Assignment – Assessment of Numerical Methods
In my current project, I need to present, analyze and perform a quantitative data regarding two variables:
(a) The dependant variable, which comprises of parental attitudes behaviour and knowledge towards children with ADHD; and the (b) independent variable – an intervention with the parents, which is the administration of the online course aimed at improving scores of the independent variable. The aim is to provide statistical evidence if the intervention had a significant effect on the parental attitudes and behaviour.
The first task of course is to define the two groups as Control or A – parents who did not take the course, and B- who had taken the course. A system of scoring needs to be devised so that any one parent’s perceptions and attitudes are accurately reflected i.e. on a score of 0-100, based on the questionnaire designed rigorously for the task.(Johnson 1984). Thereafter, the main task ahead is to compare the performance score of these two groups to draw conclusions.
The preliminary data analysis is based on calculating the means of the two groups.[ Ň = ∑x/n ]i.e. the sum total of all observed scores divided by the number of participants in each group. This will immediately give us an idea whether the scores for group B i.e. parents who had taken the course, were sufficiently higher compared to those who had not (group A). But this is not sufficient to tell us whether the difference in scores is by chance alone or whether they are significant enough to conclude that the online course had made a real difference. The concept of normal distributions and standard deviations are applicable in this situation. (Salkind, 2000). If the number of parents observed are represented on a chart, on the y-axis and the score categories (e.g. 20-40, 40-60, so on)on the x-axis, and provided that the number of observations are high enough, the shape of the curve will resemble that of a bell ( Gaussian curve).(Cohen 1989) The highest number of observations tend to be concentrated around the mean (calculated above), while those who have scored very low or very high will be further out. This is known as the normal distribution. At the same time it can be numerically measured, how much further from the mean the scores are distributed. In normal distribution curves, about 68 % of scores tend to lie within ine standard deviation of the mean. For example, if the standard deviation in this case is about 10 points on the 0-100 score and the mean score is 70, then 68% of parents have scored between 60 and 80. (70-10 to 70+10). Standard deviations are calculated by a formula s = √[∑ (x- mean)/n-1], where differences in each score from the mean are calculated, added up, divided by the number of observations (less one) and their square root obtained.
The final concept to use is that of standard error and confidence intervals. The standard error is defined as standard deviation divided by square root of sample size (s/√n)and multiplying it by Z-value, a number that calculates the number of standard deviations from the mean that our value will be likely to lie within. For example to be 95 % sure that our value is truly representative of the data, it must lie within 1.96 standard deviations – this is expressed as : for confidence level of 95 % the Z-value is 1.96. Thus applying it to standard error at 95 % confidence level, standard error (SE) = s/√n x 1.96. Finally, confidence intervals are calculated as :
Confidence intervals (CI) = Mean ± s/√n x 1.96 at confidence level of 95 %. In other words, we can say with a 95 % accuracy that the mean is a true representative sample, and has not occurred by chance alone. By this method we can calculate individually the mean, standard deviation, standard error and confidence intervals of the two groups A and B.
In order to compare the two group scores and find if they are significantly different, however, we have to apply special parametric tests like the Student T-test, which is outside the scope of this section.
Cohen, L. & Manion, L. (1989). Research methods in education. London: Routledge
Johnson, N. (1984). Sex, colour, and rites of passage in ethnographic research, Human Organization, 43(2), 108-120.
Salkind, N.J. (2000). Statistics for people who (think they) hate statistics. Thousand Oaks, CA: Sage.