Statistics is used to organize and understand data through research design, quantification, description, and analysis. It involves measures of central tendency like mean, median, and mode to provide an overview of a population or sample, as well as measures of variability. Inferential statistics uses probability to compare sample means and make conclusions about populations. The goal is to determine the probability that differences observed in a sample reflect real differences in the overall population from which the sample was drawn.

1. Statistics Orientation
Darrin Coe, Ph.D.

2. What?
 Statistics is a mathematical tool for
organizing and understanding information
or data
 Collection of information or data = research
design and methods
 Quantification of information or data = placing
data into analyzable formats.
 Description of information or data = initial global
picture of the data or phenomena
 Analysis of information or data = causality,
prediction, understanding of the data or
phenomena

3. In many ways statistics is
Simply the study of probability and
odds; possibilities and perhapses

4. Where? How?
 Statistics is used to study phenomena that
can be operationalized, and quantified:
 Hope and forgiveness -- psychology
 Economic trends -- economics
 Movement of quarks -- physics
 Increases in marijuana yield -- biology
 Probabilities of yield when combining peanut
butter and chocolate – marketing/business
 Inflation change over time -- economics
 Causal effects of isolation on mental illness –
penology

5. When?
 Statistics and statistical analyses are
used for doing quantitative research
 Used only with data that has been
collected in a quantifiable form and has
been operationalized as a quantity of
some construct.

6. Who?
 Statistics are generally used by
researchers who are:
 Positivists
 Empiricists
 Realists
 They believe there is an objective,
quantifiable reality that exists beyond
our subjective perceptions.

7. Data, Data, Data
 types of data
 Nominal – consists of labels, no absolute
zero point, no standardized measure, no
rank ordering (men, women, Floridian,
Dakotan)
 Ordinal – labels, rank ordered, no
standard measure, no absolute zero
point (less happy, happy, more happy)

8. More Data, Data, Data
 Types of data (continued)
 Interval – rank ordered, standard
measure between intervals, no absolute
zero point (Fahrenheit temperature
scale).
 Ratio - rank ordered, standard measure
between intervals, absolute zero point
(Kelvin temperature scale, number of
eye blinks in 1 minute, number of joints
smoked in 1 hour)

9. Let’s Get Organized: Summary
Stats
-- used to organize data and provide
overview style picture of a population
or sample.
-- Measures of central tendency
-- Mean, median, mode
-- Measures of variability
-- range, minimum, maximum,
variance, standard deviation.

10. Standardized Statistics
Z – scores
-- generally used when population
data is known.
T-Scores
-- generally used when population
data is unknown and needs to be
approximated.
Confidence Intervals
-- used to indicate where true scores
fall.

11. Scores of Relationship
 Correlations – how strongly variables
are related, or how strong one
variable predicts another variable.
-- Pearson’s
-- Used with continuous data
-- Spearman’s
-- used with nominal/ordinal data

12. So how significant is it?
 Often referred to as the “p-level”
 Generally = .05, .01, or .001
 Also referred to as “alpha”
 Alpha = the probability that you
would get a result given that the null
hypothesis is true in the population.
 P-level is arbitrary and determined by
scientific tradition.

13. More significance
 A significant result simply means that
a null hypothesis is not true.
 Significance equals “yes” or “no”
 Significance does not equal “proof” or
“truth”
 Significance does not prove the
research hypothesis.

14. Probability
 The bridge that connects samples with the
populations they are drawn from.
 A proportion consisting of a specific result
over all possible results.
 Given 10 baggies, 3 with MJ and 7 with
ditchweed, the probability of buying a dime bag
of ditchweed is p(dw)=7/10 or 70% probable
you’ll get screwed, so find a new dealer.

15. Yep, it’s probable.
 Probability guides research sampling
methods.
 Probability is tied to the normal
distribution and allows for the
development of an overall picture of
population by considering the
distribution of a sample.

16. Inferential Statistics
 Using probability to compare the
means of two or more groups in a
sample to make conclusions about a
given population.

17. Types of inferential stats
procedures
 Comparing two different groups
 Comparing one group to itself.
 Comparing more than two different
groups
 Comparing one group to itself
multiple times.
 Comparing the effects of multiple
variables on one group.

18. What?
 Inferential statistics at it’s foundation
uses the standard deviation or the
variance of two or more groups to
compare the means of some outcome
measure or measures.

19. What??
 This comparison results in a
probability that there is or is not a
statistical difference between the
means. This probability tells us how
much we can infer about the
population from which the sample
was taken.

20. Final Word
 Statistics is probability.
 Probability is relate to research
design
 Research design is related to validity
 Validity is related to reality.
 Statistics = the probability of reality
Fun huh?