The Chi-Squared () test is a statistical tool used to determine if there is a significant association between two variables or if an observed distribution differs from an expected one.
In coastal studies, it is frequently applied to analyze sediment size distribution or the frequency of specific landforms along a stretch of coastline.
The process begins with a null hypothesis (), which assumes there is no significant relationship between the variables and any observed patterns are due to random chance.
The formula for the test statistic is: where represents the Observed values (actual data collected) and represents the Expected values (the average or theoretical distribution).
To interpret the result, the calculated value is compared against a critical value from a distribution table, using degrees of freedom (, where is the number of categories).
| Concept | Observed Data () | Expected Data () |
|---|---|---|
| Definition | Real-world measurements collected in the field. | Theoretical values assuming a random or uniform distribution. |
| Role in | Provides the basis for the actual pattern. | Acts as the baseline for the null hypothesis. |
| Level of Significance | 95% Confidence () | 99% Confidence () |
|---|---|---|
| Meaning | 5% probability the result is due to chance. | 1% probability the result is due to chance. |
| Requirement | Calculated > Critical Value at 0.05. | Calculated > Critical Value at 0.01. |
Check the Null Hypothesis: Always ensure your null hypothesis is stated as 'no significant association' or 'no significant difference' to allow for objective testing.
Degrees of Freedom: A common mistake is using the total sample size () instead of the number of categories minus one () for the degrees of freedom.
Evaluate, Don't Just Describe: In qualitative questions, avoid simply listing costs or impacts; explain why a specific factor (like ethics or long-term time scales) makes a strategy successful or unsuccessful.
Critical Value Comparison: If your calculated is higher than the critical value, you must explicitly state that you 'reject the null hypothesis' and that the result is 'statistically significant'.