Psych Assessment Module C2 watermark.pdf

CHAPTER 2-BASIC STATISTICS IN TESTING AND INTERPRETATION Learning Outcomes 1. examine the different statistics applied in psychological testing. 2. identify the different frames of reference in testing (score interpretation). UNIT 1-BASIC STATISTICS Why we need Statistics in T...

CHAPTER 2-BASIC STATISTICS IN TESTING AND INTERPRETATION Learning Outcomes 1. examine the different statistics applied in psychological testing. 2. identify the different frames of reference in testing (score interpretation). UNIT 1-BASIC STATISTICS Why we need Statistics in Testing?  For purposes of description- numbers provide convenient summaries and allow us to evaluate some observations relative to others. (Ex. A score of 60 means is it below the average or the same?)  To make inferences- these are logical deductions about events that cannot be observed directly. (Ex. One can infer the percentage of people who watched a certain TV show thru a simple survey) Statistics and principles of measurement lie at the center of the modern science of psychology. Scientific statements are usually based on careful study, and such systematic study requires some numerical analysis. Types of Statistics Descriptive- numbers and graphs are used to describe, condense, or represent data. - Frequency Distributions - Grouped frequency distribution- helps organize scores into a still more compact form. - Graphs – frequency distribution are transformed into a pie charts, bar graphs (for discrete or categorical data) and histograms or frequency polygons. Inferential statistics- are methods used to make inferences from observations of a small group known as a sample to a larger group of individuals known as population. Variables and Constant (Urbina, 20114) - Variable- anything that varies - Continuous variables such as time, distance, and temperature, on the other hand, have infinite ranges and really cannot be counted - Discrete variables are those with a finite range of values—or a potentially infinite, but countable, range of values - Dichotomous variables, -are discrete variables that can assume only two values, such as true– false or the outcome of coin tosses. - Polytomous variables -are discrete variables that can assume more than two values, such as marital status, race, and so on - Constant – anything that does not vary The Meaning of Numbers -because numbers can be used in a multitude of ways, there is a need for a system for classifying different levels of measurement on the basis of the relationships between numbers and the objects or events to which the numbers are applied. BPSYCH8 Psychological Assessment 12   These systems will depend on the types of statistical operations that are logically feasible depending on how numbers are used. What is Measurement? - It is the assignment of numbers to properties or attributes of people, objects, or events using a set of rules. Characteristics of Measurement:  It focuses on attributes of people, objects or events not on actual people, objects or events.  Uses a set of rules to quantify these which are standardized, clear, understandable and easy to apply  Consists of scaling and classification; scaling deals with assignment of numbers so as to quantify them; - Classification- refers to defining people, events or objects fall into the same or different categories Properties of Scales Magnitude- is the property of “moreness.” A scale has the property of magnitude if we can say that a particular instance of the attribute represents more, less, or equal amounts of the given quantity than does another instance. (On a scale of height, for example, if we can say that John is taller than Fred, then the scale has the property of magnitude) Equal intervals- when a scale has the property of equal intervals, the relationship between the measured units and some outcome can be described by a straight line or a linear equation. Absolute Zero (0) - is obtained when nothing of the property being measured exists. For example, if you are measuring heart rate and observe that your patient has a rate of 0 and has died, then you would conclude that there is no heart rate at all. Types of Scale (Urbina, 2014; Kaplan & Saccuzzo, 2018) 1. NOMINAL- Scale- (Identity only) - not really a scale but naming or describing things (e.g. occupation, ethnic group, assignment of numbers instead of words - only for classification (age, gender) - cannot compared quantitatively - any amount of difference between things may not be known. 2. ORDINAL scale (Identity + Rank) - more precise measurement than nominal because it classifies but has the property of order or magnitude as well. - variable being measured is ranked or ordered according to some dimensions without regard for differences in the distance between scores (e.g. 100m sprint) 3. INTERVAL (Identity + rank + equality of units) - classifies variables, ranked them but also represent the difference between them - do not have a true zero, instead, use constant units of measurements so that differences on a characteristic can be stated and compared. (e.g. intelligence tests) BPSYCH8 Psychological Assessment 13  - they have equal-unit scales 4. RATIO scale (Identity + rank + equality of units + additivity) - the highest or ideal level of measurement because they have a true value of zero (0) - An interval scale in which people’s distances are given relative to a rational zero. (e,g, person’s income level, reaction time to a particular stimulus) The relevance (Scales of measurement) to Psych testing- it helps to keep the relativity in the meaning of numbers in proper perspective and the limitations in the meaning of scores have to be understood and the inaccurate inferences that are likely to be made on the basis of these scores because measurement process are inexact. (Urbina, 2014) Permissible Operations The level of measurement is important because it defines which mathematical operations one can apply to numerical data  For nominal data, each observation can be placed in only one mutually exclusive category. For example, you are a member of only one gender. One can use nominal data to create frequency distributions, but no mathematical manipulations of the data are permissible.  Ordinal measurements can be manipulated using arithmetic; however, the result is often difficult to interpret because it reflects neither the magnitudes of the manipulated observations nor the true amounts of the property that have been measured. For example, if the heights of 15 children are rank ordered, knowing a given child’s rank does not reveal how tall he or she stands. Averages of these ranks are equally uninformative about height.  With interval data, one can apply any arithmetic operation to the differences between scores. The results can be interpreted in relation to the magnitudes of the underlying property.  Interval data cannot be used to make statements about ratios. For example, if IQ is measured on an interval scale, one cannot say that an IQ of 160 is twice as high as an IQ of 80. This mathematical operation is reserved for ratio scales, for which any mathematical operation is permissible Frequency distribution  displays scores on a variable or a measure to reflect how frequently each value was obtained. With a frequency distribution, one defines: - all the possible scores and determines how many people obtained each of those scores. - usually, scores are arranged on the horizontal axis from the lowest to the highest value. - the vertical axis reflects how many times each of the values on the horizontal axis was observed.  For most distributions of test scores, the frequency distribution is bell shaped, with the greatest frequency of scores toward the center of the distribution and decreasing scores as the values  A single test score means more if one relates it to other test scores. A distribution of scores summarizes the scores for a group of individuals. In testing, there are many ways to record a distribution of scores BPSYCH8 Psychological Assessment 14  Percentile ranks vs percentile  Percentile ranks replace simple ranks when we want to adjust for the number of scores in a group. A percentile rank answers the question, “What percent of the scores fall below a particular score (Xi)?” In other words, it indicates what percentage of scores fall below a particular score.  Percentiles are the specific scores or points within a distribution. Percentiles divide the total frequency for a set of observations into hundredths. It indicates the particular score, below which a defined percentage of scores falls.  To calculate a percentile rank, you need only follow these simple steps: (1) determine how many cases fall below the score of interest, (2) determine how many cases are in the group, (3) divide the number of cases below the score of interest (Step 1) by the total number of cases in the group (Step 2), and (4) multiply the result of Step 3 by 100. The formula is: (Source: Kaplan & Saccuzzo, 2018) Steps 1. Arrange data in ascending order—that is, the lowest score first, the second lowest score second, and so on. 2. Determine the number of cases with worse rates than the score of interest. 3. Determine the number of cases in the sample. 4. Divide the number of scores worse than the score of interest (Step 2) by the total number of scores (Step 3): 5. Multiply by 100: BPSYCH8 Psychological Assessment 15