(This Annexure is attached for information purposes only)

Introductory information:

1In statistics, a confidence interval is a particular kind of interval estimate of a population parameter. Instead of estimating the parameter by a single value, an interval likely to include the parameter is given. Thus, confidence intervals are used to indicate the reliability of an estimate. How likely the interval is to contain the parameter is determined by the confidence level or confidence coefficient. Increasing the desired confidence level will widen the confidence interval.

A confidence interval is always qualified by a particular confidence level, usually expressed as a percentage. The end points of the confidence interval are referred to as confidence limits.

1 Interval estimation [online] available from https:llen.wikipedia.orglwiki/Interval_estimation

Step 1

Action to be performed:

To install the Analysis ToolPak:

To use the Analysis ToolPak:

Expected result:

Step 2

Action to be performed:

From the descriptive statistics calculate the following:

=    PERCENTILE (A1:A40,0.9)   =   2.478 (for the data used in this example)

where:

"A1:A40" = Range were data is entered in Microsoft Excel spread sheet

"0,9"         = The percentile to be calculated, in this case the 90th percentile

Interpretation:

From the calculation performed above it can already be estimated that this HEG in NOT statistically correct defined, as:

Step 3

Action to be performed:

Determine if 95% of the samples taken falls within two standard deviations (2SD) form the mean value.

Example:

Interpretation:

One out of 13 samples represent 7.69 % of the sample group (e.g. 1/13 x 100 = 7.69%).

This is more than the allowable 5% and therefore the HEG cannot be seen as statistically correctly defined.

Step 4

Action to be performed:

Draw a histogram to graphically indicate the data.

Expected result:

Interpretation:

From the histogram, it is also clear that the HEG is NOT statistically correctly defined (no bell curve). Only two things can be done to correct this situation:

Step 5

Action to be performed:

Conduct an investigation to determine if more than one HEG is being represented by the data. This can be done by investigation and following the methodology as explained, up to this point (for example):

After investigation, the HEG was divided into two separate HEGs (intake-side HEG and return-side HEG).

The data collected was then allocated to the two HEGs and the statistical analysis revealed the following:

CALCULATIONS

Interpretation:

From the above it can already be estimated that this HEG is statistically correctly defined, as the mean value (1.47) falls within the "B Category' and the 90th percentile value (1.825) also falls within the "B Category".

DOES 95% OF THE SAMPLES FALL  WITHIN TWO STANDARD DEVIATIONS (SD) FROM THE MEAN?

This is within the allowable 5% and therefore the HEG is statistically correctly defined.

CALCULATIONS

2 X SD                    =   0.274434

Mean - 2SD         =   -2.11128

Mean + 2SD        =   2.660149

90th percentile =  2.504

Interpretation:

From the above it can already be estimated that this HEG is statistically correctly defined, as the mean value (2.39) falls within the "A Category" and the 90th percentile value (2.504) also falls within the "A Category".

DOES 95% OF THE SAMPLES FALL WITHIN TWO STANDARD DEVIATIONS (SD) FROM THE MEAN?

(A)        95% of the samples must be between mean - 2SD (-2.514) and mean + 2SD (7.286)

(B)        From "DATA": 0 sample < mean - 2SD and 0 samples > mean + 2SD

Step 6 - Paired T-test