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PSY201H1 (45)
Chapter 2

Chapter Two PSY201

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University of Toronto St. George
Kristie Dukewich

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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