218 Descriptive Stats

Front 1

Objective of Descriptive stats

Back 1

tabulation of data
central tendendy, variablilty "dispersion"

Front 2

Frequency

Back 2

number of cases in the class interval

Front 3

Cumulative Frequency

Back 3

number of cases in that class interval or lower

Front 4

Proportion

Back 4

number of cases in that class interval divided by the total number of cases (n)
-more useful to know and requires less info to interpret

Front 5

Cumulative proportion

Back 5

number of cases in that class interval or lower divided by the total number of cases (n)

Front 6

Cumulative percent

Back 6

cumulative porportion X 100
(Percent = proportion X100)

Front 7

Steps to determine XXX frequency?

Back 7

1. range +1
2. determine interval width : i (range/N - chose somthing evenly divisible)
3. use the lowest score in the distribution as the min value in the lowest interval. add i to each interval and work up
4. tally scores
5. Add tallies for interval frequency

review slides

Front 8

Why make grouped freq. dis?

Back 8

allow graphical displays

Front 9

Frequency Histograms (bars touch)

Back 9

x-axis = score values for grouped or ungrouped data
y-axis = frequency (number of cases)

*interval widths on the x-axis includes true limits and midpoint is marked

*include labels!

*nominal data (ie. religions) bars don't touch!

Front 10

Frequency Polygons (dots and lines)

Back 10

x-axis = midpoints plotted of each interval and connect the dots

Front 11

Cumulative Frequency Polygons (dots and lines going up)

Back 11

instead of graphing straight frequency, cumulative frequency is graphed (number of cases in that intercal or lower)

x-axis = true upper limit of each interval
y-axis = frenqency

Front 12

Stem and Leaf Plots

Back 12

Combines useful feature of histograms and frequency disributions

stems = class interval
leafs = specific scores within the intercal ordered from lowest to highest

*rotate 90 degrees and you have a histrogram

*preserves raw data (great!)

Front 13

intraocular inspection

Back 13

visual analysis

Front 14

mean

Back 14

sum of all scored divided by number of scores (n, sample size)

using a freq. dis. multiply each freq dis. add them up and divide by n

drawback: heavily influenced by extreme scores, instead use median

Front 15

median

Back 15

divides distribution into 2 equal halves

tie scores: if median lies between intervals with tied scores, take limits lower interval limit + number below the apparent median (if falls on a score count as .5) divided by the total amount of repeating scores

Front 16

mode

Back 16

most frequent score in the distribution
useful measure
*can have multiple modes (bi-modal/trimodal) if there are less frequent numbers between the two modes - judgement call needed at times or if two numbers (beside each other) are the same ie.7,8 both are the modes

Front 17

when to use which measures of central tendency

Back 17

bimodal distributions, use mode
one modal distribution, use median
no extremes, use mean
if symmetric distribution, mean=median=mode (essentially equal) but use mean because mean uses all info

Front 18

+/- skews measures of distribution

Back 18

-positively skewed (mode to the leeft), mean > median and no longer representative of central tendency
-negatively skewed (mode peaks to the right), mean < median and no longer representative of central tendency

Front 19

measures of variability

Back 19

provide a quantitive measure of the degree to which scores in a distribution are spread out or clustered together

Front 20

range (whole numbers)

Back 20

(highest-lowest+1)

(with exact measures just use highest-lowest score)

as a statistic:

you cannot observe in a sample a range that is greater than the population range
*sample range will average out to be lower than pop range, not a good characteristic (bias low)

Front 21

variation, variance, and standard deviation notation

Back 21

variation - SSx (has to be positive, if negative, you're wrong)
variance - pop: o2(sigma squared) sample: s2
standard - pop: (sigma) sample: s

Front 22

variance

Back 22

average variation
SSx/N

Front 23

variation (if neg answer, wrong)

Back 23

SUMxi2

Front 24

standard d

Back 24

square-root of the variance (ssx/N)

Front 25

sample variability computations

Back 25

variance: ssx/(n-1)

n-1 because we lost some of the variability because we used the sample mean to calculate the variation

Front 26

comparison/transfer

Back 26

see slides

Front 27

z-scores

Back 27

re-expresses raw scores in units of sd
-number represents units of standard deviations

*requires knowing the parameters of mew and sigma



properties:
-useful for interval scales
-mean always 0
-sd of a set of z-scores is 1
-variance of a set of z-scores is 1
-sum of squares (SSx) of a set of z-scores = N(pop) or n-i (sample)

Front 28

statistic vs parameter

Back 28

-both are a number that calculate data that quantifies a characteristic of the sample, but STATISTICS ARE FOR SAMPLES
AND PARAMETERS ARE FOR POPS

Front 29

x-axis

Back 29

abscissa

Front 30

y-axis

Back 30

yordinate

Front 31

continuous data

Back 31

use limits

Front 32

SD scores

Back 32

smaller = closer to the mean

Front 33

Averaging several means

Back 33

meanxn +mean2xn2 / n + n2

Front 34

inferential stats

Back 34

making inferences about a pop based on a sample set of numbers

Front 35

sum of scores quantity scored

Back 35

(x1+x2+x3)2

Front 36

sum of squared raw scores

Back 36

x12+x22+x32

Front 37

range and number of possible scores

Back 37

range: highest - lowest
number of possible scores: highest-lowest +1

Front 38

transformations if a constant (k) is added/subtracted the...

Back 38

MEAN of the transformed scores is changed by the value of the constant.!
(SD and variance dont change)

Front 39

transformation: If every score in a distribution is
multiplied by a constant (k), the

Back 39

the mean of the transformed scores becomes the product of the old mean and the constant.!

SD of the transformed scores is the product of the original standard deviation x the constant.
The variance of the
transformed scores is the product of the original variance x the square of the
constant (i.e., k2).!

Front 40

semi interquartile range

Back 40

q3-q1/2

Front 41

the purpose of the finite sample correction for the standard deviation and
variance statistic

Back 41

We use (n-1) to correct for the variation that is present in a sample that is, on
average, too low when we calculate variation around an estimated sample mean.

Front 42

rules for transformations

Back 42

divide by a constant, add to equal group A varibale

SD by same constant