M7 - Correlation Flashcards
Correlation tool for:
Nominal and nominal
Ordinal and ordinal
Interval scaled and interval scaled
Phi
Spearman rank
Bravais pearson
Covariance
What
Formula
Measures the strength of the relationship between two interval-scaled variables
Whats the problem with covariance measure?
Only valid for n data pairs in the pop.
If the n data pairs are a sample out of a larger pop and the equation shall yield an estimate of the cov of the pop, the equation is only correct if x and y are the pop.s’ means
If they are the sample means, it is biased and the values need to be normalized
Values for covariance
Cov > 0 hoher positiver zamhang
Cov < 0 hoher negativer zamhang
Cov =0 kein zamhang
Bravais-pearson corr coeff
What
Values
Compared to covariance?
Measures the strebgth of the relship. between two interval-scaled vatiables
-1 perfect negative corr
+1 perfect positive corr
Compared to the covariance a comparison of different corr values is simplified since normalization has been carried out
Which corr strengths are worth reporting?
1 perfect corr
- 85-1 very strong corr
- 6-0.85 strong corr
- 4-0.6 medium corr
Control variables?
For what reason?
Variables test causal relationships
take all other variable into account that could have an
effect on B (at least those that are correlated with A), even if we are not
interested in their effect on B →
“Control variables”.
Reason: no omitted variable bias
Omitted variables
If a and k are not correlated?
If a and k are correlated?
Omitted variables
If a and k are not correlated?
–> harmless
If a and k are correlated?
- -> harmful
- -> effect of k ln b is wrongly attributed to a due to the corr between a and k
Cramer’s V Phi
Strength of the corr. between two/more nominal variables between 0-1
Spearman’s Rho
What?
Used when
Rank correlation
Used when two variables are
- ordinal, but not metric
- metric, but highly non-linear
Correlation of ordinal variables
Which vatiables?
2 variables, which are ….. but not …..
Which are …. but highly non-…..
Correlation of ordinal variables
Which vatiables?
2 variables, which are ORDINAL but not METRIC
Which are METRIC but highly non-LINEAR
Bravais - pearson corr coeff
Is a measure of … between two … variables
Shows the …. of the ….
No …. possible
Is a measure of association between two metric variables
Shows the strength of the corr
No forecasting
Regression
Closely related to ….
suited for ….
highly …..
Regression
Closely related to correlation
suited for forecasting
highly generalizable
Terminology
Y - …. variable : regress….
X - …. variable : regress….
Model:
Whats the structural and stochastic term?
The structural term accounts for the …. influence.
The stochastic term accounts for the ….. / ….. influence.
Terminology
Y - DEPENDENT variable : regressAND
X - INDEPENDENT variable : regressOR
Model: y= b0 + b1x + u
Whats the structural and stochastic term?
The structural term accounts for the SYSTEMATIC influence.
The stochastic term accounts for the NON-SYSTEMATIC/ RANDOM influence.
What effects are covered by The stpchastic term u?
- measuring errors (imprecis measure of y)
- incomplete coverage of the covariates (omitted variable bias)
