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

4321 -

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

• Count, Percent, Frequency

• Shows how often something occurs or a response is given

Measures of central tendency

• Mean, median, mode

• 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

Count Percentage Mean

Reporting Counts, Percents or Means

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