NCA Plot I

NCA analysis starts with estimating the size of the space that is expected to be empty given the hypothesis. By default, the software assumes that the expected empty space is in the upper left corner, representing the hypothesis that the presence or a high value of X is necessary for the presence of a high value of Y. The space without cases is called the empty space or ceiling zone. NCA draws a border line called ceiling line between the space without cases and the space with cases. The ceiling-accuracy (c-accuracy) is the percentage of cases on or below the ceiling line. Let’s formulate the first necessity hypotheses: That the vaccination of a country’s population is a necessary condition for its life expectancy.

NCA Plot II

The second hypothesis is that the basic education level of a country’s population is a necessary condition for its life expectancy.

Statistical Test

The p-value protects the analyst from concluding that the empty space is empty because of necessity, whereas actually it is a random result of unrelated variables.

As a general rule of thumb, an effect size between 0 and 0.1 indicates a small effect, between 0.1 and 0.3 a medium effect, between 0.3 and 0.5 a large effect, and larger than 0.5 a very large effect to exist for non linear lines only. Often, an effect size large than 0.1 is used as a threshold to consider the effect size as really meaningful in theory and practice.

Preparing the analysis, this might take a few seconds...
Do test for   : ce_fdh - Vaccination
Done test for : ce_fdh - Vaccination 
Do test for   : cr_fdh - Vaccination
Done test for : cr_fdh - Vaccination 
Do test for   : ce_fdh - Basic.education
Done test for : ce_fdh - Basic.education 
Do test for   : cr_fdh - Basic.education
Done test for : cr_fdh - Basic.education


--------------------------------------------------------------------------------
                ce_fdh p     cr_fdh p    
Vaccination     0.392  0.000 0.360  0.000
Basic.education 0.396  0.000 0.341  0.000
--------------------------------------------------------------------------------

We can see that the effect size for immunization is 0.36 and for basic education is 0.34. Both would be considered large effects.

The p-values of less than 0.05 indicate that the empty space is empty because of necessity and that it is very unlikely that the observed data pattern is caused by two variables that are unrelated.

Bottleneck Table

A condition is a bottleneck for a desired outcome if it does not have that required level. How do you find these levels? A necessary condition analysis in degree can be done with the bottleneck table.

The bottleneck table enables us to find the levels of the conditions that are required for a given level of the outcome. It helps to focus resource allocation in order to be able to reach the desired level of life expectancy.

NN means that the condition is not necessary for the corresponding level of the outcome. In the default bottleneck, X and Y values are expressed as percentages of the range.

For example, we can see from the bottleneck table that a vaccination level of 68.4% is necessary in order to achieve a life expectancy level of 80,


--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
Y        1    2   
0       NN   NN  
10      NN   NN  
20      12.7 NN  
30      12.7 NN  
40      20.6 42.9
50      42.9 42.9
60      50.8 61.8
70      65.1 70.8
80      69.8 73.7
90      79.4 80.0
100     93.7 95.4

--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
Y        1    2   
0       NN   NN  
10      NN   NN  
20      NN   NN  
30      10.0 NN  
40      21.7 13.5
50      33.3 27.6
60      45.0 41.7
70      56.7 55.7
80      68.4 69.8
90      80.1 83.9
100     91.8 98.0