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Appraisal in Counseling Session 2 Schedule Finish History Statistical Concepts Scales of measurement Norm-referenced versus Criterionreferenced instruments Measures of Central Tendency The Normal Curve Measures of Variability Types of Scores Statistics in Appraisal 1. 2. 3. 4. 5. 6. 7. A language, communication, from one professional to another. How much confidence can I put in this instrument’s scores? Will I consistently get the same scores every time I administer the instrument? Do the scores really measure the concept or construct I want to measure? What can this instrument tell us? What can it not tell us? What is the meaning of the score(s)? Compared to…? How can scores be explained? Assessment Standards for Educational and Psychological Testing – any method used to measure characteristics of people, programs or objects. Anastasi & Urbina– objective, standardized measure of a sample of behavior Cronbach – systematic procedure for observing behavior and describing it with the aid of numerical scales or fixed categories. Samples of Behavior Usually measuring constructs such as intelligence, interest, etc. which cannot be measured directly. Since only samples are gathered must determine if sample is how person usually acts and are inferences we are making correct. Use objective, standardized and systematic measures to gather samples. Assessment Integral to Counseling Assessing client problems. Conceptualizing and defining client problems Selecting and implementing effective treatment Evaluating counseling. Benefits of Using Testing Aids focusing on developmental issues Aids problem solving Helps decision making Psychoeducational tools Data indicate about 73% of counselors responded tests very important or important; only 9% said never used. Minimum Competency for Proper Test Use Proper testing environment Examinee follows directions so test scores are accurate Avoid coaching or training Scoring errors Avoid scoring & recording errors Keep scoring keys & test materials secure Know your instrument’s psychometric properties Counseling and interpretation Establish rapport Know the instrument and the construct completely Willing to interpret & offer guidance Avoid labeling people on basis of test scores Careful about assuming norms for one group apply to other groups Do your homework Statistics Scales of Measurement Nominal Ordinal Interval Ration Nominal categories, not ranked manipulating the numbers arithmetically makes no sense Example: Continent of Birth 1 Asia 2 Africa 3 Europe 4 Latin America 5 North America … What is the arithmetic mean? Continent of Birth Continent Frequency Asia Africa Europe Middle East Latin America North America US America Caribbean New Zealand Total % Cumulative % 151 22 31 8 7 1 7 5 1 64.8 9.4 13.3 3.4 3.0 .4 3.0 2.1 .4 64.8 74.2 87.6 91.0 94.0 94.4 97.4 99.6 100.0 233 100.0 100.0 Frequency Distribution 160 140 120 100 80 60 40 20 0 Asia Africa Europe Middle East Latin America North America US America Caribbean New Zealand Ordinal categories in rank order manipulating the numbers arithmetically may not make sense. Example Opinions…Likert-like scale Median, Mode, Range, Percentile. Not the arithmetic mean Instructions: Please mark the number from the scale that best corresponds to your answer. 1------------------------------2---------------------------3---------------------------4 Strongly Disagree Agree Strongly Disagree Somewhat Somewhat Agree I think of myself as being U.S. American. 1------------------------------2---------------------------3---------------------------4 Ordinal Data US Ident 1 N=233 Code 1.00 2.00 2.50 3.00 4.00 Total Missing Total Freq 130 56 1 33 12 232 1 233 Median 1.0000 Mode 1.00 Minimum 1.00 Maximum 4.00 Range 4.00 (Max-Min)+1 Percent 55.8 24.0 .4 14.2 5.2 Strongly Strongly Strongly Strongly Cumulative Percent 56.0 80.2 80.6 94.8 100.0 99.6 .4 100.0 Disagree Disagree Disagree Agree Interval/Ratio Data Interval and ratio are similar Interval Ratio continuous variable can be represented numerically Mean, median, mode, frequency, range, percentage, percentile may not make sense when we talk about ratio for instance…IQ…..is someone who has an IQ of 50 half as intelligent as someone with an IQ of 100? Or does a zero IQ mean an absence of intelligence? Examples: IQ or scores on an achievement test or the GRE, MAT, SAT continuous data with true zeros. Height, weight, age Norm referenced vs. Criterion referenced Measures of Central Tendency Mode Median Mean Measures of Central Tendency Mode is the most frequent score can describe multimodal curves least stable of the measures because it is not readily repeatable it is affected by the number of people taking the test not affected by extreme scores NOIR Measures of Central Tendency Median middle score achieved 50% of the scores are higher than this score and 50% are lower than this score. If there is no middle, we create it. The median can tell us more about data which is skewed versus data which is “normal” It is not effected by extreme scores No indication of multimodalness. IR Measures of Central Tendency Mean algebraic arithmetic average sum of the scores/number of observations it is affected by extreme scores most frequently used Measure because it lends itself readily to more complex manipulations. Used most extensively to describe normal distributions. NOIR Variability Measures of Dispersion Measure of the spread of scores Range Variance The range is the highest score minus the lowest score plus 1. How widely spread are the scores from the mean Standard Deviation Takes the variance and standardizes it so that the standard deviation is described in the same units as the original scores.