If there are unequal probabilities of selection for members of the sample, or if there is a small amount of (random) non-response, then the calculation of sampling weights has to be undertaken. For teacher and school data there are choices which can be made about weighting. For example, if one is conducting a survey and each student in the target population had the same probability of entering the sample, then the school weights can either be designed to reflect the probability of selecting a school, or school weights can be made proportional to the weighted number of students in the sample in the school. In this latter case, the result for a school variable means the school value given is what the ‘average student’ experiences. This matter has been discussed in more detail in the module on ‘Sample Design’.
Educational research: some basic concepts and terminology
Module 1 Sequential stages in the research process
a. Descriptive
Typically, the first step in the data analyses is to produce descriptive statistics separately for each variable. These statistics are often called univariates. Some variables are continuous – for example ‘size of school’ which can run from, say, 50 to 2,000. In this case the univariate statistics consist of a mean value for all schools, the standard deviation of the values, and a frequency distribution showing the number of schools of different sizes. Other variables are proportions or percentages. Such a variable could be the percentage of teachers with different types of teacher training. These descriptive statistics describe the characteristics of the students, teachers, and schools in the sample. If a good probability sample has been drawn, then generalizations (within narrow limits) can be made about the target population.
Often comparisons between the Ministry norms and sample
averages are made. For example, if the Ministry has stated that each student should have 1.25 square meters of space in the classroom, then this norm can be examined for each school by dividing the total number of square meters of classroom floor space in the school by the total enrolment of students in the school. This statistic may then be used to give direct feedback to the educational planners in charge of buildings about the extent to which their norms are being met.
A further use of univariates is to examine the means or percentages for particular groups in the sample. This may be urban vs. rural schools, or the schools in different regions in the country, or for boys’ schools vs. girls’ schools vs. co-educational schools. This procedure is known as cross-tabulation or break-downs. In other words, the data are cross-tabulated (or cross-classified) or broken down into segments. A simple example is shown below.
Educational research: some basic concepts and terminology
Module 1 Sequential stages in the research process
Table X Educational facilities provided for primary schools in Country X
Educational provision All schools
Rural
Schools schoolsUrban Mean S.D. Mean S.D. Mean S.D. Desks per classroom
Chairs per classroom Floor space per student Pens/Pencils per student
X X X X X X X X X X X X X X X X X X X X X X X X
The first pair of columns presents the mean value and standard deviation for all schools in the sample for desks per classroom, chairs per classroom, floor space per student, etc. However, the total sample is ‘broken down’ in the second and third pairs of columns into rural and urban schools.
b. Correlational
In this case product moment correlations or cross tabulations can be calculated. There are statistical tests which can be applied to determine whether the association is more than would occur by chance. When the association between two variables is examined, this is known as ‘bivariate’ analysis.
c. Causal
If the research design used is an experimental one, then tests can be applied to see if the performance of the experimental group (that is, the group subjected to the new treatment) is better than the control group.
Educational research: some basic concepts and terminology
Module 1 Sequential stages in the research process
There are statistical techniques for determining this. However, the use of this approach depends on the application of randomization in order to ensure that the two groups are ‘equivalent’ in all other respects.
If the research design is based on a survey, then it is possible to calculate the influence of one variable on another with other variables being “held statistically constant”. Where calculations are made of the relationships among more than two variables at the same time, this is known as ‘multivariate analysis’. It is possible to build causal models using the technique of path analysis. This technique requires the development of a causal model which
describes not only the variables (or indicators) in the model, but also the pattern of causation among them. Analyses can be conducted to estimate the ‘fit’ of the data to the model. (See Figure 2)
An example of a path model could be:
Figure 2. Example of path model
Possessions in home
Parent-child interaction
Attitudes to school
Motivation
Educational research: some basic concepts and terminology
Module 1
In this example, it is posited, that the wealth of the home
(represented by “Possessions in the Home”) influences ‘Attitudes to School’ which in turn influences both ‘Motivation’ and
‘Achievement’. ‘Parent-child Interaction’ influences ‘Motivation’ which also influences ‘Achievement’ but ‘Parent-child Interaction’ also has a direct effect on ‘Achievement’.
In survey type designs – even when causal models and path
diagrams are used – association does not prove causality. However, if there is no association, then this casts doubt upon the original assumption of causality. If there is a strong association, and if a strong association is found repeatedly in several studies, then there is reasonable ground for assuming causality.