# Appendix 2

> 1\. Index of Inconsistency

The index of inconsistency are the principal measures of response
variance for a particular response category. Random errors of
measurement in the survey process (non-sampling error) add variability
to the data we collect from respondents. When the errors are not
correlated with the answers or with each other, we call this
variability, simple response variance.\"

The **index of inconsistency** estimates the ratio of response variance
to total variance for a question answer. It is a relative measure of
response variance.

If the estimate of the index is:

> less than 20, response variance is low.
>
> between 20 and 50, response variance is moderate.
>
> greater than 50, response variance is high.

Any of these factors may cause high response variance:

> The methods used to collect the data need improvements. For example,
> the question may be unclear.
>
> The concept itself may not be measurable.
>
> Respondents may not provide reliable information to the level of
> detail asked.

2\. Formula:

  -------------- ------------- ----------- ----- --- ----------- ---- ----- ---- ----------- ----- ----------- ------- -- --
  **Number of                                                                                                             
  responses to                                                                                                            
  the same                                                                                                                
  question by                                                                                                             
  category**                                                                                                              

                                                                                                                          

  **Second       **First                                                                                                  
  interview**    interview**                                                                                              

                 1             2           ...       i                ...        n                 **Total**              

  1              **x~11~**     x~12~       ...       x~1i~            ...        x~1n~             T~21~                  

  2              x~21~         **x~22~**   ...       x~2i~            ...        x~2n~             T~22~                  

  ...            ...           ...         ...       ...              ...        ...               ...                    

  i              x~i1~         x~i2~       ...       **x~ii~**        ...        x~in~             T~2i~                  

  ...            ...           ...         ...       ...              ...        ...               ...                    

  N              x~n1~         x~n2~       ...       x~ni~            ...        **x~nn~**         T~2n~                  

  **Total**      T~11~         T~12~       ...       T~1i~            ...        T~1n~             **T**                  
  -------------- ------------- ----------- ----- --- ----------- ---- ----- ---- ----------- ----- ----------- ------- -- --

Index of Inconsistency for Answer i

T~2i~ + T~1i~ -- 2 X~ii~

IOI~i~=
\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--
x 100

(1/T)(T~1i~(T-T~2i~)+T~2i~(T-T~1i~))

Aggregate Index of Inconsistency

T -- $\sum_{i = 1}^{n}X_{\text{ii}}$

IOI= \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-- x 100

T- (1/T)x$\sum_{i = 1}^{n}{T_{1i}T_{2i}}$