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42 Cards in this Set
- Front
- Back
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What is the definition of statistics?
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The science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data.
- no data = no statistics |
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descriptive statistics
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describes a situation (census); main form of deferential statistics
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inferential statistics
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make assumptions by generalizing dat from sample to population. (probability)
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populations
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all subjects (human and non human) included in study
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sample
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a group of subjects selected from population
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qualitative variables
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can be placed into categories (gender)
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quantitative variables
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numerical, can be ordered/ranked (age, weight, temp)
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discrete variables
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can be assigned values (countable)
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continuous variables
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cannot be assigned values - infinite number of values - fractions, decimals, i.e. temperature
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nominal/category variables
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categories that cannot be ranked
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ordinal variables
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categories that can be ranked) (S, M, L)
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interval variables
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rankable data w/ precise differences, no zero (IQ, temp, SAT score)
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ratio variables
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zero exists, "twice as much" rule
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random sampling
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subjects are selected by chance (i.e. lottery)
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systematic sampling
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select every kth subjcect
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stratified sampling
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divide population into groups (called strata), sample from each group randomly.
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cluster sampling
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divide popuation into "clusters", use entire clusters as samples
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other methods: convenience sampling
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use subjects only because they are convenient (voluntary participation) - not representative of entire population
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observational study
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researcher observes & draws conclusions - can never be used to prove anthing, can only suggest something or prove causality
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experiemental study
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researcher manipulates a variable to determine how the first variable affects a second variable (sometimes can prove)
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frequency distribution
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1) find highest/lowest value, find range, divide range by # of classes = width
2) start w/ appropriate low point, add width until # of classes reached 3) class boundaries: subtract 0.5 from each low end, add 0.5 to each high end 4) tally data, write frequency & cumulative frequency |
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measures of central tendency
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mean
median mode midrange (range/2) |
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mean
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balance point for data - sensitive to extremes/outliers
sample mean: X population mean: u |
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median
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halfway point for data - resistant to extremes/outliers
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statistic
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uses data values from a sample
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parameter
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uses data values from a population
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measures of variance
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variance
standard deviation coefficient of variation range |
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variance
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average of squares of distance each value is from mean
population variance - o squared sample variance - s squared |
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standard deviation
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square root of variance
population std dev - o sample std dev - s |
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coefficient of variation
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allows comparison between different data sets with different units
std dev/mean x 100% (larger the percent, the more variation there is in the data set) |
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Rule of Thumb Estimate
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rough estimate of std dev, provided distribution is unimodal and roughly symmetric
s = range/4 |
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Empirical Rule/Normal Rule
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Approximately:
- 68% of data values within one deviation of mean (mean +/- s) - 95% within 2 deviations - 99.7% within 3 deviations |
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General Purpose Rule/Chebyshev's Theorem
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between x-ks and x+ks, at least (1-1/ksquared)x100% of data will fall.
- find k using x-ks=lower given value - plug k value into (1-1/ksquared)x100% - this % of data lies between the two given values |
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Measures of Position/Location
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z-score
percentiles Interquartile Range (IQR) |
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z-score, standard score
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same as k in General Purpose Rule, represents # of std deviations that data value is away from mean
z = (x-xbar)/s |
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percentile
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divides data set into 100 equal groups
[(# of values below x + 0.5)/total # of values] x 100% c=(np)/100 n = total # of values p = given percentile |
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Interquartile Range (IQR)
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range of middle 50% of data
Q3 - Q1 = IQR >Analyze >Descriptive Statistics >Explore |
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empirical probability
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probabilities for outcomes based on observation
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mutually exclusive events
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events A and B cannot occur at the same time
P(A or B) = P(A) + P(B) |
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not mutually exclusive
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events A and B can occur at the same time
P(A or B) = P(A) + P(B) - P(A and B) |
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independent events
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A does not affect B (i.e. flip nickel and flip dime)
P(A and B) = P(A) x P(B) |
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dependent events
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outcome or occurence of A affects outcome or occurence of B so that probability changes
P(A and B) = P(A) x P(B|A) (conditional probability) When P(A)xP(B) does not equal P(A and B), then A and B are not independent, so there is a relationship between A and B |
