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PS296 (9)
Max Gwynn (7)


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Max Gwynn

PS296 Measurement: assignment of numbers to objects, translating information about attributes or characteristics of cases into numbers. Constant: a number that keeps the same value Variable: a property that changes in value Frequency distribution: numbers are plotted in frequency of occurrence, line graph, categorical variable Bar graph: frequency of occurrence is shown by height of a bar, adjacent bars do not touch Histogram: similar to bar graph, the rectangles touch, used when variable is interval or ratio Frequency polygon: replaces bars with points, connected by lines, connect line to x axis Describe by shape, measures of central tendency (mean, median, mode), measures of dispersion (variability) Shape: -Uniform, u-shaped, symmetrical, nonsymmetrical •unimodal, bimodal, multimodal •skewness: positively skewed, negatively skewed •J distribution, Reverse J distribution •truncated: floor effect, ceiling effect (squeezed against one side or another) - mesokurtic (normal), leptokurtic (thin), platykurtic (flat) Mean: ̅ ̅ = ΣΧ/ N (sum of X’s devided by N), round to two decimal places, mean is gravity point, (mean x N should equal sum of the x’s) Variability: dispersion, how much points are spread around the mean Range= (highest score- lowest score), easy to calculate but takes into account all scores even extremes Mean deviation: Mean deviation score always equals zero Mean absolute deviation: find the mean, find the deviations of each score from the mean, Sum of squares: (the squared deviation score): Σ(X - )̅ 2 SS= sum of square deviation scores ∑ ̅ 2 S = Sum of squares divided by N-1 Square root of the variance to get S Population standard deviation: σ =2 ∑ ̅ 2 ∑ ̅ Sample Variance s = -dividing by N-1 for variance gives a less biased estimate than by N df= degrees of freedom, the number of independent pieces of information remaining after estimating one or more parameters. If you have five scores and their mean is known only the fifth is not left to vary z score: number of standard deviations from the mean z= = Standard scores: standard deviation of 0 - Makes raw scores interpretable - Allows easy comparisons - Allows to combine measures on different scales, a common metric - Positive z scores are above the mean - Negative z scores are below the mean - Larger values are further from the mean When a z score is not a standard deviation we use the Table of Normal Distribution: provides for each score area from mean to z, area in larger portion and in smaller portion Using the table: write down what is known, x, mean, draw out normal distribution, indicate where x score would fall, calculate z score, locate the score on the table to determine the area When all scores transformed into Z scores: mean=0, variance and standard deviation=1 -convert x score into z score looking up probability of getting z score (table) shows probability of drawing that score (becomes less probable further from mean) -repeated sampling, infinite number of times we would get a sample distribution of the mean Sample distribution of means: distribution of sample means over repeated sampling from a population. Take x number of scores, find mean, repeat, to it enough and the mean will be very close to the population mean. Less skewness than population Sampling error: random variability in samples (not a research mistake but due to chance differences in sample mean) Standard error: standard deviation of population divided by n Population: often don’t know about it, mean often estimated from sample means. Population mean: ᶬ Standard deviation: σ Sample: mean is unbiased estimation of population mean, should have similar shape to population (with larger sample size) Sampling distribution: mean should equal that of population, more normally distributed, samples of the same size “n”, variability depends on variability of population and sample size, as “n” increases Sample distribution variability decreases Central Limit Theorem: Population with mean x and variability x 2 Probability events sum to 1.00, if it is 1.00 it will always happen, 0 guarantee
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