## Statistics formats described

This section lists the important format settings in QPSMR Companion used for statistics.

## Mean scores, averages & other statistics from values or scores

There are two sorts of questions that will produce various statistics when used as the rows of a table. The first type are quantities, usually Integer or Float entries. For example, salary, height or volume. For these questions when you use them as the rows of the table, either a full list of values can be requested, or the statistics only. The second type is scored questions, often rating scales to which scores (values) have been assigned. For example:

Like a lot (2) Like a little (1) Indifferent (0) Dislike a little (-1) Dislike a lot (-2)

Tables which normally show the full list of values as the rows may be displayed with or without the individual rows (format **DIS**). Using format **NDIS **means that only the requested statistics are output (no distributions).

Companion shows the values to use for statistics in parentheses (as above using format **PSV**). You can control the decimal places for float entries are by format **PSD**.

When using these types of entries on your tables the following statistics may be produced:

- Base for statistics (format
**BST**) - Sum of values (format
**SUM**) - Sum of squares of values (format
**SSQ**) - Average or mean score (format
**AVG**) - Standard deviation (format
**SDV**) - Standard error (format
**SER**) - Error variance (format
**EVR**) - Mean score divided by standard error (format
**MSE**)

You can control the decimal places for **AVG **by format **DPA**. All other statistics are controlled by format **DPS**.

For tables with all rows listed (not statistics only tables), you can also request the following:

- Medians (format
**MED**) - Quartiles to Deciles (format
**ILE**) - Maximum value (format
**ILH**) - Minimum value (format
**ILL**) - Modal value (format
**MOD**)

**IMPORTANT**: The calculations listed above assume that the values are in ascending order. You should always use format **RNA **when tabulating quantity questions which list all rows.

## F-tests

If you use format **TTF **with **SHG**, Companion will perform an F-test on all the columns within each group. You can use this test to establish whether the group of columns (for example – Area) affects the row mean or average, without looking at all of the individual pairs of columns.

## Significance testing

### Levels tested

Formats **SLA**, **SLB** and **SLC **control the levels to be tested. A setting of 101 means that the level is not used. The standard setting for these formats is **SLA95**/**SLB99**/**SLC101**/**SLD101**.

If you only use lower case letters as identifiers, upper case means **SLB** level. **SLC** adds an additional + (plus) to the front of each marker. For total comparisons this may be an additional – (minus).

### Distribution Z test & t-test markers

If your table has a list of independent rows, you can use format **SIG **to mark significant differences. There must be a total row for the Z test or t-test calculations to work.

Each row of the table is treated separately and cells are marked depending on whether the prportion is different to the other columns in the same row in the column it is being compared with.

You can choose Z test to use the combined variance (pooled) with **SIG1**, or separate variances (un-pooled) with **SIG2**. You can choose t test without continuity correction **SIG3** (default), or with continuity correction **SIG4**.

For overlapping t tests the formats are **SIG5** and **SIG6**. This will not affect the tests against total for which **SIG3 **and **SIG4 **will still be used.

### Mean or average t test markers

Where a table has rows from which a mean score or average is produced, significant differences will be marked. If you do not wish to include these markers, you should set format option **TTV0**. You may choose whether to use the combined variance with **TTV1 **or separate variances with **TTV2**.

If a respondent rates two or more products, you could produce a banked table with the products as the breakdown and use column identifiers to compare them. A more accurate method which is not often used is to subtract the score for one product from the score for the other. For example, with scores 1 to 5 the relative score will be between –4 and +4. This relative score can then be tabulated and format **MSE **will give a t test value comparing the mean score with the expected fixed value of 0.0. When the expected value for a mean is zero, if format **MSE **is >1.96, this is 95% significant and >2.57 is 99%.

## Other software

Data from Companion can be output to other specialised software for further statistical tests.