Mean comparison: significance (AskiaAnalyse)

The significance test for numeric questions is used in order to see if the mean 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 significative. For example:

The test is used on independent samples.

To set up a test of this type, in the calculations section of the general tab, select significance (there are two significance calculations; select the one below median):

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:
  • All other columns: comparison of the mean of the column with the mean obtained in the other columns. You can test the against the observed in the  population.
  • All other rows: comparison of the mean of the row with the mean obtained in the other rows. You can test the against the observed in the  population.
  • Counts when independent: Note that this comparison is not applicable.
• 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=D to the significativity threshold: if D>test value, then there is a significant difference. The sign will indicate if the percentage is significantly lower (-) or higher (+) than the mean in the other columns or rows.

Standard deviation known

The sigma value D is calculated as follows:

Where D follows a normal mathematical expectation:

is the count observed in the column/row for the sample
is the count observed in the sample
 = mean 1 in the sample 1
 = mean 2 in the sample 2 (all other columns/rows)

 is the standard deviation observed in the Sample 1
is the standard deviation observed in the Sample 2
We compare the abs(D)> tα

•  = 1.65
• = 1.96
• = 2.576

if abs(D)> , there is a significative difference between  and .