1.5 General cautionary notes

Some general cautionary notes follow regarding percentages. These are both from the viewpoint of accuracy and the comparison of percentages.

The reader is also cautioned that the numerous statistical tests performed in this analysis are exploratory in nature and the results gleaned from them must be regarded as material for future research.

Finally, it is appropriate to caution the reader that in chapters 3 and 4. profiles are contrasted by means of categories that are disproportionate with respect to a baseline category. As this is different from the other comparisons of proportions (percentages) elsewhere in the report, the reader is asked to peruse the illustrative example in this chapter.

 1.5.1 Percentages

Percentages, such as completion rates, are quoted in the Data Summary appendix (§6.5) to one decimal place. solely for the arithmetic convenience of being able to have the totals add to 100% where this is relevant. However, this decimal place has no relationship at all to the level of accuracy that should be assigned to the percentages.

Percentages in the text have been rounded to whole numbers and as such may not always add to 100%. However the ease of representation and the possible false sense of accuracy expressed with one decimal place, justify this action. As is indicated in the Statistical Appendix (§6.2) there are numerous issues (e.g. sample size) that affect the accuracy of the percentage and most desirably it should always be quoted with a confidence interval or range.

The following table gives the 95% confidence interval semi-widths that are associated with a percentage from a specified sample size. For instance, with a sample size of 15 students, a completion rate of 35% would lie 19 times in 20 (95%), within the range of 35% ± 24%, which is the interval 11% to 59%. If this interval has a lower limit that is negative, it is taken as zero and if the upper limit exceeds 100 it is taken to be 100. Note also that for small percentages (i.e. 5% or less and/or for small numbers (i.e. 20 or less) the confidence interval semi-widths are at best approximate. For more details, the reader is referred to the Statistical Appendix (§6.2).

 0-9 or 90-100 10-19 or 80-89 20-29 or 70-79 30-39 or 60-69 40-49 or 50-59 10-19 11.0% 18.1% 21.9% 24.1% 25.2% 20-29 8.5% 14.0% 17.0% 18.7% 19.5% 30-49 6.8% 11.1% 13.4% 14.8% 15.4% 50-99 4.9% 8.1% 9.8% 10.8% 11.3% 100-149 3.8% 6.3% 7.6% 8.4% 8.7% 150-199 3.2% 5.3% 6.4% 7.1% 7.4% 200-499 2.5% 4.0% 4.9% 5.4% 5.6% 500-999 1.6% 2.6% 3.1% 3.4% 3.6%

Note that because of symmetry the confidence interval semi-widths are the same for percentages on either sides of 50% (e.g. n=15 and p=15% has the same semi width of 18% as does n=15 and p=85%).