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BASIC STATISTICS WE MOST OFTEN USE
Student Affairs Assessment Council
Portland State University
June 2012
Overview of the Session
• Introduction to statistics
• Things to know before you run statistics
• How to run & understand descriptive statistics using
Campus Labs
How we use statistics in assessment
• Produce information for decision making & improvement
• Take data points and transform them into information
• Descriptive rather than inferential. Need to know if do
these:
• Surveys (focus of today’s examples)
• Experiments
• Quasi-experiments
• Secondary data analysis (e.g., using institutional datasets)
• Rubrics (the scored part)
Consider these before you run statistics!
• What does your instrument measure & how well does it
do it? (reliability and validity)
• Who participated and how representative are they?
(sampling)
• What levels are you measuring, as it matters for the
types of analyses you can run (ordinal, nominal,…)
What does your instrument measure &
how well does it do it?
• Face and Content Validity
• How to do:
• Review by subject-matter expert
• Link to literature review and/or theoretical framework
• Align with content of your program.
• Pilot-test item quality with representative sample
Who participated and how representative
are they? (sampling)
• Population: Entire group that is of interest to you (e.g., all
enrolled undergraduate students).
• Sample: Sub-set of your population (e.g., sample of 1000
undergraduate students).
• Respondents: are then the number of people who
respond to your survey.
• Match to original population by looking at demographics
of your respondents
What levels are you measuring
• Statistics are appropriate or inappropriate based on the
levels of measurement in your data.
• Levels of measurement
• Nominal
• Ordinal
• Continuous
Nominal Data
• Categorizes without order = categorical data
• Applies to data which are only classified by name, labels,
or categories (e.g., gender, living on or off campus,
political affiliation, yes/no)
• N, %, Mode
Ordinal Data
• Assigned order that matters
• Differences between categories may not be equal (e.g.,
Strongly agree, Agree, Disagree, Strongly disagree)
• N , %, mode often treated as continuous
4
3
2
1
-
Continuous
• Interval & Ratio
• Categorizes based on difference,
order, AND units of equal difference
between variables (e.g., individuals’
IQ scores and difference across
and between those scores; age,
salaries)
• N, &, Mean, Median if skewed
Two kinds of statistics
• Descriptive
• Discuss a large amount of data in an abbreviated fashion
• Highlight important characteristics of data
• Inferential
• Go beyond description
• Show relationships between groups
• Use sample data to draw inferences about the population
Descriptive Statistics
Measures of
Frequency
Measures of central
tendency
• Count, Percent,
Frequency
• Mean, median,
mode
• Shows how often
something occurs
or a response is
given
• Locates the
distribution by
various points
• Show average or
most commonly
indicated
response
Measures of
dispersion or
variation
• Range, variance,
standard
deviation
• Identifies the
spread of the
scores by stating
intervals
• Range = high/low
points
• Variance or
Standard
Deviation =
difference
between observed
score and mean
Measures of
position
• Percentile ranks,
quartile ranks
• Describes how
scores fall in
relationship to one
another
• Example: Scores
that indicate a
students’ score
falls within the
90th percentile of
standardized
group
• Use this when you
need to compare
scores to a
normalized score
(usually a national
norm)
Measures of Frequency
• Acceptable for all data levels
• Count/Frequency – the # who gave response
• Percent – count/total possible responses. Use when
comparing data.
Measures of Central Tendency
• Ordinal and Continuous data
• Mean: the average (e.g., 3.25)
• Median: value of the data that occupies the middle
position when the data is ordered from smallest to largest
Mode: data point/answer that occurs most frequently
Reporting Counts, Percents or Means
Count
Percentage
Mean
Measures of Dispersion: How spread out
are the data?
• Is there a large variation in student answers to how
welcomed they feel in the Student Union?
• Standard deviation: Average distance from the mean.
• small standard deviation means that scores or values cluster
around the mean.
Inferential Statistics
• Compare groups
• Generalize from the sample to the population
• Determine if the difference between groups is dependable
or by chance
•
•
•
•
•
Correlations
Chi-square tests
T-tests
ANOVA
Regression
Comparisons in Campus Labs
• Key-Performance Indicators (KPI): track means or
percentages over time
• StudentVoice Benchmarking T-Test Calculations in their
comparative reports
• https://www.studentvoice.com/app/wiki/Print.aspx?Page=
Viewing%20Benchmark%20Project%20Results
• Directions for these under WIKI
• https://www.studentvoice.com/app/wiki/MainPage.ashx
Example of a comparative analysis report