Inferential Testing
This section explains inferential testing in Psychology. Inferential testing in psychology allows researchers to make inferences about a population based on a sample. This process goes beyond mere description of data by helping determine whether observed patterns are likely due to chance or reflect a genuine effect. Key components of inferential testing include understanding probability, significance, and the appropriate choice of statistical tests based on data characteristics and experimental design.
Statistical Testing: Introduction to the Sign Test
The sign test is a simple inferential test used to analyse difference data when dealing with repeated measures or matched pairs data that is at the nominal level (categorical data). It is particularly useful for determining if there is a significant difference between two sets of related scores (e.g., scores before and after an intervention).
When to Use the Sign Test
- Data Type: Nominal data.
- Design: Repeated measures or matched pairs.
- Purpose: To determine if there is a statistically significant difference in the direction of scores (increases or decreases).
Calculation of the Sign Test
Identify the Differences: For each pair of data, determine if there is an increase (+), decrease (-), or no change (0).
Count the Signs: Count the number of positive and negative signs, ignoring any pairs where there is no change.
Determine the Smallest Frequency: Find the smaller of the two frequencies (either + or -).
Refer to Statistical Tables: Using the calculated smallest frequency, refer to the sign test table with the appropriate sample size (N) to check for significance.
Probability and Significance
Probability refers to the likelihood of an event occurring by chance. In psychology, probability is often used to assess whether an observed effect in the data could have occurred by chance.
- Significance Levels: The most commonly used significance level is 0.05 (5%). This means that there is a 5% chance that the result occurred by chance.
- Statistical Tables and Critical Values: Statistical tables are used to find critical values, which are thresholds that indicate whether a test statistic is significant. If the calculated value of a test statistic is equal to or more extreme than the critical value, the result is considered significant.
Type I and Type II Errors
- Type I Error (False Positive): Occurs when a researcher incorrectly rejects the null hypothesis, concluding that there is a significant effect when there actually isn’t one.
- Type II Error (False Negative): Occurs when a researcher fails to reject the null hypothesis, concluding there is no effect when there actually is one.
Managing the balance between Type I and Type II errors is crucial in psychological research to ensure accuracy.
Factors Affecting the Choice of Statistical Test
The choice of statistical test depends on various factors:
- Level of Measurement: The type of data (nominal, ordinal, interval, or ratio) influences which statistical tests are suitable.
- Experimental Design: Whether the design is related (repeated measures or matched pairs) or unrelated (independent groups).
- Type of Hypothesis: Whether the hypothesis is testing a difference or a correlation.
Levels of Measurement
Nominal: Categories without any order (e.g., gender).
Ordinal: Ordered data without consistent intervals (e.g., rankings).
Interval: Continuous data with equal intervals and no true zero (e.g., temperature).
Ratio: Continuous data with equal intervals and a true zero (e.g., height, weight).
When to Use Specific Inferential Tests
Below are common statistical tests used in psychology, along with the conditions under which each test is appropriate:
| Test | Data Type | Design | Purpose |
| Sign Test | Nominal | Repeated measures | Testing for a difference |
| Spearman’s Rho | Ordinal | Correlation | Testing for a relationship |
| Pearson’s r | Interval/Ratio | Correlation | Testing for a relationship |
| Wilcoxon | Ordinal | Repeated measures | Testing for a difference |
| Mann-Whitney | Ordinal | Independent groups | Testing for a difference |
| Related t-test | Interval/Ratio | Repeated measures | Testing for a difference |
| Unrelated t-test | Interval/Ratio | Independent groups | Testing for a difference |
| Chi-Squared Test | Nominal | Independent groups | Testing for association |
Explanation of Each Test
Spearman’s Rho: Used to assess correlation when data is ordinal or ranks, testing the strength and direction of the association.
Pearson’s r: A parametric test for correlation, used with interval or ratio data to assess the strength and direction of the linear relationship between two continuous variables.
Wilcoxon Signed-Rank Test: A non-parametric test for repeated measures or matched pairs, suitable for ordinal data, that checks if there is a difference in scores.
Mann-Whitney U Test: A non-parametric test for independent groups with ordinal data, used to see if two groups differ significantly.
Related t-test (Paired t-test): A parametric test used with interval or ratio data and repeated measures design. It assesses if there is a significant difference between two related groups.
Unrelated t-test (Independent t-test): A parametric test for interval or ratio data with independent groups design, used to test if there is a significant difference between two independent groups.
Chi-Squared Test: A test for nominal data with independent groups, used to determine if there is an association between variables.
Summary
- Significance Testing: Essential for interpreting whether findings are meaningful and not due to chance.
- Error Types: Type I (false positives) and Type II (false negatives) must be considered in research conclusions.
- Choosing Tests: The choice of test is influenced by the level of measurement and study design, with specific tests applicable to specific types of data and hypotheses.
A clear understanding of these principles enables researchers to select the appropriate test, thereby ensuring that psychological research is both accurate and valid.
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