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PSY201H1 (45)
Chapter 2


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University of Toronto St. George
Kristie Dukewich

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 adja
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