Introduction
Pre-service teachers are given a course in ‘fundamental of music’ or ‘music methods’ in teacher training program. It is natural to assume that the perception of these pre-service teachers about the program and different component of this program will have a strong bearing on the time that they will teach music in their actual teaching. Therefore, it is relevant to explore this relationship for improving the curriculum of ‘music methods’ course to make it more relevant and useful. However, this is a complex task considering the fact that there are as many as seventeen components in the curriculum of ‘music methods’ course and all these seventeen are bound to show different degree of correlation with the actual time spent by the teachers in teaching music. To overcome this problem, clustering of these seventeen components into three clusters have been done and these three clusters have been used as three components of the ‘music methods’ curriculum in this study. This is a very good study and different statistical aspects of this study are critically examined in the subsequent sections.
Design of the Study
The study was to determine the predictive variables that can predict the use of music in class room by the elementary teachers and then to established correlation and / causal relationship between the two variables. The predictive variables are qualitative variables that form the components of the curriculum of ‘music methods’ course in teachers training program. However, to conduct a quantitative study involving qualitative variables, one need to go for mixed method research design (Creswell, 2008). In that sense it was a mixed method research design. This Mixed methods research design can be defined as ‘the collection and analysis of both quantitative as well as qualitative data in a single study’. In this method the data are collected either concurrently or sequentially. The most important consideration is given to integration of the data at different stages of research.
This study consisted of a questionnaire based data collection and statistical analysis of the data to extract useful information and underlying trends and relationship between different variables of interest. Such a design is very much suited to the kind of research reported in this paper. The different components of the design of this study are – subject selection, sample sampling methodology, questionnaire design and its validity test, collection of subjects’ response against different questions of the questionnaire, clustering of variables, analyzing the response of the subjects. Each of these aspects need to be critically examined, besides, the question that whether or not this was the best design of the study to examine the problem under consideration in this study. In the subsequent sections, different aspects of the study will be critically analyzed.
The researcher wanted to test his conjecture that different component of ‘musical methods’ course during teachers training program has a bearing on the actual time given by teachers on music in their teaching career. To test his conjecture, the researcher has chosen to analyze the response of the questionnaire by the teachers (subjects). While this approach is reasonably good approach and the findings from such a research design can be relied upon, a better method would have been to collect data on the dependent variable by either survey or response from the students in stead of the teachers themselves. In this research, values of both the predictive variable (use of different components of the music methods course during teachers training) as well as the predicted variable (time spent by teachers on music in their class room) are coming from the teachers only. Had the values of the predicted variable been collected from response of students in stead of the teachers themselves, the findings would have been more reliable and meaningful.
Reliability
This brings out the question of reliability in quantitative analysis. Reliability is very important in quantitative analysis, here reliability refers to how reliable is the instrument used for data collection and whether or not there is internal consistency in the data collection instrument (Cohen et al 2007). In this study, the questionnaire was the instrument of data collection. Though, the questionnaire was designed by the researcher after extensive literature review and based on his own experience as well as that of his co-workers, it was essential to test the reliability of the data collecting instrument the questionnaire. Researcher has measured the reliability of the questionnaire by test – retest method. This test was administered on 33 teachers twice at a gap of two weeks and the reliability was measured using kappa statistics K, which is coefficient of agreement for nominally scaled data (Siegel & Castellan, 1988). Thus reliability of the test instrument (the questionnaire) was confirmed before collecting the data and therefore, the study is therefore reliable.
Validity of a research method implies that the test is really measuring, what it is claiming to measure. In this research the validity of the content of the questionnaire was confirmed by getting the questionnaire analyzed by professors of elementary music education and an expert of elementary music. Thus the questionnaire can be accepted as a valid instrument for data collection.
Sampling Method and Sample Size
Sampling method is very important in any quantitative analysis. A good sampling method results in a sample, which is true representative of the population, however, if proper sampling method is not used then one may get a biased sample and there will be a huge difference between the sample statistics and population parameters. In this study stratified random sampling procedure has been used. This method throws a random and therefore, unbiased sample.
Sample size is also very important in a quantitative analysis as sample size affects the magnitude of error. A small sample size gives a larger error and vice versa. In this study, researchers have taken a sample size of minimum 100 subjects from each state. However, they have not calculated or at least not reported in this article as what the ideal sample size would have been for the maximum permissible error in this study. They have not talked about the maximum allowed error also, in this article. This information would have made the study and the article more meaningful.
Validity of the Procedures and Results
How valid is a work? Along with many other considerations, validity depends on reliability and validity of the test instrument only a valid reliable test instrument can ensure validity of the entire work. As the test instrument was reliable and valid, therefore, one can proceed to examine, whether the entire work was also valid. Besides, reliability and validity of the data collection instrument and procedures of the data collection, validity depends on how the data was analyzed quantitatively. In this study, this issue becomes vary important as this is a mixed method research, which involves quantification of qualitative variables and their statistical analysis. Besides, in this research clustering of variables with similar characteristics has also been done to synthesize lesser number of predictive variables. In this work, 17 variables have been clustered into three composite predictive variables. This clustering has been done by established statistical procedure and therefore, there is no issue with validity of this aspect. Subsequently, discriminant analysis was performed to examine the effect of each of the three predictive cluster variables on the variable to be predicted i.e. the time spent on music by the music teachers. Discriminant analysis is also a statistically established procedure and therefore, there is no issue of validity on this aspect as well. Therefore, it can be concluded that the quantitative analysis was a valid analysis of the problem under investigation.
Whether the test can be Generalized?
Generalizability refers to a conceptual framework and a methodology, which enables a researcher in entangling multiple sources of error in the measurement procedure. Generalizability of a quantitative research is very important in determining whether the findings be generalized to the wider population or is it relevant only to the regions under consideration. If the findings can be generalized, then it has wider implication as the findings can be used to fine tune and optimize not only the curriculum of ‘music method’ course in that region only, rather in the entire USA or even in other countries. Another question is can the study itself can be generalized to carry out similar research in other areas as well and will then be very useful for optimizing and fine tuning the curriculum of all the subjects. From quantitative considerations, this study has very good abilities to be generalized. However, the generalization has been done with care as it is not a purely quantitative study, in stead it is a mixed study and a mixed study cannot be generalized just like that. One need to have a good familiarity with the qualitative variables in any mixed study. In that sense the generalizability of the study is somewhat limited.
Statistics Used
In this research following statistics were used:
- Mean (M) of different predictive as well as predicted variable (s): Mean is nothing but arithmetic average and is calculated by adding all the measurements of a variable and dividing it by total number of measurements. It is essentially a measure of central tendency.
- Standard Deviation (S): It is a measure of dispersion of individual measurements of a variable from the mean. The difference of individual measurement from the mean is squared and added and then the resulting value is divided by the number of measurements, square root of which is then taken as the standard deviation. It is a measure of dispersion from the mean.
- Correlation Coefficient (r): This is measured by a formula given by Pearson. It measures the nature (positive, negative, neutral) and strength (strong, moderate, weak) of the correlation between a two variables or a pair of data set comprising of measurements for two variables.
- Kappa Statistics (k): It is a measure of consistency between identical measurements after a time interval. This is used to check test – retest reliability of a data collection instrument lke questionnaire.
Conclusions
This was a very good research with mixed method research design. A very good clustering of many similar variables into a composite variable has been done to reduce the number of predictive variables and the relationship between the independent variable and the predictive variable has been determined using discriminant analysis. There are no issues with reliability and validity of the work, however, it should be generalized with proper precaution as it a mixed method research.
References
Brennan R.L., “An NCME instruction Module on Generalizability Theory”. Web.
Cohen L., Manion L., Morrison K., “Research Methods in Education”, 6th Ed., Routledge, 2007.
Creswell, John W., “Research Design: Qualitative, Quantitative, and Mixed Methods Approaches”, 3rd Ed. New York: Sage, 2008.
Siegel, S., & Castellan, J. N. (1988). Nonparametric statistics for the behavioral sciences. New York: McGraw-Hill Book Co.