Convergent & Discriminant Validity using Correlation Coefficient

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Convergent and Discriminant Validity

Meaning of Convergent and Discriminant Validity

Campbell and Fiske (1959) proposed two aspects to asses the construct validity of a test:

1. Convergent validity: It is the degree of confidence we have that a trait is well measured by its indicators. ie. The statements measures the construct well.


2. Discriminant validity: It is the degree to which measures of different traits are unrelated. ie. Each construct measures a different attribute of the problem.

In structural equation modelling, Confirmatory Factor Analysis has been usually used to asses construct validity (Jöreskog, 1969).

Convergent & Discriminant Validity using Correlation Coefficient

To estimate the degree to which any two measures are related to each other we typically use the correlation coefficient. That is, we look at the patterns of intercorrelations among our measures. Correlations between theoretically similar measures should be “high” while correlations between theoretically dissimilar measures should be “low”. Use factor analysis to make correlation matrix in SPSS OR use Analyse»correlate»Bi-variate.

Convergent Validity

To confirm convergent validity, the results should show that there exist positive correlation between the statements that measures a construct.

Example of Convergent validity

We have four items/statements of “Self esteem” as “Respect, Care, Sincerity and Emotional Stability”. These four items should have a positive correlation between them.

Convergent and Discriminant Validity1

Discriminant Validity

To confirm discriminant validity, the results of correlation should show that there exist less or no correlation between the constructs of the problem studied.

Discriminant Validity2

we have two constructs named as “self esteem” and “locus of control”.  Self Esteem and locus of control has two items each (SE1,SE2, LOC1, LOC2). The correlation between the items in Self esteem and Locus of Control is very low ie near to no. As we know the value of correlation ranges between -1 to +1. Zero means no correlation. All the values in the above example are positive and close to zero. This shows that the construct “Self esteem” is different from the construct “locus of control”, hence discriminant validity proved.

Reference:

https://www.socialresearchmethods.net/kb/convdisc.php

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List of Journals:

1. 
   

   INTERNATIONAL JOURNAL OF SCIENCE & ENGINEERING RESEARCH – IJOSER

   
   


2. 
   

   INTERNATIONAL JOURNAL OF COMMERCE, ECONOMICS & MANAGEMENT – IJOCEM

   
   


3. 
   

   INTERNATIONAL JOURNAL OF SERVICE QUALITY – IJSQ

   
   


4. 
   

   INTERNATIONAL JOURNAL OF WEB COMPONENTS, DATA & ANALYTICS – IJWCDA

   
   

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Discriminant Validity Using SmartPLS

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Discriminant Validity

Validity Meaning

Validity is the extent to which a concept, conclusion or measurement is well-founded and corresponds accurately to the real world. In short it is to know whether it serves the purpose.

Example:

The purpose of grapes should serve its purpose by blocking the body’s production of vitamin K and making the blood thinner. when grapes fails to serve this purpose then it looses validity. Similarly, when the constructs of the questionnaire fail to measure what it has to measure, then the questionnaire looses validity. so this test is essential for a research at the initial level and this also gives the reliability of the construct.

Discriminant Validity Using SmartPLS

Discriminant validity is the degree to which any single construct is different from the other constructs in the model (Carmines and Zeller, 1979). Validity is measured with the following,

1. Content validity


2. Criterion validity


3. Construct validity – It has two, named as a) Convergent and b) Discriminant validity

Discriminant validity can also be measured with SPSS, AMOS etc. Now in this article we are going to be clear that Discriminant validity can be better measured with SmartPLS software. This company also shares its lower version at free of cost. The key is sent to us by email.

Output table of Discriminant Analysis

Discriminant Analysis: Table1

From table1, it is clear that the cross loading of the respective factor is greater than that factor’s AVE. For Example The cross loading of “Customization” is 0.837 which is greater than its respective AVE of 0.700. Since the cross loading  is greater for all the factors than the AVE of the respective construct, discriminant validity is confirmed.

More details about SmartPLS from the official website

When running the PLS and PLSc algorithm in SmartPLS, the results report includes discriminant validity assessment outcomes, in the section “Quality Criteria”. The following results are provided:

• the Fornell-Larcker criterion,


• cross-loadings, and


• the HTMT criterion results.

Recommend using the HTMT criterion to assess discriminant validity. If the HTMT value is below 0.90, discriminant validity has been established between two reflective constructs.

If you like to obtain the HTMT_Inference results, you need to run the bootstrapping routine. When starting the bootstrapping routine, it is important that you select the option “Complete Bootstrapping”. Then, in the bootstrapping results report, you find the bootstrapped HTMT criterion results in the section “Quality Criteria”.

The table of Discriminant Analysis

Please note: In SmartPLS 3.2.1 and later version, the HTMT criterion computation differs from the equation given by Henseler, Ringle and Sarstedt (2015). Instead of using the correlations between indicators, SmartPLS uses the absolute value of the correlation between indicators.

For example, when instead of using 0.1, 0.2 and -0.3, which results in an average correlation of 0 an causes problems in the original HTMT equation, SmartPLS uses 0.1, 0.2 and 0.3, which results in an average correlation of 0.2. In consequence, the HTMT criterion is normed between 0 and 1 in SmartPLS and no issues result from negative correlations.

References

Henseler, J., Ringle, C. M., and Sarstedt, M. 2015. A New Criterion for Assessing Discriminant Validity in Variance-based Structural Equation Modeling. Journal of the Academy of Marketing Science, 43(1): 115-135.

Hair, J. F., Hult, G. T. M., Ringle, C. M., and Sarstedt, M. 2017. A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM), 2nd. Ed., Sage: Thousand Oaks.

https://www.smartpls.de/documentation/discriminant-validity-assessment

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1. INTERNATIONAL JOURNAL OF SCIENCE & ENGINEERING RESEARCH – IJOSER


2. INTERNATIONAL JOURNAL OF COMMERCE, ECONOMICS & MANAGEMENT – IJOCEM


3. INTERNATIONAL JOURNAL OF SERVICE QUALITY – IJSQ


4. INTERNATIONAL JOURNAL OF WEB COMPONENTS, DATA & ANALYTICS – IJWCDA

 

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Interpretation, When & How to do Chi-Square Test

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Statistics_are in the eye of the Manipulator

Introduction

The Chi-Square (X²) statistic may be used to determine if two categorical (nominal or ordinal variables with less than 5 rankings) variables are related.  For example, you may hypothesize that gender influences a person’s political party identification. You can determine some of this information by looking at the cross tabulation and comparing the percentages of men and women for each party identification.  This statistic involves comparing your actual results with the results you would expect to have if there were NO difference between women and men in terms of their political party affiliation.

Assumptions

When you choose to analyse your data using a chi-square test for independence, you need to make sure that the data you want to analyse “passes” two assumptions.  These two assumptions are:

• Assumption #1: Your two variables should be measured at an ordinal or nominal level (i.e., categorical data). You can learn more about ordinal and nominal variables in our article: Types of Variable.


• Assumption #2: Your two variable should consist of two or more categorical, independent groups. Example independent variables that meet this criterion include gender (2 groups: Males and Females), ethnicity (e.g., 3 groups: Caucasian, African American and Hispanic), physical activity level (e.g., 4 groups: sedentary, low, moderate and high), profession (e.g., 5 groups: surgeon, doctor, nurse, dentist, therapist), and so forth.


• Assumption #3: One of the requirements for Chi-Square is that each and every cell has a frequency of 5 or greater.

Chi-Square Test Procedure in SPSS 

We show you how to interpret the results from your chi-square test for independence.

• Click Analyze > Descriptives Statistics > Crosstabs… on the top menu


• You will be presented with the following Crosstabs dialogue box:


• Transfer one of the variables into the Row(s): box and the other variable into the Column(s): box. In our example, we will transfer the Gender variable into the Row(s): box and Preferred_Learning_Medium into the Column(s): box. There are two ways to do this. You can either: (1) highlight the variable with your mouse and then use the relevant buttons to transfer the variables; or (2) drag-and-drop the variables. How do you know which variable goes in the row or column box? There is no right or wrong way. It will depend on how you want to present your data.
  

  If you want to display clustered bar charts (recommended), make sure that Display clustered bar charts checkbox is ticked.

  
  

   



• Click on the button. You will be presented with the following Crosstabs: Statistics dialogue box:


• Select the Chi-square and Phi and Cramer’s V options (for Nominal data) or Somers’d for Ordinal data.


• Click the button.


• Click the button. You will be presented with the following Crosstabs: Cell Display dialogue box:
  
  Published with written permission from SPSS Statistics, IBM Corporation.
  
  


• Select Observed from the –Counts– area, and Row, Column and Total from the –Percentages– area, check Observed.


• Once you have made your choice, click the button.


• 
  

  Click the button to generate your output.

  
  

Output

You will be presented with some tables in the Output Viewer under the title “Crosstabs”. The tables of note are presented below:

The Crosstabulation Table (Gender*Preferred Learning Medium Crosstabulation)

This table allows us to understand that both males and females prefer to learn using online materials versus books.

The Chi-Square Tests Table

When reading this table we are interested in the results of the “Pearson Chi-Square” row. We can see here that χ(1) = 0.487, p = .485. This tells us that there is no statistically significant association between Gender and Preferred Learning Medium; that is, both Males and Females equally prefer online learning versus books.

In short, Now look at the “Pearson Chi-Square Asymp. Sig (2 sided)”*. Since Chi-Square is testing the null hypothesis, the Sig value must be .05 or less for there to be a significant statistical for the relationship between the variables. In this example, the Sig. is .485, so there is no statical significance.

Look at the “Continuity Correction” line below. This will appear if you are examing variables that each have 2 possible responses. The corrected significance is .216; therefore, this also suggests that there is statistical significance between the relationship of the two variables.

The Symmetric Measures Table

The most commonly used statistic is the Phi coefficient, which ranges from 0 to 1. Higher values indicate a stronger correlation between the two variables. Phi and Cramer’s V are both tests of the strength of association. We can see that the strength of association between the variables is very weak.

Reference:

1. https://statistics.laerd.com/spss-tutorials/chi-square-test-for-association-using-spss-statistics.php


2. http://latrobe.libguides.com/SPSS/chi-square

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List of Journals:

1). International Journal Of Science & Engineering Research – IJOSER

2). International Journal Of Commerce, Economics & Management – IJOCEM

3). International Journal Of Service Quality – IJSQ

4). International Journal of Web Components, Data & Analytics – IJWCDA

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Interpretation and Steps to Test Heteroskedasticity

Interpretation and Steps to Test Heteroskedasticity

Heteroskedasticity is useful to examine whether there is a difference in the residual variance of the observation period to another period of observation. A Good regression model is not the case heteroscedasticity problem.

Statistical methods to test Heteroskedasticity

Many statistical methods are there to determine whether a model is free from the problem of heteroscedasticity or not, like

1. White Test,


2. Test Park,


3. Test Glejser.

SPSS Test will introduce one of heteroscedasticity test that can be applied in SPSS, namely

Test Glejser. Glejser test conducted by regressing absolud residual value of the independent

variable with regression equation is: Ut = A + B Xt + vi

Interpretation of Heteroskedasticity Test with Test Glejser (SPSS)

1. If the value Sig. > 0.05, then there is no problem of heteroscedasticity


2. If the value Sig. <0.05, then there is a problem of heteroscedasticity

Based on Output from the above table, Coefficients obtained value of Sig. Competence variable of 0.834, and the Sig. Motivation variable of 0.348, meaning that the value of the variable sig Competence and Motivation > 0.05, it can be concluded that there is no heteroscedasticity problem.

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INTERNATIONAL JOURNALS - SARU PUBLICATIONS

INTERNATIONAL JOURNALS - SARU PUBLICATIONS

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1. International Journal Of Commerce, Economics & Management - IJOCEM
2. International Journal Of Science & Engineering Research - IJOSER
3. International Journal Of Service Quality - IJSQ
4. International Journal Of Web components, Data & Analytics - IJWCDA

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