Statistics

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statistic

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methods of describing and interpreting quantitative data; collect, organize, summarize, analyze, and draw conclusions from data

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descriptive statistics

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organizing, summarizing, presenting quantitative data; describe the group that was assessed

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inferential statistics

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inferences about a larger group of indiv. based on data collected from a smaller group or sample

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variable

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general characteristics measured

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data

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qualitative or quantitative observations made in envt answers q's: how much, how fast, how long, how often, where, what kind (values on a given set of variables, data set)

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quantitative variable

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continuous data, numerical (age, height weight, heart rate)

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qualitative variable

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categorical data, non-numerical (gender, race, ethnic background)

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nominal

(sex, race, hair/eye color)

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name only
primitive
categorical and qulitative
cannot +, -, x, /
no absolute zero or equal intervals

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ordinal

(place finishes in a race, grades A,B,C,D, F)

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relative position of objects
no equal intervals nor abs. zero
magnitude (a>b, b>c, then a>c)
cannot +, -, x, /

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interval
(temperature, ACT scores)

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equal intervals betwn numbers
arbitrary zero (not absolute)
magnitude
+, -, not x or /

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ratio
(heart rate)

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absolute zero
ratios are meaningful
+, - , x, /

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random sampling

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every subj/obj has equal/indep. chance of being selected

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systematic sampling

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every 'kth' subg/obj selected

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stratified sampling

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subj/obj divided into groups/strata accord to charact. important to study, random sample drawn form each group

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cluster sampling

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clusters of subj/obj randomly selected from intact groups, subj, or obj

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convenience sampling

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selection based on convenience

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ways to misrepresent data

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1. suspect samples
very large or very small
2. ambiguous averages
several types = different results
3. changing subj/reference

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ways to misrepresent data

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4. detached stats
works 4X faster, 40% markup
5. implied connections
may reduce, could work for you
6. misleading graphs

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misleading stats

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7. faulty survey questions
leading q's, forced response,
not having not applicable option

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frequency distributions

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1. raw data = original form
2. frequency = number of times value occurs
3. classes = grouping of raw data into clusters of similar values

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frequency distribution

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organizing raw data in table form using classes and frequencies

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categorical frequency distrib

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data can be places in specific categories
(nominal or ordinal level data)

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grouped freq. distrib

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interval or ratio data grouped into similar classes
(clusters of similar values)

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ungrouped freq. distrib

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class interval on one unit
(small data set)

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class limits

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boundary betwn two class intervals, includes lower and upper (similar to rounding rules)

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lower class limit

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lowest value data can take to be consid. a member of the Class

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upper class limits

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uppermost value data can take to be consid. a member of the Group

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class width

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subtract the lower (or upper) class limit from the lower (or upper) class limit of the Next Class
(10.5-5.5=5CW)

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cumulative frequency

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total numb. raw scores that fall at or below the value of interest
(freq.+freq, starting from bottom,-up- until reach total # of classes)

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percent

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frequency divided by the total number of observations (x100%)
(freq. / total classes(teams)x100)

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cumulative percent

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cum. freq / total number of observations
(%+% all the way from bottom to top, totaling 100% at top)

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relative frequency

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proportion of freq's relative to sample size (freq / total number of classes (teams) NOT x100)

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RULES for freq dist

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1. between 5 and 20 classes
2. mutually exclusive (no overlap)
3. continuous (no skip #'s)
4. exhaustive (all data w/in classes)
5. equal in width
6. lowest scores at bottom of table

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histogram
(bar graph)

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vertical bars of various heights representing freq's
CLASSES = X axis 9horizontal)
FREQ's = Y axis (vertical)
NO gaps btwn interval and ratio
gaps btwn nominal and ordinal

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frequency polygon
(line graph)

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lines connect pts plotted for freq's at Midpoint of classes
freq's represent. by heights of points
dots connected by straight lines
line drawn back to x axis at beg. and end (L, H)

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ogive
(line graph)

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represents Cumulative Freq for classes
aka cum. freq. polygon
open ended
(classes on Y axis)

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relative frequency graphs

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proportion of freq's relative to sample size (like a percent)
(classes on x axis, rel freq on y axis)
polygon, ogive, and histogram

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misleading graphs

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watch the reference points!

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statistic

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data values from SAMPLE

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parameter

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data values from a POPULATION

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outlier

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extreme value in data set,
single observation in data set

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central tendency

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measure of average, or middle of data
typical response
inc. mean, median, and mode

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mean

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arithmetic average, affect by outliers
add up all observ's
x-bar for sample
u for population
E for summation

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median

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half-way point in data set
symbolized by MD, arrange data in order, select middle pt.
not affected by outliers
good measure in Ordinal data

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mode

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most freq. occurring observation
best measure for Nominal data
can have zero, one or more than one
(bimodal)

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distributions

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layout of observ's
pattern of raw data
can be symmetric, + or - skewed

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symmetric distrib

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data values evenly distrib on both sides of mean
mean, median and mode all at cntr
(IQ scores, heights for adult males)

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pos. skewed distrib

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maj of data fall to L of mean, cluster at lower end of distrib (tail points to higher values (pos))
cent tend values from low to hgh: mode, median, mean
(household income in US)

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neg. skewed distrib

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maj of data fall to R of mean and cluster at higher end of distrib (tail points to lower values (neg))
cent tend values from low to hgh: mean, median, mode
(4th grd spel test to univ studnts)

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standard deviation POPULATION

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square root of variance
(/N)

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standard deviation SAMPLE

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not as much variance as pop
(n-1)

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range

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symbol R=highest value - lowest value
affected by outliers
doesn't take cent tend into consideration

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variation

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how spread out are observ's
range, variance, stand deviation

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empirical rule

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dist. is symmetrical (bell curve)
68% data values fall in 1 stnd. dev of the mean
95% data values fall in 2
99.7% data values fall in 3

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parameter

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characteristic of Population
given greek letters

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statistic

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characteristic of a sample
given latin letters

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central tendency

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typical score

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mean

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INTERVAL and RATIO

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median

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ORDINAL

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mode

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NOMINAL

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most affected by outliers

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central tend = MEAN
variability = RANGE