Analysis without factor

Example: The length measurements of 15 steel wire coils has been done and the obtained values are:

^{click here to download the data}

To use the tool Summary by Factor the user must follow these steps:

1. Access the menu:

Action → Basic Statistics → Summary by Factor

2. The following window will appear;

3. With the cursor in the field Data Set, we select the column (table or row) that contains the data, which must be numeric. As in this case we have no factors, the field Factors should not be selected.

4. In the board Statistics, select among the options Minimum, Maximum, 1st Quartile, 3rd Quartile, Mean, Median, SE of mean, Standard Deviation, Sum, Sum^2, Variance, Range, Asymmetry, Kurtosis, LL (Mean CI), UL (Mean CI), Frequency. In this example, we will select all the functions, except Frequency because this function is the count of the data as the repetition of their values in each factor and here we have no factor;

5. We can also select a Graphic Analysis to the data. In this example we select this option.

6. In the board Show Results, choose between Current Cell or New Sheet. We suggest the option New Sheet, because Action does not have the undo command.

REMARK: When choosing the option Current Cell, the results will be printed from the cell where the cursor is. In this case, the user must put the cursor in an appropriate position previously (before step 1).

7. To finish, click Ok.

Results and Interpretation

Once the process is finished, the following results will be shown:

• The mean and median, 69.33 and 68.79, respectively, are representatives of the wire coils lengths global distribution in the sample.
• The resulting variability is considerable if the wire coils lengths are close. This can be seen through the dispersion measures.
• The distribution function is flatten than the Normal distribution, because the Kurtosis, -0.75, is less than zero. Once the value of the asymmetry is positive but small, the distribution function tail is slightly longer on the right side, that is, the distribution is asymmetric to the right. 

Both mean and median can be considered representatives of the sample data general distribution because both have close values. However, when the median value is very different from the mean, it is always advisable to consider the median as the most important reference value.