Norms and Basic Statistics for Testing Psychological Assessment PDF

NORMS AND BASIC STATISTICS FOR TESTING PS Y CH O L OGI CA L A SS ES S MEN T Why We Need Statistics? Statistical methods serve two important purposes in the quest for scientific understanding: First, statistics are used for purposes of description. Numbers provide convenient summaries and...

NORMS AND BASIC STATISTICS FOR TESTING PS Y CH O L OGI CA L A SS ES S MEN T Why We Need Statistics? Statistical methods serve two important purposes in the quest for scientific understanding: First, statistics are used for purposes of description. Numbers provide convenient summaries and allow us to evaluate some observations relative to others For example, if you get a score of 54 on a psychology examination, you probably want to know what 54 means Is 54 lower than the average score or is it about the same?  Tests are devices used to translate observations into numbers Why We Need Statistics in Psychological Assessment? Rules and number systems are important tools for learning about human behavior Stand up if you think this is true and sit We use statistics to make down if you think it’s false inferences, which are logical deductions about events that cannot be observed directly Will you be happy if you get a score of 54 on a test? Why We Need Statistics? WOULD YOU RATHER A. Score of 54 out of 60, but 95% of your classmates got a perfect score. OR B. Score 54 out of 100, but 98% of your classmates got a score below 30. Knowing the answer can make the feedback you get from your examination more meaningful. Why We Need Statistics? 54 54 Why We Need Statistics? Second, statistics can be utilized to make inferences, which are logical deductions about events that cannot be observed directly For example, you do not know how many people watched a particular television movie unless you ask everyone. However, by using scientific sample surveys, you can infer the percentage of people who saw the film Two Kinds of Statistics 1. Descriptive Statistics 2. Inferential Statistics Descriptive Statistics These are methods used to provide a concise description of a collection of quantitative information Descriptive statistics are brief informational coefficients that summarize a given data set, which can be either a representation of the entire population or a sample of a population Descriptive statistics are broken down into measures of central tendency and measures of variability (spread) Inferential Statistics These are methods used to make inferences from observations of a small group of people known as a sample to a larger group of individuals known as the population Typically, the psychologist wants to make statements about the larger group but cannot possibly make all the necessary observations. Instead, he or she observes a relatively small group of subjects (sample) and uses inferential statistics to estimate the characteristics of the larger group SCALES OF MEASUREMENT B A S I C S TA TI S TI C S REFRESHER Properties of Scales Three important properties make scales of measurement different from one another which are: Magnitude Equal Intervals Absolute 0 (Zero) Magnitude 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 Adrian is shorter than Denzel, then the scale has the property of magnitude Magnitude There are scales that do not have the property of magnitude For example, a coach assigning identification numbers to teams such as Team 1, Team 2, and Team 3 does not have the property of magnitude However, if these teams are ranked based on the number of games they have won, then the new numbering system would have the property of magnitude Equal Intervals A scale has the property of equal intervals if the difference between two points at any place on the scale has the same meaning as the difference between two other points that differ by the same number of scale units For example, the difference between inch 2 and inch 4 on a ruler represents the same quantity as the difference between inch 10 and inch 12: exactly 2 inches Equal Intervals However, a psychological test rarely has the property of equal intervals For example, the difference between IQs of 45 and 50 does not mean the same thing as the difference between IQs of 105 and 110 Although each of these differences is 5 points, the 5 points at the first level do not mean the same thing as 5 points at the second Absolute 0 (Zero) Absolute 0 (Zero) is obtained when nothing of the property being measured exists (nothingness) 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 Absolute 0 (Zero) For many psychological properties, it is extremely difficult, if not impossible, to define an absolute 0 point For example, if one measures shyness on a scale from 0 to 10, then it is hard to define what it means for a person to have absolutely no shyness TYPES OF SCALES BASIC STATISTICS REFRE SHE R Types of Scales Nominal Ordinal Interval Ratio Nominal A nominal scale does not have the property of magnitude, equal intervals, or an absolute 0 Nominal scales are really not scales at all; their only purpose is to name objects For example, the numbers in the back of the jersey of basketball or football players are nominal because they are not used to quantify, they are only used to label the player Ordinal A scale with the property of magnitude but not equal intervals or an absolute 0 is an ordinal scale This scale allows you to rank individuals or objects but not say anything about the meaning of the differences between ranks If you were to rank the members of your class by height, then you would have an ordinal scale. For example, if Vin is the tallest, Rovi the second tallest, and Peter the third tallest, you would assign them the ranks of 1, 2, & 3, respectively but you would not give consideration as to how many inches are their difference between each other Interval When a scale has the properties of magnitude and equal intervals but not absolute 0, we refer to it as an interval scale The most common example of an interval scale is the measurement of temperature in degrees Fahrenheit. This temperature scale clearly has the property of magnitude, because 35°F is warmer than 32°F Also, the difference between 90°F and 80°F is equal to a similar difference of 10 degrees at any point on the scale. There is no absolute 0 because 0° in Fahrenheit still refers to a degree of temperature which is a temperature that is very cold Example: Grades & temperature Ratio A scale that has all three properties (magnitude, equal intervals, and an absolute 0) is called a ratio scale For example, consider the number of yards gained by running backs in football teams. Zero yards actually mean that the player has gained no yards at all If one player has gained 1000 yards and another has gained only 500, then we can say that the first athlete has gained twice as many yards as the second Ratio Another example is the speed of travel. For instance, 0 miles per hour (mph) is the point at which there is no speed at all. If you are driving onto a highway at 30 mph and increase your speed to 60 when you merge, then you have doubled your speed FREQUENCY DISTRIBUTIONS BASIC STATISTICS REFRE SHE R A single test score means more if one relates it to other test scores DISTRIBUTION A distribution of scores summarizes the OF SCORES scores for a group of individuals. In testing, there are many ways to record distributions of scores which will be discussed later Frequency Distribution It 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 Frequency Distribution greatest frequency of scores toward the center of the distribution and decreasing scores as the values become greater or less than the value in the center of the distribution Class Interval Whenever you draw a frequency distribution or a frequency polygon, you must decide on the width of the class interval Class Interval The number of categories of equal length (width) that will be used to group the data Range must be calculated to get the class interval (biggest number minus the smallest number) RANGE 89, 75, 53,39 98- 11 = 89, 98, 74, 11, 87 18, 15, 34, 77 CLASS INTERVAL Range / No. Classes 87 range Length of class interval: 9 9.6 or 10 class interval Percentile Ranks This answers the question “What percent of the scores fall below a particular score” The percentile rank of a score is the percentage of scores in its frequency distribution that are equal to or lower than it. For example, you might know that you scored 67 out of 90 on a test but that figure has no real meaning unless you know what percentile you fall into. If you know that your score is in the 90th percentile, that means you scored better than 90% of people who took the test. Describing Distributions Statistics are used to summarize data. If you consider a set of scores, the mass of information may be too much to interpret all at once. That is why we need these numerical conveniences to help summarize the information: Mean Standard Deviation Z-Score Standard Normal Deviation T-Score Quartiles and Deciles Mean The arithmetic average score in a distribution is called the mean The sum of all the numbers in the data set divided by the number of elements To calculate the mean, we total the scores, and we divide the sum with the number of cases MEAN (EXAMPLE) 14 + 35 + 23 + 56 + 76 + 16 + 21 + 25 + 26 + 10 + 54 + 45 + 12 + 22 + 15 SUM / NUMBER OF ELEMENTS: MEAN (EXAMPLE) 14 + 35 + 23 + 56 + 76 + 16 + 21 + 25 + 26 + 10 + 54 + 45 + 12 + 22 + 15 SUM / NUMBER OF ELEMENTS: 450/ 15 = 30 MEAN 30 IS JUST AN AVERAGE! Standard Deviation This is an approximation of the average deviation around the mean. This is basically the degree of variation in test scores How far each score lies from the mean High SD= values are far from the mean Low SD= values are clustered close to the mean  One problem with means and standard deviations is that they do not convey enough information for us to make meaningful assessments or accurate interpretations of data Z-Score The Z-score transforms data into standardized units that are easier to interpret. This describes a value’s relationship to the mean of a group of values Z-scores have a mean of 0 and a standard deviation of ±1 SINO MAS ANGAT? SINO MAS SMART? MAHIRAP MATH TEST BABAGSAK MATH TEST 100/300 65/100  Formula for Z scores IOQ TEST SBKN TEST My score: 100 My score: 65 Mean: 150 Mean: 40 SD: 50 SD: 20 Z= -1 Z= 1.25  T-scores have the same purpose with Z-score which is to transform data into standardized units that are T-Score easier to interpret. This describes a value’s relationship to the mean of a group of values T-scores have a mean of 50 and a standard deviation of 10 Deciles These are similar to quartiles except that they use points that mark 10% rather than 25% intervals Correlation Is a measure of the relationship between two or more variables Correlation coefficient (r) A number that represents the strength and direction of a relationship existing between two variables Positive and Negative Correlation Positive Correlation refers to when the Scores in BRS are high while the scores in MTS high as well. This can also happen when both scores are low Negative Correlation happens when the two scores contradict with each other. When one is high, the other score is low Strength of Correlation If the relationship is a strong one, the number will be closer to +1.00 or to -1.00 Example: +.89 is equally strong as -.89 -.90 is stronger than.45 Correlation Correlation coefficient ranges from -1.00 to +1.00 The nearer to 1; stronger relationship The nearer to 0; weaker relationship The symbol represents the type of relationship (negative=inverse; positive=direct) We use inverse rather than indirect Regression This may be defined broadly as the analysis of relationships among variables for the purpose of understanding how one variable may predict another Simple Regression involves one independent variable, which is typically referred to as the predictor variable, and one dependent variable typically referred to as the outcome variable. The statistical tool utilized for this is the T-Test Regression Multiple Regression is the statistical technique that can be used to analyze the relationship between a single dependent variable and several independent variables The statistical tool that can be utilized for this is the ANOVA END OF LESSON