Bivariate data

Explanation as the goal of political science

x --> y

5 key questions of causation

1) existence
2) direction
3) strength
4) statistical significance
5) causality

existence

is there a relationship between these 2 variables?

direction

what is shape of relationship?

strength

how many values of DV are explained by variables of IV?

statistical significance

is this observed relationship due to chance?

causality

Is IV causing variation in DV?

when IV: Nominal/Ordinal and DV Interval/Ratio, then appropriate procedures are

ANOVA
Difference of means

when IV: I/R and DV I/R, then appropriate procedures are

regression
correlation

Interpreting measures of association

existence, direction, strength

-1 = ..... 0= ...... 1=

=strong negative .... = no relationship ... = strong positivr

p=

probability of findings occurring if null hypothesis is true

what is goal when determining confidence goal?

.05 or less

the stronger the relationship...

the more significant it is

what is lambda

measure of association that ranges from 0 to 1 and shows strength of relationship between 2 nominal variables

how to calculate lambda

Ewithout - Ewith / Ewithout

Regression finds line that ...

best fits data points

goal of regression

find equation for straight line that best fits relationship

straight line equation

y= a + bX

y - intercept = a
slope of line = b

regression equation

Y = a+BX+E (greek sigma)

a= constant
b= regression coefficient
e = error

ordinary least squares regression

minimizes the shared distances from regression line

r - squared =

% of total variation in Y explained by X

appropriate procedures vary according to variables ..

level of measurement

when IV: N/O and DV N/O, then appropriate procedures are

contingency tables ( crosstabs)

what makes crosstabs easier to understand

percentages in columns

the more column percentages change

the stronger the relationship is

statistical significance is affected by

strength of relationships
# of observations

measure of association is also called

Kendall's Tau - there is relationship if not 0

is p is not below 0.05

we can not say relationship is significant

when is bivariate regression data appropriate

Both IV and DV are I/R

what can bivariate regression tell us

whether x and y are related in a linear way

direction of relationship and how much a given change in x will move y

the constant tells us ...

the predicted value of y when x = 0

the meaning of the regression coefficient

the regression coefficient tells us the effect on y for every unit increase in x