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Colin Clarke-Hill and Ismo Kuhanen

Analysing Quantitative Data 1

Forming the Hypothesis

Inferential Methods - an overview

Research Methods

Analysing Quantitative Data 2

Research Methods

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Formulating the Hypothesis

• Often in research studies we wish to test whether a particular phenomenon exists or not, or more likely, if a certain relationship between two or more variables is present.

• This leads the researcher into the need to set or formulate a hypothesis

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Hypothesising

• At a simple level we use a hypothesis to allow us to understand the nature of the data that we have collected. We use the hypothesis to show that a particular set of facts about a population is true.

• In such a situation when we set a hypothesis we are really setting THREE hypotheses, as the creation of one implies two others.

• No I have not been drinking !!

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Hypothesis

• For example. Let us say that we want to establish that Dutch consumers are more likely to own bicycles than British consumers.

• H1: A greater proportion of Dutch consumers own bicycles than of British consumers

• H2: A smaller proportion of Dutch consumers own bicycles than of British consumers

• H3: The proportions of Dutch and British consumers who own bicycles are the same.

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Hypothesis

• Any one of the three hypotheses could reflect the the actual situation. The hypotheses that have been constructed are:– Mutually exclusive– Mutually exhaustive

• Competing hypotheses - support of one implies the rejection of others.

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Hypothesis

• What this does not tell us is which WAY the relationship is Look at the descriptive statistics for that.

• Often we want to test a relationship between a set of variables so that we can be more certain about something.

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Hypothesis

• The Null Hypothesis - the term null hypothesis reflects the concept that this is a hypothesis of NO difference. For this reason the null hypothesis always includes a statement of equality.

• The Alternative Hypothesis - is the complement of the null hypothesis, that is it postulates a difference or an inequality.

• HINT: only the null hypothesis can be tested. Also we can never PROVE a hypothesis.

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Hypothesis

• When the null hypothesis is rejected it is only then that we obtain indirect support for the alternative hypothesis. We test pairs of hypotheses.

• Because we are almost always dealing with samples, we need to understand the nature of our sample and its population, and the degree of significance we require.

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Hypothesis

Steps in Hypothesis testing:

• Formulate the null hypothesis

• Specify the significance level

• Select an appropriate statistical test

• Identify the probability distribution of the test statistic and define the region of rejection

• Compute the value of the test statistic and decide whether to accept of reject the null hypothesis.

See Saunders & Thornhill page 316

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Some test that can be used

Typical questions:

• Are the variables significantly associated

• Are these groups significantly different

• What is the strength of the relationship between the variables and is it significant

• Can I make any predictions. Hint - be careful - correlation vs causation problems

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Tests typically used

• Chi-Squared Test - tests whether the values for a set of variables are independent or associated. It is based on a comparison. You create a Chi-squared contingency table from your data set by using cross tabulations. Chi-square tests are commonly used with questionnaire data.

• Use with significance levels.• Hint - changing the levels of significance can alter

the association between the variables

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Tests

• If you want to test whether or not two groups or categories are significantly different, then use one of the t-tests.

• If we wish to test the same thing but with more than two groups we then have to look at the one-way ANOVA and use the F-Statistic

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Tests

• How do we assess the strength of a relationship ?

• We use the correlation co-efficient. This allows us to think about the Cause and the Effect issue. Smoking and Cancer.

• Correlation co-efficient is between +1 & -1

• We speak of positive or negative correlations

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Tests

• Correlations are useful to the analyst. It allows the researcher to model the variables.

• We can also use tests to measure the strength of the relationship. Pearson’s product moment correlation or the Spearman’s rank correlation is suitable.

• Correlations usually generate equations from plotted data. At its simplest, we can correlate 2 variables say wages and prices.

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Cause and Effect

• Cause and Effect can be forecast using regression analysis. We can create equations to model the relationship between the variables - two - simple regression, more that two - multiple regression. From the calculation we can estimate the Regression Co-efficient or R2 .

• Again tests for significance will apply.

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Cause and Effect

• The regression equations and analysis will also tell us not only the confidence that we have but also the percentage of coverage.

• For example : Only 14 % of business success was explained by the firm’s Marketing Relationships.

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Cause and Effect

• Correlation does not prove causality. All that is expressed is the degree of covariance between the variables. Any notion of causuality must come from practical knowledge or theoretical insight into the subject matter, preferably supported by longitudinal data. Viz: Smoking and Cancer, Passive Smoking and Cancer etc.

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Other Statistical Tools for Analysis

• Multivariate Analysis

• Cluster Analysis

• Factor Analysis

• etc...

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Multivariate Analysis

• This is a variation on the ANOVA, involving multiple variables. It is one of the most versatile of methods. Often known as MANOVA and used in experimental design.

• You must really know your stats to set up a MANOVA table. SPSS does it for you.

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Cluster Analysis

• Used to reduce the complexity of your data. Cluster Analysis seeks to reduce the number of objects for which measurements have been made.

• By looking at the similarities and differences between the scores, each object is grouped with others having similar characteristics to form clusters.

• Cluster analysis is widely used in segmentation studies

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Factor Analysis

• Refers to techniques that aims to describe a large number of variables by means of a smaller set of composite variables called factors and thus help us interpret the data. This is known as Common Factor Analysis.

• The original variables can then be discussed in terms of the common underlying dimensions.

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Some texts to look up

• Diamantopoulos and Schlegelmilch - Taking the fear out of Data Analysis, Dryden Press, 1997. ( EXCELLENT)

• Hooley and Hussey - Quantitative Methods in Marketing, Dryden Press, 1995. An excellent collection of papers.

• Robson - Real World Research, Blackwell, 1993. An excellent RM 499 book to complement Saunders et al.

Analysing Quantitative Data 2Analysing Quantitative Data 2