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Descriptive StatisticsEducating students on when to
use descriptive statistics
Descriptive Statistics
Link: http://www.wolframalpha.com/
examples/Statistics.html
The Goal: “Describe or summarize your research data. This allows you to make sense of your set of data and make the key characteristics easily understandable to others.”
(Research Methods, 374)
Note: Statistics are numerical processes that add depth to quantitative data sets.
Note: Qualitative sets provide value through rich description, but can be coded numerically to then use statistical methods.
We will use Star Wars to learn about Descriptive Statistics.
3 Levels of Descriptive Statistics
1. Padawan: Central Tendency
2. Jedi Knight: Variability and Frequency Distribution
3. Jedi Master: Relations among Variables Don’t give into the hate of statistics.
Don’t give in to the Dark Side.
Use the force. Make your data depthful, you will.
Padawan Level: Central TendencyMean, Median, and Mode
Measure of Variability: “The single numerical value that is considered the most typical of the values of a quantitative variable.”
(Research Methods, 383)
Mean● In a set of data, the average
of all numbers is the “mean” of the data set.
● This can be used to discuss very general results.
● Moving forward with Mean:○ Variance○ Standard Deviation
How could this be used in your research?
What type of analysis could this create?
Median● In a set of data, the middle of
all numbers is the “median” of the data set.
● This can be used to discuss very general results.
● Moving forward with Median:○ Range
How could this be used in your research?
What type of analysis could this create?
Mode● In a set of data, the most
frequent number is the “mode” of the data set.
● This can be used to compare other numbers to the mode.
● Moving forward with Mode: ○ Frequency Distribution
How could this be used in your research?
What type of analysis could this create?
Moving to Level 2...
Jedi Knight Level: Frequency and VariabilityFrequency Distribution, Range, Variance, and
Standard Deviation
Frequency Distribution: Systematic arrangement of data values in which the unique data values are rank ordered and the frequencies are provided for each of these values.” (Research Methods, 377)
Measure of Variability: “A numerical index that provides information about how spread out or how much variation is present in a variable.” (Research Methods, 385)
Frequency Distribution● Arrangement of data to
expose the repetitive nature of a variable within the data set
● This pattern can be converted into percentages to expose basic groupings.
How could this be used in your research?
What type of analysis could this create?
Range● Distance between highest
and lowest number in a data set.
● Range= H-L● Super basic and should only
be used to introduce other measures of variability
How could this be used in your research?
What type of analysis could this create?
Variance● Average deviation of the
data values from their mean in squared units.
● Formula:
Variance= Σ(X-A)2
n● Variance is used to build
standard deviation
How could this be used in your research?
What type of analysis could this create?
Standard Deviation● Square root of the variance
SD: √Variance● Approximation of how far
each number in a data set is from the mean.
● Larger the value: Data spread is wide
● Smaller the value: Data spread is small
How could this be used in your research?
What type of analysis could this create?
Normal Curve:● Normal distribution is bell
shaped● If data is “normally”
distributed, this shape would appear…
● When this shape is not present, your data is “skewed” (limitation)
● Further Study: Z Scores
Moving to Level 3...
Nice work, everyone!
Jedi Master Level: Relationship among VariablesDifference between Means, Correlation Coefficient,
Regression Analysis, Contingency Tables
Relationship among Variables: Measurement of how different variables -dependent and independent- are related.
Difference between Means● Method to standardize data
to measure difference in variable data sets
● Cohen’s d formula● Useful for:
○ Pre-test/Post-Test○ Use of Control Group
How could this be used in your research?
What type of analysis could this create?
Correlation Coefficient● Measurement regarding the strength and linear direction of
two variables● Negative Correlation
Correlation Coefficient● Correlation: Association or Connection of Variables● Positive Correlation: Variables move in same direction● Negative Correlation: Variables move in opposite directions
Regression Analysis● Set of procedures used to
explain or predict the values of a dependent variable based on values of one or more independent variable
● Creates a Regression Line that exposes analysis pattern in a data set
Contingency Tables● Table built to analyze
relationship amongst categories of data sets○ Gender to Variable○ Age to Variable○ Education Level to
Variable○ Other demographic
How could this be used in your research?
What type of analysis could this create?
Congratulations! Pat on back, you deserve!
Tell me more about how to organize your data...