CMNS 260 Lecture Notes - Lecture 10: Falsifiability, Statistical Inference, Descriptive Statistics
8 May 2018
School
Department
Course
Professor
1
Quantitative Data, Bivariate & Multivariate Statistics
Studying relationships between two variables (Bivariate Statistics)
• Do the patterns in the tables & graphs mean that there is a relationship between the two
variables?
• If there is a relationship, how strong is it? Are the results statistically significant? Are the results
meaningful?
• Common Methods for studying relationships
o Create contingency tables (cross-tabulations & percentaged tables)
o Create Graphs, Charts (like scattergrams or plots)
o Use measures of association
Bivariate statistics: Key terms
• A bivariate statistic is a statistical measure that involves two variables only.
• Correlation refers to the idea that two variables vary together, such that knowing the values in
one variable provides information about values found in another variable.
• Independence refers to the absence of a statistical relationship between two variables (i.e.,
when knowing the values on one variable provides no information about the values that will be
found on another variable). There is no association between them.
Correlations– relationships between two variables
• When change in one variable is associated with a systematic change in another variable the
statistical relationship is called a correlation.
• Why seek correlations?
o Description (to identify relationships)
o Explanation (to understand past events)
o Prediction (to forecast future events)
• How accurate is the prediction likely to be?
o Depends on the strength of the relationship or association.
Types of Hypotheses
• Keyword: A non-directional hypothesis includes a proposition that has at least one independent
and one dependent variable, but does not posit the magnitude or direction of the relationship
between the variables.
• Keyword: A directional hypothesis includes a proposition that has at least one independent and
one dependent variable, and posits the magnitude or direction of the relationship between the
variables.
• Past keod: A ull hpothesis is a hypothesis that says there is no relationship or association
between two variables, or no effect. (p.89)
Statistical Methods: Cross-tabulations & contingency tables
• Keyword: A cross-tabulation involves placing data for two variables in a contingency table to
show the number or percentage of cases at the intersection of categories of the two variables.
• Keyword: A contingency table is a table that shows the cross-tabulation of two or more
variables. It usually shows bivariate quantitative data for variables in the form of percentages
across rows or down columns for the categories of one variable.
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