Where have you been

1
Where have you been?

• Renan Levine
• POL 242
• January 10/12, 2006

2
Theories and Data I

• An empirical theory of politics is an attempt to
  explain why people behave the way they do
  politically. 
• We observe characteristics of people,
  governments, organizations, states, etc.
• Characteristics that differ from one person,
  (etc) to another are called one variables. 

3
Recall Types of Variables

• Nominal variable has categories that have no
  numerical properties and cannot be ordered or
  ranked. Example Provinces
• Ordinal variables are ordered or ranked, but
  there is no equal unit size between categories
• Interval variables are measured using a scale in
  which the units of measurement are all equal in
  size.
• A36 Arik Sharon Feeling Thermometer
• Number of police officers per province per
  100,000 people

4
Theories and Data II

• We scrutinize variables that are related to each
  other.
• We strive to identify causes for effects we
  observe.
• Why do people vote for the Green Party?
• Why do some countries enjoy a high degree of
  sustained growth but not others?
• Why has there been a big increase in gun-related
  homicides in the GTA?
• We try to explain the dependent variable. 

5
Hypotheses and Variables

• A statement positing a relationship between two
  variables is called a hypothesis.
• A hypothesis posits a relationship between
  independent variable(s) and dependent variables.
  Independent variables influence the values of the
  dependent variable. 
• Hence, the dependent variable depends on
  independent variable(s).

6
Descriptive Statistics

• mean, median, mode.
• Later T-tests, ANOVA to compare differences.
• variance / standard deviation,
• skewness and kurtosis,
• Exercise Run a T-test using
• Israel Election 2003 with B92 Gender 1,2
  or
• CBS News Dataset with SEX 1,2

7
Crosstabs

• Relationship between two variables can be
  compared in a tabular form.
• Remember to recode data in order to make the
  crosstab easier to interpret.
• gtgt Remember???
• Measures of association (Cramers V, Kendalls
  Tau) can be used to observe strength of comparison

8
Association

9
Cronbachs Alpha and Indexing

• How well do two or more variables go together?
• Cronbachs alpha used to determine if more than
  one item is measuring the same thing.
• If the alpha is high, then yes, they do go
  together, they are presumably measuring the same
  thing, and they can be combined into an index.

10
Today Correlations

• Measure strength of relationship of interval or
  ratio variables
• Positive Relationship
• If two variables are related positively or
  directly, they track together high values on
  Variable X are associated with high values on
  Variable Y.
• Negative or Inverse Relationship
• Alternatively, they can be inversely or
  negatively related where high values of X are
  associated with low values of Y.
• With a correlation, you can begin to think about
  predicting values of Y based on a value of X.
• Go to http//individual.utoronto.ca/renan/pol242/
  1-6correlation.html

11
Correlation r

• Correlation is a measure of a relationship
  between variables. Measured with a coefficient
  Pearsons r that ranges from -1 to 1.
• r S(Zx Zy)/n 1
• ZxZ scores for X variable and Z scores for Y
  variable. Sum the products and divide by number
  of paired cases minus one.
• How to calculate Z scores can be found on-line.
• The closer the coefficient is to the absolute
  value of 1 the stronger the relationship between
  the variables being correlated.
• Values closer to 0 indicate that there is little
  or no linear relationship.
• Generally, 0.2-0.4 is weak, 0.4-0.6 is okay, 0.6
  or higher is strong.
• If correlation is very high, then its probably
  something related that you might considering
  indexing or choosing just one variable.

12
Problems with Correlations

• Two problems
• Spurious correlations.
• Third Variable Error Appear correlated because
  something else is really causing the two to be
  related.
• Sensitivity to extreme outliers
• Restricted range
• Part of range has a relationship or a different
  relationship than another part of the range.
• Curvilinear relationships
• Solution Partial Correlation

13
Examples

• Provinces
• Turnout and Age
• Turnout and SPENDHLT of Govt Expenditures
  Spent on Health 2005
• Police and SPENDEDU of Govt Expenditures
  Spent on Education 2005

14
What if non-interval/non-ratio?

• Measurements read and interpreted the same way,
  but instead of Pearsons product-moment
  correlation coefficient (Pearsons r), you use
• Spearman ordinal x ordinal
• Point-biserial one interval/ratio, one
  dichotomous
• Phi two dichotomous variables