topic 15 correlation spss
TRANSCRIPT
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Correlation : SPSS/STATA
Srinivasulu RajendranCentre for the Study of Regional Development (CSRD)
Jawaharlal Nehru University (JNU)New Delhi
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Objective of the session
To understand CORRELATION
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1. What is the procedure to perform Correlation & Regression?2. How do we interpret results?
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Identify the relationship between variables that we want to perform Scatter plot for outliers and type of relationship
Monthly HH food Expenditure and HHSIZE
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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
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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
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Scatterplot might not look promising at first
Double click on chart to open a CHART EDIT window
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use Options →Bin Element Simply CLOSE this box.Bins are applied automatically.
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BINS
Dot size now shows
number of cases with
each pair of X, Y values
DO NOT CLOSE CHART EDITOR YET!
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Add Fit Line (Regression)In Chart
Editor:Elements
→Fit Line at Total
Close dialog box that opens
Close Chart Editor window
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Edited ScatterplotDistribution
of cases shown by dots (bins)
Trend shown by fit line.
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Type of CorrelationBivariate Correlations.Partial CorrelationsDistances
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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.)
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ObjectiveWe are interested in whether an monthly HH
food expenditure was correlated with hhsize.
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Step 1
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The Bivariate Correlations dialog box will appear
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List of Variables
Right arrow
button to add
selected variable(
s)
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Step 2
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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.
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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.
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Click on the Continue button.
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Step 3
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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.
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SPSS Output of Correlation Matrix
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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
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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
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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
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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.
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Step 1
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How to perform Partial Correl: SPSSAnalyze –> Correlate –> Partial...
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You will be presented with the “Partial Correlations" dialogue box:
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Step 2
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Click right click on variables and select “Display Variable”
Click “Sort Alphabetically “
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Step 3
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Step 4
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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.
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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
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Step 5
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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
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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?]
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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.