Chapter 11: Inferential Statistics
In psychological research, the ultimate aim is to go beyond merely describing data from a sample. Researchers strive to make meaningful inferences about a larger population based on the sample data they collect. While descriptive statistics such as means, medians, and correlation coefficients are valuable for summarising sample data, they are often just the first step. The real challenge lies in determining whether the patterns observed in a sample reflect true phenomena in the population or are merely the result of random chance. This is where inferential statistics plays a crucial role.
Imagine a researcher studying depression symptoms among 50 adults diagnosed with clinical depression. Calculating the average number of symptoms in this sample provides a snapshot of the group. However, the researcher’s goal is not limited to this specific sample; they aim to understand the broader population of individuals with clinical depression. This process of making inferences about population parameters based on sample statistics is central to inferential statistics.
Yet, drawing conclusions about a population from a sample is not without challenges. Sampling error, which refers to the random variability inherent in selecting a subset of individuals, can result in fluctuating sample statistics. For instance, the average number of depressive symptoms might be 8.73 in one sample, 6.45 in another, and 9.44 in a third. Similarly, correlations between two variables could vary from +0.24 to -0.04 to +0.15 across samples. These variations, stemming from random chance, complicate the task of discerning whether observed relationships or differences in a sample truly exist in the population or are mere artifacts of sampling error.
To address this challenge, researchers turn to null hypothesis testing, a cornerstone of inferential statistics. This systematic approach helps distinguish between two possibilities for any observed statistical relationship:
- The relationship exists in the population, and the sample reflects this genuine pattern.
- The relationship is a product of sampling error, with no real effect in the population.
By applying statistical techniques, researchers can assess the likelihood of their findings arising by chance under the assumption that the null hypothesis is true. This chapter delves into the principles and applications of inferential statistics, with a particular focus on null hypothesis testing, its underlying logic, and the tools researchers use to draw conclusions about populations. We will also explore common misconceptions, limitations, and alternative methods, providing a comprehensive understanding of this critical aspect of research methodology.
Learning Objectives
By the end of this chapter, you should be able to:
- Understand statistical significance and the p-value: Define the p-value and explain its correct interpretation as the probability of obtaining an observed result if the null hypothesis is true.
- Critically evaluate the use of p-values: Assess the limitations of relying on a rigid p < 0.05 threshold to determine significance and understand how this practice can lead to arbitrary distinctions between “significant” and “non-significant” results.
- Incorporate effect sizes and confidence intervals: Explain the importance of reporting effect sizes to convey the strength of a relationship and use confidence intervals to provide a range of plausible values for population parameters.
- Address the file drawer problem and p-hacking: Understand how practices like selective reporting and p-hacking contribute to distorted research findings. Learn how transparency measures, such as registered reports and sharing non-significant results, can improve the reliability of scientific research.
- Explore alternatives to null hypothesis testing: Recognise the limitations of null hypothesis testing and explore alternative approaches like Bayesian statistics, which provide more nuanced insights by updating probabilities based on observed data.
