Statistics
The science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data. [Blu4 Page 3]
The science of collecting, describing, and interpreting data. [JK10 Page 4]
An experiment: a planned activity whose results yield a set of data [JK10 page 8]
Descriptive Statistics and Inferential Statistics
Descriptive Statistics
Inferential Statistics
Collecting data, Organizing data, Summarizing
data,Presenting data. The statistician tries to
describe a situation. [Blu4 Page 4]
The statistician tries to make inferences from samples to populations. It consists of
generalizing from samples to populations, performing estimations and hypothesis tests,
determining relationships among variables, and making predictions. [Blu4 pages 4-5]
The area called hypothesis testing is a decision-making process for evaluating claims
about a population, based on information obtained from samples. [Blu4 page 4]
Collecting, Presenting, Describing… it’s what
most people think of when they hear the word
“statistics” [JK10 page 4]
The technique of interpreting the values resulting from the descriptive techniques and making
decisions and drawing conclusions about the population. [JK10 page 4]
Probability distinguished from Statistics
[JK10 page 27]
Probability
Statistics
You know the possible results.
You answer questions like “what is the likelihood of some particular
outcome?”
You don’t know what’s in the box.
Take a sample,
describe the sample (descriptive statistics),
make inferences about what’s in the box based on what’s in the
sample (inferential statistics.)
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Populations and Samples
A Population
A Sample
A population consists of all subjects (human or otherwise) that are
being studied. [Blu4 page 4]
A sample is a group of subjects selected from a population. [Blu4 page
4]
A collection, or set, of individuals, objects, or events whose properties
are to be analyzed. [JK10 page 7]
A sample is a subset of a population [JK10 page 8]
A sample survey rather than a census [JK10 page 20]
A census [JK10 page 20]
A Parameter
A parameter is a numerical value summarizing all of the data of an
entire population [JK10 page 8]
A Statistic
A statistic is a numerical value summarizing the sample data. [JK10
page 8]
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Variables and Data
Variable (n)
Data
Random Variables
Data Set
Data value, or
Datum
A characteristic or
attribute that can assume
different values [Blu4 page
3]
The values (measurements
or observations) that the
variables can assume.
[Blu4 page 3]
Variables whose values
are determined by chance
[Blu4 Page 3]
A collection of data values
[Blu4 page 4]
Each value in a data set is
called a data value, or
datum. [Blu4 page 4]
A characteristic of interest
about each individual
element of a population or
sample [JK10 page 8]
The set of values collected
from the variable from
each of the elements that
belong to the sample.
[JK10 page 8]
The value of the variable
associated with one
element of a population or
a sample. This value may
be a number, a word, or a
symbol. [JK10 page 8]
Qualitative Variables and Quantitative Variables
Qualitative Variables
Quantitative Variables
Variables that can be placed into distinct
categories, according to some characteristic or
attribute. Examples: M/F, religious preference,
geographic location. [Blu4 page 6]
Numerical values. They can be ordered or ranked. Examples: age, weight, temperature.
[Blu4 page 6] A variable that “quantifies” an element of a population. [JK10 page 10]
A variable that describes or categorizes an
element of a population. Synonyms: “attribute”,
“categorical variable” [JK10 page 9]
Discrete variables
Countable. Examples: How many children in
a family, how many phone calls received.
[Blu4 page 6]
Continuous variables
Can assume an infinite number of “between”
values. Measurements. Including fractions
and decimals [Blu4 page 6]
Can assume a countable number of values.
Isolated points along a line interval. There
are gaps between possible values. [JK10 page
11]
“15” means “14.5-15.5” which means
“14.5 ≤ 𝑥 < 15”. [Blu4 page 7]
Can assume an uncountable number of
values. Any value along a line interval,
including every possible value between any
two values.
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Measurement Scales: Nominal, Ordinal, Interval, Ratio
Nominal level of
measurement
Ordinal level of
measurement
Interval level of
measurement
Ratio level of
measurement
Classifies data into mutually
exclusive (non-overlapping)
exhausting categories in which no
order or ranking can be imposed
on the data. Examples: zip code,
political party, marital status [Blu4
pages 7-8]
Classifies data into categories that
can be ranked; however, precise
differences between the ranks do
not exist. Examples: A,B,C,D,F;
small, medium, large. [Blu4 page
8]
Ranks data, and precise
differences between units of
measure do exist; however, there
is no meaningful zero. Examples:
IQ scores, temperature
measurements. [Blu4 page 8]
Interval measurement and there’s
a concept of a true zero. And
true ratios exist when the same
variable is measured on two
different members of the
population. Examples: height,
weight, area, count of some
event. [Blu4 page 8]
Characterizes/ Describes / Names
an element of a population.
Arithmetic operations are not
meaningful on nominal variables.
There is no sense of higher or
lower. [JK10 page 10, modified]
A qualitative variable that
incorporates an ordered position,
or ranking. [JK10 page 10]
These are examples of qualitative variables.
These are examples of quantitative variables.
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Kinds of surveys
Kind of surveys [Blu4 pages 9-10]
Advantages
Disadvantages
Telephone surveys
Mailed questionnaire
surveys
Personal interview
surveys
Less costly than personal
interview.
Maybe more candid responses.
Wider geographic area can be
covered.
Less expensive.
Anonymity of respondents.
Low response rate.
Inappropriate answers.
Some may find questions difficult
or hard to understand.
Can obtain in-depth responses.
Miss the phoneless, no answers.
Unlisted numbers. Cell numbers.
Tone of voice can influence
response.
Interviews must be trained.
Costly.
Other data collection methods
[Blu4 page 10]
Surveying records
Direct observation
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Sampling methods
A sampling frame is a list, or set, of the elements belonging to the population from which the sample will be drawn. Ideally, the sampling frame
should be identical to the population with every element of the population included once and only once. [JK10 page 20]
Random Sampling
Using chance methods or random numbers
[Blu4 page 11]
Systematic sampling
th
Select every k subject [Blu4 page 12]
…starting from a first element, which is
randomly selected from the first k elements.
[JK10 page 23]
Cluster sampling
Convenience sampling
Divide population into groups. Select some
groups to be in the sample. [Blu4 page 12]
Whoever’s available [Blu4 page 13]
Stratified sampling
Divide population into groups (“strata”) and
sample some from each group. [Blu4 page 12]
..and then selecting a number of items from
each of the strata by means of a simple
random sampling technique.” [JK10 page 24]
Volunteer sampling
…stratifying the population… and then
selecting some or all of the items from some,
but not all, of the strata. [JK10 page 25]
Biased sampling method: A sampling method that produces data that systematically differ from the sampled population. [JK10 page 18]
Judgment samples: Samples that are selected on the basis of being judged “typical”. [JK10 page 21]
Probability samples: Sames in which the elements to be selected are drawn on the basis of probability. Each element in a population has a
certain probability of being selected as part of the same.[ JK10 page 21]
Excellent tree diagram of sampling techniques on [JK10 page 21]. Definitions follow for “single-stage sampling”, “simple random sample”,
“multistage random sampling”, “proportional stratified sample”
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The data collection process
[JK10 Page 19]
1.
2.
3.
4.
5.
Define the objectives of the survey or study.
Define the variable and the population of interest.
Define the data collection and the data measuring schemes.
Collect your sample. Select the subjects to be sampled and collect the data.
Review of the sampling process upon completion of collection.
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Kinds of studies
Observational study
Experimental study
The researcher observes what is
happening or what has happened
in the past and tries to draw
conclusions based on these
observations. [Blu4 page 14]
The researcher manipulates one of the variables and tries to determine how the manipulation influences
other variables. [Blu4 page 14]
Independent Variable
Dependent Variable
(also known as the Explanatory variable)
(also known as the outcome variable)
The variable that is being manipulated by the
The resultant variable. [Blu4 page 14]
researcher. [Blu4 page 14]
A confounding variable is one that influences the dependent or outcome variable but cannot be separated
from the independent variable. The Hawthorne Effect is when subjects who are aware that they are
subjects in an experiment change their behavior in ways that affect the results of the study.
Advantages and disadvantages – discussion on [Blu4 pages 14-15]
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Misuses and Abuses of Statistics
[Blu4 pages 16-18]
Suspect Samples
Ambiguous Averages
Changing the Subject
Detached statistics
Implied connections
Misleading graphs
Faulty survey questions
 Was the sample size too small?
 Were the subjects selected properly, without bias?
 Is the sample representative of the population?
Choosing the one statistic to support a particular position and ignoring the rest
 Talking about measurements or talking about percentages. And if talking about percentages, percent of
what?
 Changing the timeframe [my addition]
No comparison is present
Hedging: “may help”, “studies suggest”, “in some people”
(details discussed elsewhere)
It’s all in the wording.
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