Crosstabs Correlation Regression And Scatter Dot Plot Education Essay

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Correlation

In general, correlation looks at the relationship between two variables in a linear fashion. We can find out correlation in many ways, SPSS provides following ways:

Through Cross tabulation : A correlation between two dichotomous or categorical variables is called Phi coefficient and is available in SPSS through Analyze menu Descriptive StatisticsCrosstabs….

Through Correlation : A pearson product moment correlation coefficient describes the relationship between two continuous variables and is available in SPSS through Analyze menu CorrelateBivariate… (normally bivariate is used, you may choose partial or distances according to your requirements). This correlation might be used in case of continuous and categorical variables. You can use a pearson product moment correlation to correlate a dichotomous and a continuous variable. However, the proportion of each category of the dichotomous variable must be appropriately equal and variables be coded as 0 and 1.

The bivariate correlation (zero-order correlation), signifies the correlation between two continuous variables and is the most common measure of linear relationships. The possible values in this correlation range from -1 to +1. The value indicates the strength in relationship and sign(- or +) indicates the direction.

The partial correlation shows a single measure of linear association between two variables. This correlation adjusts for the effects of one or more additional variables.

In case, the assumptions underlying the correlation cannot be met, the non parametric Spearman's rank-order correlation can be used.

Assumptions in Correlations :

Related pairs - data must be collected from related pairs, i.e. same participant should provide scores of both the variables.

Scale of measurement - data should be ratio or interval in nature.

Normality - the scores of each variable should be normally distributed.

Linearity - there must be linear relationship between two variables.

Homoscedasticity - the variability in scores for one variable is approximately the same at all values of the other variables. That is, it is concerned with how the scores cluster uniformly around the regression line.

Note: Assumptions 1 and 2 are related to research design. Assumption 3 can be tested using the procedures outlined in previous chapters of basics. Assumption 4 and 5 can be tested through scatterdots of the variables.

Working Example 1 :

Sandhya Gupta wants to see the scatter plot of information availability (cause) and online ordering (effect) by the respondents.

In values column, the descriptives are:

Info : 1(Not important), 2(Less Important), 3(Important), 4(Very Important), 5(Extremely Important)

Order : 1 (Never), 2(Occasionally), 3(Considerably), 4(Almost Always), 5(Always)

Enter the data in the data view as shown below.

Cross tabs

Open the Cross tabs dialogue box as shown in the starting of this chapter. Following dialogue box will open.

Select the relevant variables in their respective Row(s) and Column(s). You may also choose the check box of display clustered bar charts.

Click on Statistics… button to choose the tests. You may click the check box of chi square and Correlations, to see the relevant results. After selecting, click Continue. The previous dialogue box of Crosstabs will be seen again. Click OK to open the output viewer.

The Output :

CROSSTABS

/TABLES=Info BY Order

/FORMAT=AVALUE TABLES

/STATISTICS=CHISQ CORR

/CELLS=COUNT

/COUNT ROUND CELL

/BARCHART.

Case Processing Summary

Cases

Valid

Missing

Total

N

Percent

N

Percent

N

Percent

Availability of Updated information * Online Ordering

29

100.0%

0

.0%

29

100.0%

The table above shows, Case processing summary with the valid and missing values of the variables.

Availability of Updated information * Online Ordering Crosstabulation

Count

Online Ordering

Total

Occasionally

Considerably

Almost Always

Always

Availability of Updated information

Not Important

3

0

0

0

3

Less Important

0

2

0

0

2

Important

0

0

2

1

3

Very Important

0

1

16

2

19

Extremely Important

0

0

2

0

2

Total

3

3

20

3

29

The table above shows, cross tabulation of two variables in our working example.

Chi-Square Tests

Value

df

Asymp. Sig. (2-sided)

Pearson Chi-Square

49.470a

12

.000

Likelihood Ratio

31.487

12

.002

Linear-by-Linear Association

16.473

1

.000

N of Valid Cases

29

a. 19 cells (95.0%) have expected count less than 5. The minimum expected count is .21.

The table above shows that Chi square value of 49.470 (df=12, N=29), p<0.05 is significant at 12 degree of freedom, showing that there is significant difference in expected and observed frequencies.

Symmetric Measures

Value

Asymp. Std. Errora

Approx. Tb

Approx. Sig.

Interval by Interval

Pearson's R

.767

.109

6.212

.000c

Ordinal by Ordinal

Spearman Correlation

.533

.200

3.273

.003c

N of Valid Cases

29

a. Not assuming the null hypothesis.

b. Using the asymptotic standard error assuming the null hypothesis.

c. Based on normal approximation.

The table above shows Symmetric Measures with interval by interval and ordinal by ordinal values.

The figure above shows Bar Chart of variables Availability of Updated Information and Online Ordering Cross tabulation results.

Correlations

Open the Bivariate Correlations dialogue box as shown in the starting of this chapter. Following dialogue box will open.

Select the variable and send it in Variables list box by clicking right arrow button. Similarly do this for other variables. Click Pearson check box and Flag significant correlations check box as shown in the figure below. See that test of significance is set according to the requirement. In our case it is two tailed.

Click Options… button to open its sub dialogue box. Select the Statistics and Missing values options according to your requirement. Click Continue to close the sub dialogue box. The previous dialogue box will appear again. Click OK to see the output viewer.

The Output :

CORRELATIONS

/VARIABLES=Info Order

/PRINT=TWOTAIL NOSIG

/STATISTICS DESCRIPTIVES XPROD

/MISSING=PAIRWISE.

Descriptive Statistics

Mean

Std. Deviation

N

Availability of Updated information

3.52

1.090

29

Online Ordering

3.79

.774

29

Correlations

Availability of Updated information

Online Ordering

Availability of Updated information

Pearson Correlation

1

.767**

Sig. (2-tailed)

.000

Sum of Squares and Cross-products

33.241

18.103

Covariance

1.187

.647

N

29

29

Online Ordering

Pearson Correlation

.767**

1

Sig. (2-tailed)

.000

Sum of Squares and Cross-products

18.103

16.759

Covariance

.647

.599

N

29

29

**. Correlation is significant at the 0.01 level (2-tailed).

The bivariate correlation is undertaken between the respondents. It was hypothesized that a relationship exists between availability of updated information and online ordering. The result above shows that, there exists a positive relationship between availability of updated information and online ordering (r=.767, p<0.05).

Regression

We will use working example 1 for regression analysis also.

Click Analyze menuRegressionLinear…. This will open Linear Regression Dialogue box.

Select the dependent variable and send it in Dependent list box by clicking upper right arrow button. Similarly, select the independent variable and send it in Independent(s) list box by clicking second right arrow button, as shown in the figure below.

Click Statistics… button to open its sub dialogue box. Select the required statistics as shown in the figure below. Click Continue to close the sub dialogue box. Previous dialogue box will reappear.

Click Plots… to open Plots sub dialogue box. Select the plots as required by you. Click Continue to close the sub dialogue box. Previous dialogue box will reappear.

Click Options… to open Options sub dialogue box. Select the options as required by you. Click Continue to close the sub dialogue box. Previous dialogue box will reappear. Click OK to see the output viewer.

The Output:

REGRESSION

/MISSING LISTWISE

/STATISTICS COEFF OUTS R ANOVA

/CRITERIA=PIN(.05) POUT(.10)

/NOORIGIN

/DEPENDENT Order

/METHOD=ENTER Info

/RESIDUALS HIST(ZRESID) NORM(ZRESID).

Variables Entered/Removedb

Model

Variables Entered

Variables Removed

Method

1

Availability of Updated informationa

.

Enter

a. All requested variables entered.

b. Dependent Variable: Online Ordering

The table above shows the variables entered or removed in the model.

Model Summaryb

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.767a

.588

.573

.506

a. Predictors: (Constant), Availability of Updated information

b. Dependent Variable: Online Ordering

The table above shows the model summary.

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

9.859

1

9.859

38.583

.000a

Residual

6.899

27

.256

Total

16.759

28

a. Predictors: (Constant), Availability of Updated information

b. Dependent Variable: Online Ordering

The table above shows the ANOVA values with sum of squares, degrees of freedom, mean square, F statistics and level of significance.

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

1.878

.322

5.825

.000

Availability of Updated information

.545

.088

.767

6.212

.000

a. Dependent Variable: Online Ordering

Residuals Statisticsa

Minimum

Maximum

Mean

Std. Deviation

N

Predicted Value

2.42

4.60

3.79

.593

29

Residual

-1.056

1.489

.000

.496

29

Std. Predicted Value

-2.310

1.361

.000

1.000

29

Std. Residual

-2.089

2.945

.000

.982

29

a. Dependent Variable: Online Ordering

The table above shows the residual statistics with predicted value, residual, standard predicted values and standard residual values.

The figure above shows the Histogram of dependent variable online ordering.

The figure above shows the Normal P-P plot of Regression Standard Residual values.

Scatter /Dot Plot

We will use working example 1 for regression analysis also.

Click Graphs menuLegacy DialogsScatter /Dot…. This will open Scatter /Dot dialogue box.

Click Simple Scatter button and click Define to open Simple Scatterplot dialogue box.

Select the variables of Y Axis and X Axis according to your requirement. In our working example, the variables are entered as shown in the figure below.

Click Options… button to open Options sub dialogue box. Select the options accordingly. Click Continue to close this sub dialogue box. Previous dialogue box will reappear. Click OK to see the output viewer.

The Output:

GRAPH

/SCATTERPLOT(BIVAR)=Info WITH Order

/MISSING=LISTWISE.

The figure above shows simple scatter plot of the both the variables in the working example 1.

SPSS Procedure for Correlation, Regression and Scatter /Dot Plot

After the input data has been typed according to the variables desired according to the problem, proceed according to following steps in respective cases.

Correlation through Crosstabs :

Select Analyze menu Descriptive StatisticsCrosstabs….

Select the relevant variables in their respective Row(s) and Column(s). You may also choose the check box of display clustered bar charts.

Click on Statistics… button to choose the tests. You may click the check box of chi square and Correlations, to see the relevant results. After selecting, click Continue. The previous dialogue box of Crosstabs will be seen again. Click OK to open the output viewer.

Bivariate Correlation :

Select Analyze menu CorrelateBivariate… to open its dialogue box.

Select the variable and send it in Variables list box by clicking right arrow button. Similarly do this for other variables. Click Pearson check box and Flag significant correlations check box. See that test of significance is set according to the requirement.

Click Options… button to open its sub dialogue box. Select the Statistics and Missing values options according to your requirement. Click Continue to close the sub dialogue box. The previous dialogue box will appear again. Click OK to see the output viewer.

Regression :

Click Analyze menuRegressionLinear…. This will open Linear Regression Dialogue box.

Select the dependent variable and send it in Dependent list box by clicking upper right arrow button. Similarly, select the independent variable and send it in Independent(s) list box by clicking second right arrow button.

Click Statistics… button to open its sub dialogue box. Select the required statistics as shown in the figure below. Click Continue to close the sub dialogue box. Previous dialogue box will reappear.

Click Plots… to open Plots sub dialogue box. Select the plots as required by you. Click Continue to close the sub dialogue box. Previous dialogue box will reappear.

Click Options… to open Options sub dialogue box. Select the options as required by you. Click Continue to close the sub dialogue box. Previous dialogue box will reappear. Click OK to see the output viewer.

Scatter /Dot Plot :

Click Graphs menuLegacy DialogsScatter /Dot…. This will open Scatter /Dot dialogue box.

Click Simple Scatter button and click Define to open Simple Scatterplot dialogue box.

Select the variables of Y Axis and X Axis according to your requirement.

Click Options… button to open Options sub dialogue box. Select the options accordingly. Click Continue to close this sub dialogue box. Previous dialogue box will reappear. Click OK to see the output viewer.

Excercise

Eighteen students have taken Common Admission Test (CAT) after their graduation. They were also given their aptitude had both CAT percentile and their graduation percentage. Meenu, a researcher wants to see the relationship between the scores of CAT and graduation through correlation analysis.

Graduation percentage 70 60 65 68 70 75 80 89 90 95 65 68 72 78 87 91 82 84

CAT percentile 80 85 70 65 69 89 99 95 94 98 80 75 89 88 90 89 94 93

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