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"A generalization predicting that a relationship exists between variables. Many generalizations about politics are a sort of folklore. Others proceed from earlier work carried out by social scientists. Within the social sciences most statements about behaviour relate to large groups of people. Hence, testing any hypothesis in the field of political science will involve statistical method. It will be dealing with probabilities.
To test a hypothesis one must pose a null hypothesis. If we wanted to test the validity of the common generalization, 'manual workers tend to vote for the Labour Party' we would begin by assuming the statement was untrue. The investigation would require a sample survey in which manual workers were identified and questions put to them. It would need to be done in several constituencies in different parts of the country. Having collated the data we would use the evidence to test the null hypothesis, employing statistical techniques to assess the probability of acquiring such data if the null hypothesis were correct. These techniques are known as 'significance tests'. They estimate the probability that the rejection of a null hypothesis is a mistake. If the statistical tests indicates that the odds against it being a mistake are 1000 to one, then this is stated as a '.001 level of significance'.
The fact that the research showed that it was highly likely that manual workers 'tend' to vote for the Labour vote would not satisfy most political scientists. They also want to understand those who did not. Consequently much more work would need to be done to refine the hypothesis and define the tendency with more accuracy. Whatever the case, a hypothesis in the social sciences about a group or socio-demographic category can never tell us about the behaviour of an individual in that group or category."
Hypothesis. (1999). In F. Bealey. The Blackwell Dictionary of Political Science, Oxford, United Kingdom: Blackwell Publishers.
Quantitative research studies produce results that can be used to describe or note numerical changes in measurable characteristics of a population of interest; generalize to other, similar situations; provide explanations of predictions; and explain causal relationships. The fundamental philosophy underlying quantitative research is known as positivism, which is based on the scientific method of research. Measurement is necessary if the scientific method is to be used. The scientific method involves an empirical or theoretical basis for the investigation of populations and samples. Hypotheses must be formulated, and observable and measurable data must be gathered. Appropriate mathematical procedures must be used for the statistical analyses required for hypothesis testing.
Quantitative methods depend on the design of the study (experimental, quasi-experimental, non-experimental). Study design takes into account all those elements that surround the plan for the investigation, such as research question or problem statement, research objectives, operational definitions, scope of inferences to be made, assumptions and limitations of the study, independent and dependent variables, treatment and controls, instrumentation, systematic data collection actions, statistical analysis, time lines, and reporting procedures. The elements of a research study and experimental, quasi-experimental, and nonexperimental designs are discussed here.
First, an empirical or theoretical basis for the research problem should be established. This basis may emanate from personal experiences or established theory relevant to the study. From this basis, the researcher may formulate a research question or problem statement.
Operational definitions describe the meaning of specific terms used in a study. They specify the procedures or operations to be followed in producing or measuring complex constructs that hold different meanings for different people. For example, intelligence may be defined for research purposes by scores on the Stanford-Binet Intelligence Scale.
Quantitative methods include the target group (population) to which the researcher wishes to generalize and the group from which data are collected (sample). Early in the planning phase, the researcher should determine the scope of inference for results of the study. The scope of inference pertains to populations of interest, procedures used to select the sample(s), method for assigning subjects to groups, and the type of statistical analysis to be conducted.
Complex questions to compare responses of two or more groups or show relationships between two or more variables are best answered by hypothesis testing. A hypothesis is a statement of the researcher's expectations about a relationship between variables.
Statements of hypotheses may be written in the alternative or null form. A directional alternative hypothesis states the researcher's predicted direction of change, difference between two or more sample means, or relationship among variables. An example of a directional alternative hypothesis is as follows:
Third-grade students who use reading comprehension strategies will score higher on the State Achievement Test than their counterparts who do not use reading comprehension strategies.
A nondirectional alternative hypothesis states the researcher's predictions without giving the direction of the difference. For example:
There will be a difference in the scores on the State Achievement Test between third-grade students who use reading comprehension strategies and those who do not.
Stated in the null form, hypotheses can be tested for statistically significant differences between groups on the dependent variable(s) or statistically significant relationships between and among variables. The null hypothesis uses the form of “no difference” or “no relationship.” Following is an example of a null hypothesis:
There will be no difference in the scores on the State Achievement Test between third-grade students who use reading comprehension strategies and those who do not.
It is important that hypotheses to be tested are stated in the null form because the interpretation of the results of inferential statistics is based on probability. Testing the null hypothesis allows researchers to test whether differences in observed scores are real, or due to chance or error; thus, the null hypothesis can be rejected or retained.
Survey forms, inventories, tests, and other data collection instruments returned by participants should be screened prior to the analysis. John Tukey suggested that exploratory data analysis be conducted using graphical techniques such as plots and data summaries in order to take a preliminary look at the data. Exploratory analysis provides insight into the underlying structure of the data. The existence of missing cases, outliers, data entry errors, unexpected or interesting patterns in the data, and whether or not assumptions of the planned analysis are met can be checked with exploratory procedures.
Important considerations for the choice of a statistical test for a particular study are (a) type of research questions to be answered or hypotheses to be tested; (b) number of independent and dependent variables; (c) number of covariates; (d) scale of the measurement instrument(s) (nominal, ordinal, interval, ratio); and (e) type of distribution (normal or non-normal). Examples of statistical procedures commonly used in educational research are t test for independent samples, analysis of variance, analysis of covariance, multivariate procedures, Pearson product-moment correlation, Mann–Whitney U test, Kruskal–Wallis test, and Friedman's chi-square test.
The level of statistical significance that the researcher sets for a study is closely related to hypothesis testing. This is called the alpha level. It is the level of probability that indicates the maximum risk a researcher is willing to take that observed differences are due to chance. The alpha level may be set at .01, meaning that 1 out of 100 times the results will be due to chance; more commonly, the alpha level is set at .05, meaning that 5 out of 100 times observed results will be due to chance. Alpha levels are often depicted on the normal curve as the critical region, and the researcher must reject the null hypothesis if the data fall into the predetermined critical region. When this occurs, the researcher must conclude that the findings are statistically significant. If the researcher rejects a true null hypothesis (there is, in fact, no difference between the means), a Type I error has occurred. Essentially, the researcher is saying there is a difference when there is none. On the other hand, if a researcher fails to reject a false null (there is, in fact, a difference), a Type II error has occurred. In this case, the researcher is saying there is no difference when a difference exists. The power in hypothesis testing is the probability of correctly rejecting a false null hypothesis. The cost of committing a Type I or Type II error rests with the consequences of the decisions made as a result of the test. Tests of statistical significance provide information on whether to reject or fail to reject the null hypothesis; however, an effect size (R2, eta2, phi, or Cohen's d) should be calculated to identify the strength of the conclusions about differences in means or relationships among variables.
Salkind, Neil J. 2010. Encyclopedia of Research Design. Thousand Oaks, CA: SAGE Publications, Inc. doi: 10.4135/9781412961288.
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SAGE Research Methods is a research methods tool created to help researchers, faculty and students with their research projects. SAGE Research Methods links over 175,000 pages of SAGE’s renowned book, journal and reference content. Researchers can explore methods concepts to help them design research projects, understand particular methods or identify a new method, conduct their research, and write up their findings. Since SAGE Research Methods focuses on methodology rather than disciplines, it can be used across the social sciences, health sciences, and more. Subject coverage includes sociology, health, criminology, education, anthropology, psychology, business, political science, history, economics, among others.
Sage Research Methods has a feature called a Methods Map that can help you explore different types of Research Designs.
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