Correlation : SPSS/STATA

Srinivasulu RajendranCentre for the Study of Regional Development (CSRD)

Jawaharlal Nehru University (JNU)New Delhi

Indiar.srinivasulu@gmail.com

Objective of the session

To understand CORRELATION

1. What is the procedure to perform Correlation & Regression?2. How do we interpret results?

Identify the relationship between variables that we want to perform Scatter plot for outliers and type of relationship

Monthly HH food Expenditure and HHSIZE

Interpreting Correlation Coefficient r

strong correlation: r > .70 or r < –.70moderate correlation: r is between .30 & .70

or r is between –.30 and –.70weak correlation: r is between 0 and .30

or r is between 0 and –.30 .

| | |r = -1.0 r = -.9 r = -.7 r = -.5 r = -.3 r = 0 r = .3 r = .5 r = .7 r = .9 r = 1.0

weak correlation

moderate correlation

strong correlation

GENERATE A SCATTERPLOT TO SEETHE RELATIONSHIPS

Go to Graphs → Legacy dialogues→ Scatter/Dot → Simple

Click on DEPENDENT “mfx”. and move it to the Y-Axis

Click on the “hhsize”. and move it to the X-Axis

Click OK

Scatterplot might not look promising at first

Double click on chart to open a CHART EDIT window

use Options →Bin Element Simply CLOSE this box.Bins are applied automatically.

BINS

Dot size now shows

number of cases with

each pair of X, Y values

DO NOT CLOSE CHART EDITOR YET!

Add Fit Line (Regression)In Chart

Editor:Elements

→Fit Line at Total

Close dialog box that opens

Close Chart Editor window

Edited ScatterplotDistribution

of cases shown by dots (bins)

Trend shown by fit line.

Type of CorrelationBivariate Correlations.Partial CorrelationsDistances

BIVARIATE CORRELATIONS

In Bivariate Correlations, the relationship between two variables is measured. The degree of relationship (how closely they are related) could be either positive or negative. The maximum number could be either +1 (positive) or -1 (negative). This number is the correlation coefficient. A zero correlation indicates no relationship. Remember that you will want to perform a scatter plot before performing the correlation (to see if the assumptions have been met.)

ObjectiveWe are interested in whether an monthly HH

food expenditure was correlated with hhsize.

Step 1

The Bivariate Correlations dialog box will appear

List of Variables

Right arrow

button to add

selected variable(

s)

Step 2

Select one of the variables that you want to correlate by clicking on it in the left hand pane of the Bivariate Correlations dialog box i.e mfx and hhsize

Check the type of correlation coefficients that you require (Pearson for parametric, and Kendall’s tau-b and Spearman for non-parametric).

Select the appropriate Test: Pearson’s correlation coefficient assumes that each pair of variables is bivariate normal and it is a measure of linear association. Two variables can be perfectly related, but if the relationship is not linear, Pearson’s correlation coefficient is not an appropriate statistic for measuring their association.

Test of Significance: You can select two-tailed or one-tailed probabilities. If the direction of association is known in advance, select One-tailed. Otherwise, select Two-tailed.

Flag significant correlations. Correlation coefficients significant at the 0.05 level are identified with a single asterisk, and those significant at the 0.01 level are identified with two asterisks.

Click on the Options… button to select statistics, and select Means and SD and control the missing value by clicking “Exclude Cases pairwise.

Click on the Continue button.

Step 3

Click the OK button in the Bivariate Correlations dialog box to run the analysis. The output will be displayed in a separate SPSS Viewer window.

SPSS Output of Correlation Matrix

The Descriptive Statistics section gives the mean, standard deviation, and number of observations (N) for each of the variables that you specified.

Descriptive Statistics

 

MeanStd.

Deviation NHousehold size

4.34 1.919 1237

Monthly hh food expenditure (taka)

4411.25 2717.13 1237

The correlations table displays Pearson correlation coefficients, significance values, and the number of cases with non-missing values (N).

The values of the correlation coefficient range from -1 to 1.

The sign of the correlation coefficient indicates the direction of the relationship (positive or negative).

The absolute value of the correlation coefficient indicates the strength, with larger absolute values indicating stronger relationships.

The correlation coefficients on the main diagonal are always 1, because each variable has a perfect positive linear relationship with itself.

Correlations

   

Household size

Monthly hh food

expenditure

(taka)Household size

Pearson Correlation

1 .608**

Sig. (1-tailed)  

.000

N 1237 1237

Monthly hh food expenditure (taka)

Pearson Correlation

.608** 1

Sig. (1-tailed)

.000 

N 1237 1237

The significance of each correlation coefficient is also displayed in the correlation table.

The significance level (or p-value) is the probability of obtaining results as extreme as the one observed. If the significance level is very small (less than 0.05) then the correlation is significant and the two variables are linearly related. If the significance level is relatively large (for example, 0.50) then the correlation is not significant and the two variables are not linearly related.

Correlations

   

Household size

Monthly hh food

expenditure

(taka)Household size

Pearson Correlation

1 .608**

Sig. (1-tailed)  

.000

N 1237 1237

Monthly hh food expenditure (taka)

Pearson Correlation

.608** 1

Sig. (1-tailed)

.000 

N 1237 1237

Partial CorrelationsThe Partial Correlations procedure computes

partial correlation coefficients that describe the linear relationship between two variables while controlling for the effects of one or more additional variables. Correlations are measures of linear association. Two variables can be perfectly related, but if the relationship is not linear, a correlation coefficient is not a proper statistic to measure their association.

Step 1

How to perform Partial Correl: SPSSAnalyze –> Correlate –> Partial...

You will be presented with the “Partial Correlations" dialogue box:

Step 2

Click right click on variables and select “Display Variable”

Click “Sort Alphabetically “

Step 3

Step 4

Select one of the variables that you want to correlate by clicking on it in the left hand pane of the Bivariate Correlations dialog box i.e mfx and hhsize

In this case, we can see the correlation between monthly HH food expenditure and household size when head of education maintain constant.

Test of Significance: You can select two-tailed or one-tailed probabilities. If the direction of association is known in advance, select One-tailed. Otherwise, select Two-tailed.

Flag significant correlations. Correlation coefficients significant at the 0.05 level are identified with a single asterisk, and those significant at the 0.01 level are identified with two asterisks.

Click OK to get results

Step 5

As we can see, the positive correlation between mfx and hhsize when hh_edu is maintained constant is significant at 1% level (p > 0.00)

Correlations

Control VariablesHousehol

d size

Monthly hh food

expenditure

(taka)(sum) head_eduHousehold size Correlation 1.000 .606

Significance (1-tailed)

. .000

df 0 1232

Monthly hh food expenditure (taka)

Correlation .606 1.000

Significance (1-tailed)

.000 .

df 1232 0

Hands-on Exercises

Find out the correlation relationship between per capita total monthly expenditure and household size and identify the nature of relationship and define the reasons?

Find out the correlation relationship between per capita total monthly expenditure and household size by controlling the village those who have adopted technology and not adopted tech?

Find out the correlation relationship between per capita food expenditure and non-food expenditure by controlling district effect? [Hint: it is two tail why?]

Distances

This procedure calculates any of a wide variety of statistics measuring either similarities or dissimilarities (distances), either between pairs of variables or between pairs of cases. These similarity or distance measures can then be used with other procedures, such as factor analysis, cluster analysis, or multidimensional scaling, to help analyze complex data sets.