ Zero on Celsius is temperature at which water freezes
+ difference of heat of 8 → 9, 11 → 12 is same on either Celsius/Kelvin
+ cannot compute ratios with Cels

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