# developing literacy in quantitative

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DEVELOPING LITERACY IN QUANTITATIVERESEARCH METHODSDr Christina HughesUniversity of WarwickC.L.Hughes@warwick.ac.ukThese materials have two inter-related aims. The primary aim is to develop students' literacy in the use and reading of research that uses quantitative data. The second is to enhance students' confidence in their understandings of such approaches. To achieve these aims the package will introduce students to a number of basic statistical techniques that are used in social research. In addition the materials will explore some common concepts that underpin quantitative social research.The specific objectives are: To develop understandings of the relationship between different types of quantitative data and their implications for descriptive and inferential statistical techniques; To develop understandings of the statistical techniques of: measures of central tendency, measures of dispersion; To explore the meanings of correlation and causality in relation to quantitative social research; To explore uses, and misuses, of official statistics.Quantitative techniques are most commonly associated with survey and experimental research designs. As the name suggests, quantitative research is concerned with the collection and analysis of data in numeric form. It tends to emphasize relatively large-scale and representative sets of data, and is often (problematically) presented or perceived as being about the gathering of `facts'. Because of strong associations that are made between statistics as social facts and dominant ideas of science as objective and detached, quantitative strategies are often viewed as more valid.Many small-scale research studies that use questionnaires as a form of data collection will not need to go beyond the use of descriptive statistics and the exploration of the interrelationships between pairs of variables. It will be adequate to say that so many respondents (either the number or the proportion of the total) answered given questions in a certain way; and that the answers given to particular questions appear to be related. Such an analysis will make wide use of proportions and percentages, and of the various measures of central tendency (averages) and of dispersion (ranges).You may, however, wish or need to go beyond this level of analysis, and make use of inferential statistics or multivariate methods of analysis. There are dozens of inferential statistics available: three commonly used examples are Chi-square; Kolmogorov-Smirnov and Student's t-test. The functions of these statistics vary but they are typically used to compare the measurements you have collected from your sample for a particular variable with another sample or a population in order that a judgement may be made on how similar or dissimilar they are. It is important to note that all of these inferential statistics make certain assumptions about both the nature of your data and how it was collected. This means that you have to be clear whether your data is, for example, nominal, ordinal, interval or ratio. If these assumptions do not hold these measures should not be used.Multivariate methods of analysis may be used to explore the interrelationships among three or more variables simultaneously. Commonly used examples include multiple regression, cluster analysis and factor analysis. While you do not need to have an extensive mathematical knowledge to apply these techniques, as they are all available as part of computer software packages, you should at least have an understanding of their principles and purposes.One key point to be aware of when carrying out quantitative analysis is the question of causality. One of the purposes of analysis is to seek explanation and understanding. We would like to be able to say that something is so because of something else. However, just because two variables of which you have measurements appear to be related, this does not mean that they are. Statistical associations between two variables may be a matter of chance, or due to the effect of some third variable. In order to demonstrate causality, you also have to find, or at least suggest, a mechanism linking the variables together.[Extracted from Blaxter, Hughes and Tight, 1996]BibliographyThis bibliography includes texts that are useful for students new to quantitative techniques and those that are useful for the more advanced. The asterisk (*) indicates those that are introductory. The key publishers of methodology texts are Sage, Routledge and Open University Press. If you wish to extend your reading or keep up to date with developments you should put your name on these publishers' catalogue mailing lists. There are also a number of journals that are primarily concerned with developments in methodology. These include: The International Journal of Social Research Methodology and Social Research Online ( http://www.socresonline.org.uk). In addition, secondary sources produced by the Office for National Statistics for the Government Statistical Service can be obtained from The Office for National Statistics, 1 Drummond Gate, London, SW1V 2QQ or through the STATBASE on-line directory.Black, T (1999) Doing Quantitative Research in the Social Sciences: An Integrated Approach to Research Design, Measurement and Statistics, London, SageBlaxter, L, Hughes, C and Tight, M (1996) How to Research, Buckingham, Open University Press*Bowling, A (1997) Research Methods in Health: Investigating Health and Health Services, Buckingham, Open University Press*Bryman, A and Cramer, D (1990) Quantitative Data Analysis for Social Scientists, London, RoutledgeCalder, J (1996) Statistical Techniques, in R Sapsford and V Jupp (Eds) Data Collection and Analysis, London, Sage, pp 225-261Cramer, D (1994) Introducing Statistics for Social Research: Step-by-step calculations and computer techniques using SPSS, London, RoutledgeDenscombe, M (1998) The Good Research Guide: For small scale social research projects, Buckingham, Open University Press*De Vaus, D (1991) Surveys in Social Research, Sydney, NSW, Allen and UnwinHek, G, Judd, M and Moule, P (1996) Making Sense of Research: An Introduction for Nurses, London, Cassell*Hinton, P (1995) Statistics Explained: A guide for social science students, London, Routledge*Leary, M (1991) Introduction to Behavioural Research Methods, Belmont, Calif, Wadsworth PublishingLevitas, R and Guy, W (1996) Interpreting Official Statistics, London, RoutledgePersell, C and Maisel, R (1995) How Sampling Works, Newbury Park, Calif, Pine ForgePilcher, D (1990) Data Analysis for the Helping Professions: A Practical Guide, Newbury Park, Calif, SageSapsford, R (1996) Extracting and Presenting Statistics, in R Sapsford and V Jupp (Eds) Data Collection and Analysis, London, Sage, pp 184-224Solomon, R and Winch, C (1994) Calculating and Computing for Social Science and Arts Students, Buckingham, Open University Press*Stanley, L (Ed) (1990) Feminist Praxis, London, RoutledgeTownsend, P (1996) The Struggle for Independent Statistics on Poverty, in R Levitas and W Guy (Eds) Interpreting Official Statistics, London, Routledge, pp 26-44Traub, R (1994) Reliability for the Social Sciences: Theory and Application, Thousand Oaks, Calif, SageWright, D (1997) Understanding Statistics: An introduction for the social sciences, London, Sage*TYPES OF QUANTITATIVE DATANominal dataNominal data come from counting things and placing them in a category. They are the lowest level of quantitative data in the sense that they allow little by way of statistical manipulation compared with the other types. Typically there is a head count of members of a particular category, such as female/male or African Caribbean/South Asian. These categories are based simply on names; there is no underlying order to the names.Used for the following descriptive statistics: proportions, percentages, ratios.Ordinal dataLike nominal data, ordinal data are based on counts of things assigned to specific categories but in this case the categories stand in some clear, ordered, ranked relationship. The categories are `in order'. This means that the data in each category can be compared with the data in the other categories as being higher or lower than, more or less than, etc. those in other categories. The most obvious examples of ordinal data come from the use of questionnaires in which respondents are asked to respond to a five-point Likert scale. It is worth stressing that rank order is all that can be inferred. With ordinal data we do not know the cause of the order or by how much they differ.Used for the following descriptive statistics: proportions, percentages, ratios.Interval dataInterval data are like ordinal data but the categories are ranked on a scale. This means that the `distance' between the categories is a known factor and can be pulled into the analysis. The researcher can not only deal with the data in terms of `more than' or `less than' but also say how much more or how much less. The ranking of the categories is proportionate and this allows for direct contrast and comparison. Calendar years are one example. This allows the researcher to use addition and subtraction (but not multiplication and division) to contrast the difference between various periods.Used for the following descriptive statistics: measures of central tendency (mode, median, mean)Ratio dataRatio data are like interval data except that the categories exist on a scale which has a `true zero' or an absolute reference point. When the categories concern things like incomes, distances and weights they give rise to ratio data because the scales have a zero point. Calendar years, in the previous example, do not exist on such a scale because the year 0 does not denote the beginning of all time and history. The important thing about the scale having a true zero is that the researcher can compare and contrast the data for each category in terms of ratios, using multiplication and division, rather than being

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