Data

Copy and paste the text below. It is read-only. Select All

Measurement involves the use of certain devices or rules for assigning numbers to objects or events. Urbina, p. 34 ("the assignment of numbers to events... one of the foundations of science." Aiken, p. 39) types of measurement scales (table 2.1, p. 38) nominal ordinal interval ratio NOIR: remember this acronym (black in French) NOIR will list these in order from simplest to most complex . N: 1 property O: 2 properties I: 3 properties R: 4 properties. There are separate flashcards for each of these Types of statistics Descriptive Inferential Descriptive statistics: measures of central tendency mean (statistical average) median (lands in the middle of all scores listed in numerical order) mode (most frequently occurring value in a distribution) variability "the degree to which the scores in a sample differ from each other or, as more commonly expressed, differ from the mean of the sample" (Penguin Dictionary of Psychology) Most common measures range variance standard deviation range range is the simplest measure of score variability (the boundaries between which variation occurs) subtract the value of the lowest score from the value of highest score to get the range; example high score = 10 low score = - 2 range = 8 Variation and the "standard deviation" (S.D.) definition of SD = a measure of variability, in a sample of scores, from the mean of that sample *the most widely used measure of variability *the most dependable measure of variability The larger the S.D., the wider the variability (spread) of scores away from the mean computing the S.D. you can estimate the S.D. by taking the range of scores and dividing by 6 (the approximate number of standard deviations in a normal curve); e.g., high score = 76, low score = 10, range = 66 standard deviation (estimated) = 11 the normal curve (also called Gaussian distribution) The theoretically expected probability distribution when samples are drawn from an infinite population in which all events are equally likely to occur. Penguin Dictionary ...the type of distribution expected when the same measurement is taken several times and the variation about the mean value is random. APA Dictionary of Psychology value of the normal curve the most prominent probability distribution in stats used throughout the natural and social sciences as a simple model for complex phenomena user-friendly analytically (i.e., a large number of results can be derived from it) based on the "central limit theorem" (i.e., under mild conditions a large number of random variables are distributed approximately normally) "bell" shape makes it convenient for modeling a large variety of real world variables Properties of the normal curve bell shaped bilaterally symmetrical with each half containing 50% of the area under the curve tails approach but never touch the baseline (thus extends to ± infinity) unimodal (a single point of maximum frequency or maximum height-- ONE MODE.) mean, median, mode coincide at the center of the distribution statistical properties of the normal curve The range of scores under the normal curve can be divided into approximately 6 S.D.'s 3 S.D.'s above the mean 3 S.D.'s below the mean (scores more than 3 S.D.'s above or below the mean occur very rarely) 50% of the scores in a normal curve fall above the mean and 50% fall below the mean about 34% of scores fall between the mean and 1 S.D. (above or below the mean) 34% (above) and 34% (below) = 68% of scores fall within +/- 1 S.D. of the mean wider variability... about 28% of scores fall between 1 to 2 S.D.'s from the mean about 14% fall between the range of +1 S.D. to +2 S.D about 14% fall between the range of - 1 S.D. to - 2 S.D overall, about 95% of scores fall within +/- 2 S.D. of the mean even wider variability... about 4% of scores falls between 2 to 3 S.D.'s from the mean about 2% fall between the range of +2 S.D. to +3 S.D about 2% fall between the range of - 2 S.D. to - 3 S.D overall, about 99% of scores fall within +/- 2 S.D. of the mean S.D.'s and percentiles +1 S.D. = 84th percentile ("in a room of 100 people, about 16 will score higher") +2 S.D. = 97th percentile +3 S.D. = 99th percentile -1 S.D. = 16th percentile ("in a room of 100 people, about 84 will score higher") - 2 S.D. = 3rd percentile - 3 S.D. = 1st percentile Kurtosis: score variability Kurtosis refers to the degree to which scores cluster about the mean (i.e., degree of variability in scores) A normal curve (or distribution or variability of scores) is mesokurtic Two other possibilities, platykurtic distributions and leptokurtic distributions leptokurtic ("leapin' leptokurtic") A normal curve where most of the scores cluster around the middle of the distribution platykurtic ("plateau" or "flat-ykurtic") Lots of variation in scores, more scores in the tails of the curve and fewer scores in the mid-range Non-normal curves or "skewed" ("asymmetrical") distributions ("the tail is the clue to the skew") long tail pointing in the positive direction: positively skewed long tail pointing in the negative direction: negatively skewed variables vs. constants variables vary and constants do not. example of constant: Pi (3.14....) is a constant because its value remains the same example of variable: average income in a group of people types of variables: discrete discrete variables have a finite range of values. discrete variables are dichotomous if there are only 2 values possible (you will have a boy or a girl. You will flip heads or tails on a coin.) discrete variables are polytomous if more than 2 values are possible (rolling dice, you could roll any value 2-12) *in principle, discrete variables can be counted precisely without error. types of variables: continuous continuous variables cannot really be counted (ex: time, temperature, distance) these variables theoretically keep going into infinity. When we "measure" these, we are more or less making approximations. ***psychological testing and behavioral sciences are primarily interested in measuring continuous variables (degree of anxiety, how extraverted a person is, etc) so when scores are reported, we should make it clear that they are estimates and inexact. nominal scales (#1, simplest--one property) simplest level of Stevens' classification. nomen means "name" "nominal" implies the numbers are used only to label (name) an individual or class/category. (ex: Social Security #) the ONLY property of nominal scales is identity. ordinal scales (#2--two properties) in addition to the property of identity, these numbers ALSO have the property of "rank order." this means they can be arranged on the basis of a single variable that orders their position (example, if a list of kids in a class were ordered iby GPA from lowest to highest, it would have a "rank order" and it would be an ordinal scale) interval scales (#3--three properties) also known as equal-unit scales they have the properties of identity, rank order AND the distance between numbers (ex: see page 40 for an example about minutes and hours and days that is too complicated for me to rephrase... lol) ratio scales (#4, most complex---four properties) have properties of identity, rank order, distance between numbers AND "additivity" "additivity" means they can be added, subtracted, multiplied, divided... with meaningful results. ratio scales have a zero point (see pg 41 for this... I don't get it... lol) This means that it measures things that start at zero. (spead for example, or money- you can have zero money in your account so a measure could be 0 to 5,000 to 10,000 and so on). definition of statistics a branch of mathematics dedicated to organizing, depicting, summarizing, analyzing (and otherwise dealing with) numerical data descriptive statistics vs. inferential statistics numbers and graphs used to describe, condense, or represent data are descriptive. when data is used to estimate or test hypotheses, it is inferential. ex: the exact number of ATS counseling students who are missing chunks of hair next Tuesday would be descriptive statistics. If I estimated that 30 of us would be missing hair chunks based on probability or data from this time last year, it would be inferential statistics. bimodal/ multimodal when a distribution of values has more than one mode (if this were a curve, it would look like a 2 hump camel or a wavy line with multiple humps.) quartiles measures of variability that divide the distribution of scores into four quarters. (pgs 48-49) GOOOOOOOOOOSH... this stuff blows my brain into tiny bits. I am praying this part isn't on the exam!!!! Interquartile range the distance between the highest value in the bottom quartile and the highest value in the third quartile, thus covering the middle fifty percent of a distribution semi-interquartile range half the distance of the interquartile range. To compute it, just divide the interquartile range by two. variance a measure of total variability of the distribution. Computed by squaring the difference between each value and the mean, then adding the squared numbers, and dividing the result by sample size. For a distribution of 3, 7 and 8 and 10, the mean is 28/4=7, the variance is ((3-7)² + (7-7)² + (8-7)² + (10-7)²)÷4= (16+0+1+9)÷4 = 6.5. standard deviation The square root of the variance. If the variance is 6.5, the SD is 2.55. It is the quintessential measure of variability for testing. standard normal distribution A distribution creating a bell curve with a mean of zero and a standard deviation of one. standard error An estimate of the error in the sample mean compared to the population mean. Computed by taking the standard deviation of the sample and dividing it by the sample size. for a sample of 3, 7, 8 and 10, the SD is 2.55, the sample size is 4 and the standard error is 2.55 /2 = 1.28. skewness symbolized Sk. The degree of assymetry of a distribution. positive skewness The long tail of the skewed distribution curve points toward more positive numbers (to the right) negative skewness The long tail of the skewed distribution curve points toward more negative numbers (to the left).