Significance (AskiaAnalyse)

The significance test for closed questions is used in order to see if the proportion observed () in the sample i () is different from the proportion observed in the sample N.

In the table, “–“ or “+” signs are displayed to indicate where the difference is significant. For example:

To set up a test of this type, in the calculations section of the general tab, select significance:

To define the parameters of the test, in the general tab right-click significance, select properties..., then click advanced options. Then, set the options as follows:

• Test against: Select what comparison will be made, as follows:
  • Counts when independent: comparison of cell with total (). You can test the against the observed in the population N. For more detail, see the explanation below.
  • All other columns: comparison of the column profile with the percentage obtained in the average other columns. You can test the against the observed in the  population. For more detail, see the explanation below.
  • All other rows: comparison of the row profile with the percentage obtained in the other rows. You can test the against the observed in the  population. For more detail, see the explanation below.
• Count threshold: The minimum count to be taken into account in a cell.
• High significativity (%): The percentage at which values are to be regarded as being highly significant (e.g. 99%).
• Normal significativity (%): The percentage at which values are to be regarded as being normal significance (e.g. 95%).
• Low significativity (%): The percentage at which values are to be regarded as being of low significance (e.g. 90%).
• Standard deviation known: See standard deviation known.

In the table, significance is indicated by + and - symbols as follows:

• High threshold: +++ or ---
• Medium threshold: ++ or --
• Lower threshold: + or -

Note: it is possible to define a threshold as zero, so that the test is not run at that threshold:

The test allows the comparison of test values with threshold values.

To take the decision, we compare the calculated Sigma to the significativity threshold: if the Sigma is greater than the test value, then there is a significant difference. The sign will indicate if the percentage is significantly decreasing (-) or increasing (+).

Counts when independent (Khi²)

is calculated as follows:

is the count observed in sample i and  is the expected count in the global sample N.

We calculated the with k-1 degrees of freedom and the probability that the variable is dependent.

N is the total sample size.

Then we compare the  and

If the following is the case, then we conclude that the proportions are significantly different from the others:

All other columns/rows

All other columns (j)	All other rows (i)

Standard deviation known

If the standard deviation is known, we use a normal law where  is a calculated estimator as follows:

for:

If the standard deviation is unknown (which is the default in askiaanalyse), we use a normal law for: