Statistical Definitions to Study for First Exam
Terms
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- Define inference.
- An inference is simply a deductive analysis.
- What types of studies gather information about validity?
- Validation studies.
- What is Psychological Assessment?
- A purposive, data-gathering enterprise that defies description. Procedures change depending on what you are gathering.
- What is Psychological Testing?
- A process of measuring psychologically related variables by means, devices, or procedures designed to obtain a sample of behavior.
- How does the structure of an interview increase reliability?
- To approach the interview the same way each time, increases ability to make an evaluation and boosts reliability.
- How does behavioral observation evolve as you learn how to assess clients?
- You learn to interview objectively, keep behavioral observations clear, and teach clients to problem solve.
- What is a good test?
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One that:
is reliable, valid, and has norms. - History of Statistics: Talk about Darwin, Freud, and Galton.
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- History of Statistics: Talk about Binet.
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- History of Statistics: Talk about Leipzig, Germany.
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- History of Statistics: Talk about early testing.
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- What is Personality Testing? How did it come about?
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- What is Statistics?
- Things that underlie testing. Measurement is the act of assigning numbers (Mild, moderate, severe) to characteristics of objects (depression) according to different rules (on how to administer, interpret, test).
- What is Measurement?
- Measurement is the act of assigning numbers⬦.
- What is the difference between Discrete scales and Continuous scales of measurement?
- Discrete scales are not helpful (male or female, age…don’t give much information about person). Continuous (contains error) scale used most frequently in Psychological Testing.
- Key to Psychological Testing is wrapped up in one important concept. What is that concept?
- Key: Nothing in Psych Testing is perfect. Numbers on a continuous scale contains error. We will never come up with a real score.
- Explain the concept of error.
- Any factor entering into process that is not directly relevant to whatever we are measuring. Ex. administrator has bad day or goes too quickly. Minimize difficulties person will be facing.
- Describe the four major scales.
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- Describe a Nominal Scale.
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- Describe an Ordinal Scale.
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- Describe an Interval Scale.
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- Describe a Ratio Scale.
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- Why are intelligence, aptitude, and personality test scores basically and strictly speaking ordinal?
- They indicate with more or less accuracy not the amount of intelligence, aptitude and personality traits, but rather the rank order and position of individuals.
- How are test results communicated?
- One way is a frequency distribution. All possible scores are listed with all the times each score occurred. 200 people = 200 IQ scores. One way to measure this is to measure how often they occur. The average score is supposed to be 100, we can assume that most numbers occur around 100, with less above and less below.
- Explain the Bell Curve.
- Bell Curve: See p. 31 for picture, fig. 2.3 -- These numerical operations are used by all test instructors. When 100 is the most often IQ score. SD = 15, then 115 is one standard deviation above the mean. This is all based on the Bell shaped curve. The middle is the mean. If we add the sliced sections to the right it will be labeled +1, +2, +3, and to the left is -1, -2, -3 etc. If the SD is 15, then you add or subtract the SD from the score of 100 to determine your clients score. Because of the concept of the Bell Curve, the mean is 15, however, in personality it is 50. The key word is deviates. How a person deviates from the norm.
- Explain Analysis of Variance.
- Analysis of variance analyzes variability among tests. This helps us to understand how things are correlated. We not only look at how are things the same, but also how they vary or differ.
- Bell Curve explained with regard to how scores vary from one another.
- From this perspective, (bell curve where 100 is the most frequent score and 15 is SD) 68% of population falls between -1 and +1. (34 + 34). 96% falls between -2 and +2 (14 + 14 more). We are classifying people, rank ordering people so it’s an ordinal scale. If someone comes up with an IQ score of 70, we can say for example, that approx. 95-97 % of the other individuals will score more than 70. So we are classifying them and rank ordering them to understand that there are a large number of individuals with greater intellectual abilities than them. On the converse, they are more intellectually endowed than 2-3 % of the population. We always start with the mean or the average. This is a form of number communication that does not have to be a mystery. Keep in mind the measurement of error (range). Everything rests on Bell shaped curve. Key is mean and SD. Range of numbers across the curve: -1, 2, 14, 34, 34, 14, 2, 1. SD is 15. On another note, the larger sample and wider range of abilities tested the closer the curve will approximate the normal bell curve. In other words, the more people you test the better you’ll approximate the general population.
- Definitions and Symbols: Mean
- Mean (M) is just the average of the scores. Take all scores, add, divide by amt. of people and you have the mean.
- Definitions and Symbols: Median
- Median is what is called the middle score of the distribution (what is between the lowest and highest score),
- Definitions and Symbols: Mode
- Mode is the most frequently occurring score
- Definitions and Symbols: Variability
- Variability is an indication of how scores in a distribution are scattered or disbursed. It can be a narrow or wide range between highest and lowest score.
- Definitions and Symbols: Standard Deviation
- Standard Deviation is a measure of variability. It is the square root of the variance.
- Definitions and Symbols: M
- M = Mean
- Definitions and Symbols: X
- X = Score
- Definitions and Symbols: Greek symbol that looks similar to an E
- E = to sum
- Definitions and Symbols: N
- N = number of individuals in group
- Definitions and Symbols: SD
- SD = standard deviation
- Definitions and Symbols: Multimodal
- Multimodal = when scores do not fall into a normal distribution (distribution with more than one peak)
- Definitions and Symbols: Skewed
- Skewed = majority of people score in low range or high range (as compared with normal distribution)
- Definitions and Symbols: Positively skewed
- Positively skewed = majority of scores are at lower end of distribution (opposite of what makes sense}.
- Definitions and Symbols: Negatively skewed
- Negatively skewed = majority of scores are at higher end of distribution (opposite of what makes sense, however, when you consider that the mean is skewed negatively when the scores are mostly higher, it does make sense)
- Definitions and Symbols: Percentile Rank
- Percentile rank = can be determined for any distribution of scores, not just for normalized distributions. To find the percentile, we first have to determine how many people out of the group had each score, and then we calculate the percentage of people out of the total group who received that score. For example, for the score of 60, we can see that four people received that score, and 4 divided by the total group of 25 is equal to 16%. As stated earlier, percentiles are the percent of people who received a score at or below a given raw score. Therefore, to get percentiles, we add the percentage of people who had a score at or below each of the raw scores. To continue (table 2.4, p. 33) add the percentage of people at each score that are at and lower than 60 (4+8+8+20+24+16=80). In interpreting your score of 60, a counselor might say, “Eighty percent of the norming group had a score at or below yours.†Another example would be I have a score of 50. Six (6) people had a score of 50, and 6 divided by the total group of 25 is equal to 24%. Now, to get percentile, we add the percentage of people who had a score at or below 50 (4+8+8+20+24=64). In interpreting your score of 50, a counselor might say, “Sixty-four percent of the norming group had a score at or below your score.â€
- Definitions and Symbols: Percentile Bands
- Percentile Bands = relate to the above percentile rank and are used on Armed Services Aptitude Battery based on standard error of measurement (see Chap. 3). Percentile Bands are useful because they can show a range of where clients could expect their scores to fall if they took the instrument multiple times.
- Definitions and Symbols: Random Sample
- Random Sample = a sample of the larger population where every member has an equal chance of being selected. However, it is hard to gather this wide of a sample.
- Definitions and Symbols: Stratified Sample
- ⬢ Stratified Sample = sample drawn from larger population based on certain demographic characteristics. US Census reports are consulted to make sure the percentage of individuals in the smaller sample match the percentages of individuals in the larger population.
- Definitions and Symbols: Cluster Sampling
- Cluster Sampling = randomly selected larger units of all (elementary schools, hospitals, etc.)
- Definitions and Symbols: Criterion Referenced
- Criterion Referenced: To compare an individual’s performance with an established standard or criterion.
- Definitions and Symbols: Norm Referenced
- Norm Referenced: To compare an individual’s performance with other people’s performance on the instrument.
- Different kinds of scores: Raw Score
- Raw Score: the simplest of the scoring methods which is meaningless without any other interpretive data. Raw scores are those that have not been converted to another type of scoring (e.g., percentile, T score). On the CAS assessment, my score of 60 means nothing until we begin to examine the distribution of scores, measures of central tendency, and measures of variability. When we examine these indicators, we typically have more information with which to interpret a score. Sometimes, however, we want additional information concerning how an individual performed in comparison with the norming group. This is accomplished by converting the raw score to a percentile rank, or percentile score
- Different kinds of scores: Percentile Rank or Percentile Score
- Percentile Rank or Percentile Score: a person’s rank on the distribution. If Mary had a score of 68, then out of 100 people taking the test, 68 of them would have a score at or below Mary’s score. Remember: we calculate the percent of people who received a score at or below a given raw score, (an ordinal scale and cannot be analyzed using statistics that require interval data, p. 34…line just above fig. 2.5). Standard Scores address the limitation of unequal units of percentiles, while providing a “shorthand†method for understanding test results (p. 35 top).
- Different kinds of scores: Standard Score
- Standard Score: a standard score has a mean of 100 and a SD of 15. Raw score that has been converted from one scale into another scale, the latter scale being more widely used and interpretable. Ex. There is a test of 30 items making possible score of 60. Person gets a 45. Raw score of 45 means nothing. You must convert to scale score which is a 12. It fits into the 1-19 distribution with 9/10/11 being the mean. So the 12 signifies average. Now the raw score is converted into something meaningful. What we are talking about is how to communicate information by the use of numbers. The numbers do the talking for us. They give us a basis for how to talk about a person. They can be ranked with others and describe how many standard deviations a client’s score is from the mean (p. 35 Standard Scores).
- Different kinds of scores: T Score
- T Score: Primarily used for personality tests, MMPI, etc. Mean is 50 and SD is 10
- Different kinds of scores: A Score
- A Score: Mean is 500 SD is 100. SAT’s are A scores
- Different kinds of scores: Z Score
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Z Score Formula:
z = X – M over s (could not write equation in this flashcard format)
See Table 2.5 p. 35 - Talk about WWI and need for assessment.
- The advent of WWI created a need to do psych assessment. They used it to know where to place soldiers. This was even more important in WWII.
- Talk about WWII and need for assessment.
- They first give an exam before and after basic training to determine the areas a soldier would be best suited for. Ex. Submarines stay under water now for six months. This is an example of ability testing.