## Advanced concepts- Mathematics of work sampling

Mathematics

The calculation of the total number of observations needed to obtain the desired accuracy. As a consequence, the number of observations can be adjusted to meet certain levels of precision that are considered acceptable by the researcher. The formula used to calculate the total number of observation is:

n = (t2 * p(1-p))/m2

Where;
n = number of observations needed
t = confidence level (standard value) – the confidence level consists of the probability that the results obtained are included in a specified range. Usually researchers use a 95% probability for which t=1.96.
m = margin of error for example +/-2% accepted variation from final results.
p = estimated prevalence of targeted activity declared at the beginning of the project.
Or you can use the Observations Nomograph

For group level studies, after the total number of observations is calculated, the individual number of observations can be determined using the following formula:

nindividual = n/number of individuals

The scheduling of randomly chosen time points for observations. At this stage, the researcher has available inputs about: start date of study, total/individual number of observations, and structure of working schedule (working hours and working days taken into consideration). If the end date of the study is already established, the mean time between observations can be calculated and used for randomization of observations.

The formula used for calculating mean time between observations (MTBO expressed in minutes) is:

MTBOtotal = Total number of working minutes from start date until end date/n

MTBOindividual = Total number of working minutes from start date until end date for each individual/nindividual

When randomizing the time points for observations based on the formulas described above, there are specific guidelines that can be considered:

• to set minimum and maximum number of minutes permitted between each two consecutive observations;
• to move the end date of the study, if the MTBO is too small compared to an acceptable value and is expected to influence work efficiency;
• to make sure that an equal number of sub-cycles are taken into consideration while establishing the end date (day vs. night; week day vs. week-end day, etc.);
• to choose a normal load period by avoiding holidays and vacations period or special activities (annual conferences, seminars etc). Normally a work sampling study can range from one week to six weeks or even longer.

To conduct the data collection phase. Once the above calculations have been completed, the observations begin and activities are recorded at the agreed time intervals. When they have been completed, a reverse calculation can be used to determine the margin of error, as follows:
m = t x v( p x (100 – p) ) /n

In this case, n is the actual number of observations registered in field for all individuals or equipments (sum of all nindividual values).