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Transcript of Type author names here Social Research Methods Chapter 15: Quantitative data analysis Alan Bryman...
Type author names here
Social Research Methods
Chapter 15: Quantitative data analysis
Alan Bryman
Slides authored by Tom OwensSlides 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
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
Bryman: Social Research Methods, 4th edition
Deciding how to categorize a variable
Figure 15.1Page 336
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
Bryman: Social Research Methods, 4th edition
A bar chart (gym study)
Figure 15.2Page 338
Bryman: Social Research Methods, 4th edition
A pie chart
Main reasons for visiting the gym
Figure 14.3Page 344
Bryman: Social Research Methods, 4th edition
A histogram
Page 15.4Page 338
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
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
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
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
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
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
Bryman: Social Research Methods, 4th edition
Example of a spurious relationship
Figure 15.11Page 345
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
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
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
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
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
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
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