Discrete variable- A variable with a basic unit of measurement that cannot be
subdivided. (people)
Hypothesis- A statement about the relationship between variables that is
derived from a theory. Hypothesis are more specific than theories, and all terms
and concepts are fully defined.
Data- in social science research, information that is represented by numbers
Descriptive Statistics- The branch of statistics concerned with 1)summarizing
the distribution of a single variable 2) measuring the relationship between two or
more variables.
Measure of association- statistics that summarize the strength and direction of
the relationship between variables.
Theory- generalized explanation of the relationship between two or more
variables.
Populations- total collection of all cases in which the research is interested
Inferential statistics- statistics concerned with making generalizations from
samples to populations.
Independent variable- variable that is identified as a causal variable. the
independent variable is thought to cause the dependent variable.
level of measurement- mathematical characteristics of a variable as determined
by the measurement process. A major criterion for selecting statistical
techniques.
Statistics- set of mathematical techniques for organizing and analyzing data.
Data reduction - summarizing many scores with a few statistics
dependent variable- variable that is identified as an effect, result of outcome of
something.
Variable- any trait that can change values from case to case.
Data value- value of variable associated with one element of population
Data set-collection of measurements or observations
Univariate- summarize one variable (GPA)
Bivariate- describe relationship between two variables
Mulitivariate- descriptive statistics relationship between three or more variables
Raw Score-single measurement/observation
Continuous variable- variable with a unit of measurement that can be
subdivided. (rounding of the scores)
Research- process of gathering information systematically to answer questions
or test theories.
Sample- subset of a population in inferential statistics. Discrete variable- A
variable with a basic unit of measurement that cannot be subdivided.
Hypothesis- A statement about the relationship between variables that is
derived from a theory. Hypothesis are more specific than theories, and all terms
and concepts are fully defined.
Data- in social science research, information that is represented by numbers
- the sum of scores
Basic rule of precedence- find all squares and square roots first, multiple, divide,
Sigma, add, subtract
Validity- describe if it measures the concept it is intended to measure
Reliability- quality of measuring instrument
Nominal Level of Measurement:
 Categories are not numbers
 Gender, area code, provinces
 Cannot be ranked, added, divided
 Categories must be exhaustive (categories must exists for every score)
 Homogenous (comparable cases)
 No ambiguity exists mutually exclusive
 discrete
Ordinal Level of Measurement:
 Ranked from high to low
 More or less = classified
 Limitation-scores position respect to other scores
 discrete
Interval Level
 numbers



Ordered categories exactly the same
Distance is not equal
onlly interval ratio level can be continous
Ration Scale Equal differences on scale reflect equal difference in magnitude
 Distance is equal
******
Type
Nominal
Ordinal
Ratio
Interval
dichotomous
******
Description
Classification of objects
-can only be discrete
Variable can be ranked
-can only be discrete
Variables can be ranked,
distance is equal
-can only be continous
Variables can be ranked,
distance is not equal
-can only be continous
Variable comprises only
two categories
example
-ethic groups
-job satisfaction
productivity
Income, age ,salary
temperature
Gender
********
*****
Chapter 2
Percentage: %=    x 100 -frequency over # of cases in all categories
n
Proportion: 
N
-with small # of cases less than 20 report actual frequency
-always report proportions and percentages
Ratio compares parts to parts
 23females/19 males
 =1.21 females for every male
(1)
f2
Rates
 # of actual occurrence divided by possible occurrence



usually multiplied by 10 to eliminate decimal points
crude death rate (CDR) multiplied by 1000
CDR= # of deaths X 1000
Total pop
Percentage Change
 Measures increase or decrease in a score @ 2 different times
o {(f2-f1)} X100
f1
-2nd set(-)1st set / divide by 1st set X100
Frequency distribution
 organized table of # of individuals in each category on the scale of
measurement
 first step in any statistical analysis
 graph or table
 set of categories that make up original measurement scale
 record of the number of individuals in each category
 to understand how many times something has occurred
 first step in statistical data
 categories must be discrete 0-99/100-199/200-299 (class intervals)
 # of categories must be between 6 and 20
lower class limits- smallest # that can belong to different classe interval 0-99
upper class limits- largest number that can belong to different classe interval 0-99
Class midpoints-middle of two classes
-add lower case to upper, divide by 2
State class limits:
 class intervals that organize variables into discrete, non-overlapping
intervals.
 when stated as a discrete category
Real class limits:
 divide distance between the class intervals and add to upper class, and
subtract from lower class . ex: stated limits: 18-19, real limits: 17.5-19.5
 when stated as a continous category
Cumulative frequency and Percentage:
 give glance at how many cases fall below a given score in the distribution.
 research may want to make a point of how cases are spread acress the range
of scores.
Histograms
 each bar represents a range of values
 use real limits rather than stated limits
 values contact with each other show continuous variable




display distribution of data
used for continous, but commonly used for discrete interval ratio level
frequency always on vertical axes
tells you if the data is skewed right/left, bell-shaped
Chapter 3
Measure of Central Tendency:
Idea of the typical mean, median or mode case in the distribution

Mode



Mean






frequency that occurs most
frequently
quick easy indicator of central
tendency
nominal-level variable
seldom reported alone
"average"
add all values, divide by N of values
most commonly used measure
interval-ratio level, but also used
ordinal-level (highly skewed
distribution)
X bar
Weighted/aggregate mean
o occurance of more than one
value.
o (Xi) x (2f)
o multiply values by frequencies
Value Frequency Value X
frequency
97
4
97x4=
388
94
11
94x11 =
1034
92
12
92x12
=1104
91
21
91x21 =
1911
90
30
90x30=
2700








89
12
78
9
60
total
1
100
89x12=
1068
78x9 =
702
60z1= 60
8967
A) All scores cancel out around the
mean.
B) Uses all scores-strength, weakness
affected by every score.(skews)
C) Least squares principle- mean is
closer to all scores than the other
measures of central tendency.
mean pulled in the direction of the
extremes.
Symmetric-mean and median having
same value.
Positive Skew- skewed to left. mean is
higher in value than median
Negative skew- skewed to the right,
mean is lower in value than median.

Median





represents center of distribution of
scores
when N is odd, value of median is
unambiguous (always a middle case)
when N is even the score halfway
between the two scores must be
attained
ordinal or interval-ratio
measures position or location


good choice in extreme values
(outliers)
household income=extreme values
Percentile
 used for median. media is the 50th percentile
 identifies specific point of case
 find 37th percentile of 78,
o 78 X .37 =28.86 is the case
Decile
 divide distribution into 10's
Quartile
 divide distribution into quarters 0 q1(25%) q2(50%) q3(75%) q4(100%)
Measure of Dispersion
 How much variety of the distribution
 ex. how 'often' do graduates receive $40,000 per year.
Chapter 4
Measure of Dispersion
 variety in a distribution
 the taller the curve=less dispersion, the flater the curve=more dispersion
 amount of diversity, heterogeneity
 R -range is the distance from highest value to the lowest
o quick easy indication of variablity
o ordinal, interval-ratio
o limited= based on only 2 scores
o no information about variation between high and low scores
 Q-interquartile range, only considers the middle 50% of cases in distribution
 boxplot- Diagram of LH

o L--------Q1--------Q2--------Q3--------H
o
o based on information on five-number summary
o Q2(median) is marked with vertical line
o useful when two ore more data sets are being compared
 Good measure of dispersion:
o use all scores in distribution
o describe average deviation
o increase in value as the distribution becomes more diverse
Standard Deviation (S)
 uses all scores in distribution
 increases in value as the distribution of scores becomes more diverse
 distance between socres and mean (deviation)
 if scores are clustered around each other, deviation would be small, vise
versa.
 value of S can increase with the inclusion of one or more outliers
 units of standard deviation are the same as the units of orginal data values
 average distance of each score from the mean
 interval-ratio, but often used with ordinal-level
 the higher the SD=more distribution, lower SD=less distributions
 0 value- no dispersion


N-1 is used when working with random samples rather than entire
populations.
Index of Qualitative Variation (IQV)
 only measur of dispersion for nominal level variables (but can be used with any
variable)
 varies from 0.00 (no variation) to 1.00 (maximum variation)
 raio of the amount of variation observed in the distribution.
Variance
 measure of variation equal to the square of the standard deviation s2
 used in inferential statistics
Coefficient of Varition
 presents the standard deviation as a percentage of the mean value
 allows you to compare the variability of different variables.
The range rule of thumb-principle that many data sets (95%) of sample values lie within
two standard deviation of the mean.
Chapter 5
Normal distribution
 great importance
 combo of mean and SD can use normal distribution curve to contruct precise
descriptive statements about empirical distributions
 theoretical model, frequency polygon or line chart that is 'unimodal' (single
mode/peak) perfectly smooth, and symmetrical=mean, median and mode are
same value.
 crucial point is distance along the abscissa (horizontal)
Empirical rule
 68% of all values fall within 1 standard deviation of mean

95% of all values fall within 2 standard deviations of mean

99.7% of all values fall within 3 standard deviations of the mean
Z scores:
 percentage of are above, below or between scores in empirical distribution
 always have same value for mean and standard deviation
 convert the original units of measuremen into Z scores, "standardize the normal
curve to a distribution that has a mean of 0.
 how many standard deviation units a case is above or below a mean

a ruler from x to the mean
 when value is less than the mean, the Zscore is negative
 Ordinary values Zscore between -2 and 2
 unusual values Zscore less than -2 <-2>
Normal curve table
 Appendix A, detailed description of the area between Z score and the mean
Probability
 method for measuring and quantifying the likelihood of obtaining a specific
sample from a specific population.
 define as a fraction or a proportion.
 ratio comparing frequency of occurrence / total number of possible events
 in frequency distributions probability can be defined by proportions of
distribution
 in graphs, can be defined as a proportion of area under the curve
Unit normal table:
 lists different proportions of corresponding to each z-score location.