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Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Slides authored by Tom Owens Owens

Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

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Page 1: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Type author names here

Social Research Methods

Chapter 15: Quantitative data analysis

Alan Bryman

Slides authored by Tom OwensSlides authored by Tom Owens

Page 2: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

Introduction

• Think about data analysis at an early stage in the research process

• Decisions about methods and sample size affect the kinds of analysis you can do

Page 330

Page 3: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

Types of variable

• Interval/ratio– regular distances between all categories in range

• Ordinal – categories can be ranked, but unequal distances between

them

• Nominal– qualitatively different categories - cannot be ranked

• Dichotomous– only two categories (e.g. gender)

Page 335

Page 4: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

Deciding how to categorize a variable

Figure 15.1Page 336

Page 5: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

Univariate analysis(analysis of one variable at a time)

• Frequency tables– Number of people or cases in each category– Often expressed as percentages of sample– Interval/ratio data need to be grouped

• Diagrams– Bar chart or pie chart (nominal or ordinal

variables)– Histogram (interval/ratio variables)

Page 337

Page 6: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

A bar chart (gym study)

Figure 15.2Page 338

Page 7: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

A pie chart

Main reasons for visiting the gym

Figure 14.3Page 344

Page 8: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

A histogram

Page 15.4Page 338

Page 9: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

Measures of central tendency

• Mean– Sum all values in distribution, then divide by total

number of values

• Median– Middle point within entire range of values– Not distorted by outliers

• Mode– Most frequently occurring value

Page 338, 339

Page 10: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

Measures of dispersion

Dispersion means the amount of variation in a sample.

Measures of dispersion compare levels of variation in different samples to see if there is more variability in a variable in one sample than in another.

The range is the difference between the minimum and maximum values in a sample

The standard deviation is the average amount of variation around the mean, reducing the impact of extreme values (outliers)

Page 339

Page 11: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

Bivariate analysis(analysis of two variables at a time)

• Explores relationships between variables

• Searches for co-variance and correlations

• Cannot establish causality

• Can sometimes infer the direction of a causal relationship – If one variable is obviously independent of the other

• Contingency tables– Connects the frequencies of two variables– Helps you identify any patterns of association

Page 340, 341

Page 12: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

Pearson’s r : the relationship between two interval/ratio variables

• Coefficient shows the strength and direction of the relationship– Lies between -1 (perfect negative relationship) and +1

(perfect positive relationship)

• Relationships must be linear for the method to work, so, plot a scatter diagram first

• Coefficient of determination– Found by squaring the value of r– Shows how much of the variation in one variable is due to

the other variable?

Page 342, 344

Page 13: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

Analysing the relationships between other, or mixed types of, variables

Spearman’s rho: for the relationship between two ordinal variables, or one ordinal and one interval/ratio variable (values of -1 to +1)

Phi coefficient: for the relationship between two dichotomous variables (values of -1 to +1)

Cramer’s V: for the relationship between two nominal variables, or one nominal and one ordinal variable (values between 0 and 1)

Comparing means: when a nominal variable is identified as the independent variable, the means of the interval/ratio variable are compared for each sub-group of the nominal variable

eta: for the level of association between different types of variables, even when there is no linear relationship between them

Page 344, 345

Page 14: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

Multivariate analysis(three or more variables)

• The relationship between two variables might be spurious– Each variable could be related to a separate, third variable

• There might be an intervening variable

• A third variable might be moderating the relationship– e.g. correlation between age and exercise could be

moderated by gender

Page 345, 346

Page 15: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

Example of a spurious relationship

Figure 15.11Page 345

Page 16: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

Statistical significance

• How confident can we be that the findings from a sample can be generalised to the population as a whole?

• How risky is it to make this inference?

• Only applies to probability samples

Page 347

Page 17: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

Testing procedure for statistical significance

1. Set up a null hypothesis - suggesting no relationship between examined variables in the population from which the sample was

drawn;

2. Decide on an acceptable level of statistical significance;

3. Use a statistical test;

4. If acceptable level attained, reject null hypothesis; if not attained, accept it.

Page 347, 348

Page 18: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

…but we might be wrong to accept or reject the null hypothesis

Type I and Type II errors

Figure 15.12Page 349

Page 19: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

Tests of statistical significance

• The chi-square test– establishes how confident we can be that there is a

relationship between the two variables in the population

• Correlation and statistical significance– provides information about the likelihood that the coefficient

will be found in the population from which the sample was taken

• Comparing means and statistical significance – the F statistic– expresses the amount of explained variance in relation to

the amount of error variancePages 348,

350

Page 20: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

The chi-square test

•The chi-square (2) test is applied to contingency tables. It establishes how confident we can be that there is a relationship between the two variables in the population. The test calculates for each cell in the table an expected frequency or value - one that would occur on the basis of chance alone. The chi-square value is determined by calculating the differences between the actual and expected values for each cell and then summing those differences.

•Whether a chi-square value achieves statistical significance depends not just on its magnitude but also on the number of categories of the two variables being analysed. This latter issue is governed by what is known as the ‘degrees of freedom’ associated with the table.

Page 355

Page 21: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

Correlation and significance

• How confident can we be about a relationship between two variables?

• Whether a correlation coefficient is statistically significant depends on:– the size of the coefficient (the higher the better)– the size of the sample (the larger the better)

• e.g. if coefficient is 0.62 and p<0.05, we can reject the null hypothesis

Page 355

Page 22: Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman Slides authored by Tom Owens

Bryman: Social Research Methods, 4th edition

Comparing means

• Statistical significance of relationship between two variables’ means

• Total variation in dependent variable: – error variance (variation within subgroups of IV)– explained variance (variation between subgroups of IV)

• F statistic – expresses amount of explained variance in relation to

amount of error variance

Page 356