Chapter 10: Descriptive Statistics
Descriptive statistics form the foundation of data analysis, providing essential tools for summarising, organising, and interpreting data. In psychology, these techniques help researchers identify patterns, trends, and relationships, laying the groundwork for deeper statistical exploration. This chapter delves into the key components of descriptive statistics, including the distribution of variables, measures of central tendency, and measures of variability, each offering unique insights into the nature of the data.
Understanding a variable’s distribution is crucial for identifying how values are spread across categories or levels. Frequency tables and histograms present these distributions clearly, helping researchers spot common values, ranges, and outliers. Measures of central tendency, including the mean, median, and mode, offer different ways to pinpoint the dataset’s “typical” value, while measures of variability, such as range, standard deviation, and variance, reveal the extent to which data points cluster around or deviate from the centre.
This chapter also explores how to describe and interpret statistical relationships between variables, whether comparing groups or examining correlations between quantitative measures. Finally, the importance of effectively presenting descriptive statistics is emphasised, with guidelines for using text, figures, and tables in alignment with APA standards. Through clear organisation and systematic analysis, descriptive statistics provide a comprehensive snapshot of the data, setting the stage for meaningful research conclusions.
Learning Objectives
By the end of this chapter, you should be able to:
- Define descriptive statistics: Explain what descriptive statistics are and their role in summarising, organising, and displaying data in psychological research.
- Explain variable distributions: Define a variable’s distribution and interpret how its values are spread across participants using examples.
- Recognise distribution shapes: Identify common distribution shapes, including unimodal, bimodal, symmetrical, positively skewed, and negatively skewed patterns.
- Understand measures of central tendency: Define and calculate the mean, median, and mode, and explain when each measure is most appropriate based on data distribution and outliers.
- Understand measures of variability: Explain the range, variance, and standard deviation, and interpret what these measures reveal about data spread.
- Interpret percentile ranks and z-scores: Define percentile ranks and z-scores, calculate them, and explain their significance in comparing individual scores within a dataset.
- Describe statistical relationships between variables: Differentiate between relationships based on group differences and correlations between quantitative variables, and explain the importance of effect sizes such as Cohen’s d and correlation coefficients like Pearson’s r.
- Create and interpret data visualisations: Use bar graphs, line graphs, and scatterplots to represent and compare data, and understand the role of error bars and regression lines in these visualisations.
- Present descriptive statistics effectively: Follow APA guidelines for presenting descriptive statistics clearly and consistently in writing, tables, and figures.
- Prepare and organise data for analysis: Explain the importance of securing, organising, and formatting raw data for analysis, and understand best practices for ensuring data accuracy and clarity.
- Differentiate between planned and exploratory analyses: Explain the difference between planned (hypothesis-driven) and exploratory (data-driven) analyses and the importance of transparency when reporting these approaches.
