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MANAGEMENT RESEARCH Third Edition, 2008 Prof. M. Easterby-Smith, Prof. R. Thorpe, Prof. Paul R. Jackson. CHAPTER 10 . Summarizing and Making Inferences from Quantitative Data. Learning Objectives. To be able to choose effective ways of summarizing key features of data.
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MANAGEMENT RESEARCH Third Edition, 2008 Prof. M. Easterby-Smith, Prof. R. Thorpe, Prof. Paul R. Jackson CHAPTER 10 Summarizing and Making Inferences from Quantitative Data
Learning Objectives • To be able to choose effective ways of summarizing key features of data. • To know which summary measures to use for location and spread of data. • To understand which statistical tests to use when comparing groups and testing association between variables.
Summarizing and making inferences • Summarizing Data: The Researcher identifies what features tell the best story about the data • Going beyond a sample: Making inferences about populations from samples The Researcher looks for patterns in the data that can be used to draw conclusions about the study’s research questions
Summarizing and describing data • Showing the Shape of Data: • A Bar Chart shows the frequency distribution visually • A Histogram is a Bar Chart with scores grouped together to show features of data very easily
Key features of data: Location • Mode - the commonest value among a set of scores • Median - the value that divides a set of data in half • Mean - the average value: add all the scores and divide by the sample size: M = ΣX / n • Mid-Mean – themean of the middle half of the data
Key features of data: Spread • Range - the distance between the largest and the smallest scores • Mid-Range - the range of the middle half of the data; also known as interquartile range • Standard Deviation - measures the average spread around the mean: SD = √ (Σ(X-M)2 / n-1)
Key features of data: Symmetry • Positively Skewed Data – the tail of extreme scores is to the right • Negatively Skewed Data – the tail of extreme scores is to the left
Assessing summary measures: Robustness and efficiency • Robustness: The extent to which a summary measure is sensitive to disturbances in data quality • Efficiency: The extent to which a summary measure captures all the information within the data which is relevant to what is summarized
Going beyond a sample • Hypothesis testing: Making inferences about populations based on data from samples • Five steps • Step 1 – define a research hypothesis to be tested • Step 2 – define a null hypothesis • Step 3 - derive a summary measure of the characteristic of interest • Step 4 – choosing a reference distribution and calculating a test statistic • Step 5 – drawing a conclusion
Selecting statistical tests • Testing group differences • Comparing two groups – t test, Mann-Whitney U test • Comparing three or more groups – analysis of variance, Kruskal-Wallace test • Testing association • For category variables – chi square tests, phi coefficient • For continuous variables – correlation coefficient
Association between two variables • A Positive Association - high scores on variables go together, and low scores go together • A Negative Association - high scores on one variable go with low scores on the other • Zero Association - knowing about one variable does not help in telling us anything about the other
Further Reading • Howell, D. (2001). Statistical Methods for Psychology, 5th edition. Wadsworth. • Howell, D. (2007). Fundamental Statistics for the Behavioral Sciences, 6th edition. Wadsworth.