Analysis with a single factor and several levels

Example: The diameter measurements of pieces was performed by four operators, A, B, C and D, under the same conditions. 6 pieces were chosen randomly and the obtained measures are in the following table. In this case, we have a data set with a single factor, Operators, and four levels, Operator A, Operator B, Operator C and Operator D.

^{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, select the column(s) (table or rows) that contains the data, which must be numeric.

4. With the cursor in the field Factors, select the column or row that contains the factors related to data. The factors must be arranged in rows or columns following the same data layout. The factors cannot be put in tables, or in two or more rows or columns. However, there is no need for data and factors lines (or columns) to be aligned. But, a necessary condition is that the factors must be ordered in the same way the data they represent. That is, the first factor of the column (or row) of the factors must be correspondent to the value of the first column (or row) of data, the second factor must be related to the second value and so forth. In this example, we will select the column Factor;

REMARK: The factros can be number or letters. For instance, suppose we want to perform a basic summary about the measurements of pieces by width. Thus, widths A, B, C, D or 1, 2, 3, 3 or widths 1.25, 1.20, 1.28, 1.22 can be considered as Factors.

5. In the board Statistics, we select among the options Minimum, Maximum, 1st Quartile, 3rd Quartile, Mean, Median, SE of mean, Standard Deviatiion, Sum, Sum^2, Variance, Range, Asymmetry, Kurtosis, LL (Mean CI), UL (Mean CI) and Frequency. In this example we will select all the options.

6. We can also perform a grafic analysis. In this case we just need to select the box Graphic Analysis. In this example, we select this option;

7. 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;

8. To finish, click Ok.

Results and Interpretation

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

• The means and medians concerning each level are representatives of the global distribution of the pieces diameter measured by each operator.
  
• The resultant variability is not relevant.
• The distribution function if flatter than the Normal distribution, because the Kurtosis is negative in all levels. Once the value of Asymmetry is also negative in all levels, the distribution function tail is slightly longer on the left side, that is, the distribution is asymmetric to the left.