Hypothesis testing is a statistical method used to make decisions or draw conclusions about a population based on sample data. It helps researchers determine whether a claim or assumption holds true, using evidence instead of guesswork.
However, hypothesis testing only works correctly when certain statistical assumptions are met.
Assumptions are the basic conditions that need to be true for a statistical test to give valid results. Simply put, every hypothesis test has rules about how the data should behave. When your dataset meets these conditions, the test results are trustworthy. When it does not, the results can become biased or misleading.
These assumptions help avoid incorrect conclusions. For example, if the data is not normally distributed, running a parametric test may give inaccurate p-values or underestimate variability.
Some statistical tests rely heavily on assumptions, including:
Hypothesis testing relies on two major categories of assumptions
Statistical assumptions refer to the conditions your dataset must meet for a test to produce correct and unbiased results.
These assumptions vary depending on the test, but most parametric tests require the following:
Many hypothesis tests assume that the data (or residuals) follow a normal distribution. This is especially important for t-tests, ANOVA, and regression. Normality ensures that p-values and confidence intervals are accurate and not distorted by skewed data.
Each observation in your dataset should be independent of all others. In simple terms, one person’s score should not influence another person’s score. Violations occur in clustered data, repeated measures, or poorly designed experiments.
Also known as equal variances or homoscedasticity, this assumption means that the spread of data should be similar across groups. Tests like ANOVA and independent t-tests rely heavily on this assumption. Unequal variances can distort test statistics.
For tests like Pearson correlation and regression analysis, the relationship between variables must be linear. If the relationship is curved or non-linear, the test may underestimate or misrepresent the strength of the relationship.
Your sample must be taken randomly from the population. Random sampling reduces bias and increases the generalisability of your results. Without it, hypothesis testing becomes unreliable because the sample may not reflect the population accurately.
Beyond statistical conditions, hypothesis testing also depends on practical research assumptions about how the data was collected and measured.
The variables used in the test must be measured accurately and consistently. Poor measurement tools, incorrect scale types, or human error can lead to invalid results, no matter how strong the statistical method is.
Data must be gathered using a valid and replicable process. Surveys, experiments, and observations should follow standard procedures to avoid bias and ensure consistency.
A small sample size can make results unstable and reduce the power of the test. A sample that is too large may detect trivial differences.
Our writers are ready to deliver multiple custom topic suggestions straight to your email that aligns
with your requirements and preferences:
Below are the major tests used in research and the assumptions that come with each.
A t-test compares means between groups, but it only works correctly when certain conditions are met.
| Normality | The data, or the differences between paired observations, should follow a normal distribution. This matters most for small sample sizes (n < 30). |
| Independence | Each observation must be independent of others. In independent t-tests, the two groups must not influence each other. |
| Equal Variances (Independent t-test only) | Also called homogeneity of variance, both groups should have roughly equal spread. Levene’s test is commonly used to check this. |
Analysis of Variance (ANOVA) compares means across three or more groups. Its assumptions include:
| Independence of Observations | Participants or measurements must not influence one another. This is the most crucial assumption in ANOVA. |
| Homogeneity of Variance | The variance across the groups should be similar. If this assumption is violated, you can use Welch’s ANOVA or a non-parametric alternative. |
| Normal Distribution of Residuals | Residuals (differences between observed and predicted values) should be normally distributed. ANOVA is quite robust to minor deviations, especially with larger samples. |
The Chi-Square test is used for categorical data to test relationships between variables.
| Expected Frequencies $\ge 5$ | At least 80% of the cells should have expected counts of 5 or more. Low expected values make the $\chi^2$ (Chi-square) test unreliable. |
| Independent Categories | Each participant or observation must appear in one category only. No repeated measures or paired data are allowed (i.e., observations are independent). |
| Random Sampling | Data must come from a random and representative sample to ensure the test reflects the population accurately. |
Correlation tests measure the strength and direction of the relationship between two variables.
| Linearity | Pearson correlation requires a linear relationship between the two variables. If the relationship is curved, the Pearson coefficient ($r$) becomes misleading. |
| Homoscedasticity | The variability (spread) of the data points around the regression line should remain constant across the range of values for the independent variable. Unequal spread reduces the accuracy of the correlation and subsequent regression. |
| Normality (for Pearson) | Both variables should be approximately normally distributed. This is a technical assumption for inference (p-values, confidence intervals) but is not strictly required for the calculation of the Pearson $r$ itself. It is not required for Spearman correlation, which is rank-based. |
| Type of Data | Pearson requires continuous (interval or ratio) data. Spearman requires at least ordinal data, making it more flexible. |
Regression predicts one variable based on another and therefore comes with several assumptions.
| Linear Relationship | The relationship between the independent variable(s) and the dependent variable must be linear. |
| Independence of Errors | Residuals (errors) must be independent of one another. The Durbin–Watson test is often used to check this assumption. |
| Normal Distribution of Errors | Residuals should follow a normal distribution. This is important for calculating valid confidence intervals and $p$-values. |
| No Multicollinearity | Independent variables should not be too highly correlated with each other. High multicollinearity can make coefficient estimates unstable. |
| Homoscedasticity | The variance of residuals should remain constant across all levels of the predictor variable(s). Unequal spread (heteroscedasticity) results in biased standard errors. |
Below are simple and beginner-friendly ways to verify each assumption using commonly available tools like SPSS, R, Python, Excel, or JASP.
Normality means your data follows a bell-shaped curve. Here are easy ways to check it:
This test evaluates whether your data significantly deviates from a normal distribution.
A general test for normality, especially for larger datasets.
A visual method where points falling along the diagonal line indicate normality.
This assumption checks whether groups have similar variability.
The most widely used test for equal variances.
A classical test for homogeneity of variance.
Independence is mostly about research design rather than calculations.
Ask yourself:
If yes, independence may be violated.
Used to check whether regression residuals are independent.
Linearity ensures the relationship between variables is straight-line shaped.
Plot the two variables against each other.
Plot residuals against predicted values.
Ignoring assumptions can lead to serious statistical problems. Even small violations can distort results and lead to incorrect conclusions.
Coefficient estimates, means, or effect sizes may no longer reflect reality accurately.
P-values may become too large or too small, causing researchers to accept or reject hypotheses incorrectly.
Hypothesis tests lose their trustworthiness, making your findings questionable or invalid.
If your data does not meet the assumptions, there are practical methods to correct or work around the problem.
Transformations can help normalise data, reduce skewness, or stabilise variances.
If assumptions are severely violated, switch to tests that do not assume normality. Example alternatives include:
A resampling technique that generates thousands of simulated samples.
Modern statistics offer tests that are less sensitive to assumption violations, such as:
Larger samples reduce the impact of non-normality and provide more stable estimates.
Assumptions in hypothesis testing are the conditions that must be true for a statistical test to produce valid results. These include normality, independence, equal variances, and linearity. When these assumptions hold, your p-values and conclusions are accurate and reliable.
Assumptions prevent biased results, incorrect p-values, and misleading conclusions. Without meeting these conditions, statistical tests may produce false findings, making your research unreliable or invalid.
You can check normality using the Shapiro-Wilk test, Kolmogorov-Smirnov test, histograms, or Q-Q plots. If p > .05 or data points align with the diagonal line in a Q-Q plot, normality is likely satisfied.
When groups do not have equal variances, results from t-tests or ANOVA may be inaccurate. You can use alternatives such as Welch’s t-test or Welch’s ANOVA, which do not require equal variances.
Independence comes primarily from proper research design. For regression models, use the Durbin-Watson test to check whether residuals are independent. Values close to 2 indicate independence.
You can use data transformations (log, square root, Box-Cox), non-parametric tests (Mann-Whitney, Kruskal-Wallis), bootstrapping, or robust methods like Welch’s tests. These approaches help produce accurate results even when assumptions are not met.
No. Only parametric tests like t-tests, ANOVA, correlation (Pearson), and regression require normality. Non-parametric tests such as Mann-Whitney, Wilcoxon, and Spearman do not require a normal distribution.
Use power analysis (commonly power = 0.80, alpha = 0.05) to determine whether your sample size is large enough. Tools like G*Power, SPSS, or R make this process simple.
You can, but your results may be misleading. Ignoring assumptions often leads to incorrect p-values, biased estimates, and invalid conclusions. Always check assumptions before running tests.
ANOVA, Pearson correlation, and regression are highly sensitive to violations like non-normality, heteroscedasticity, and non-linearity. t-tests are moderately robust but still require caution with small samples.
You May Also Like
All work is written by human writers. 100% AI free, guaranteed.
100% money back guarantee if you find plagiarism in our work.
SERVICES
COMPANY DETAILS
+44 (0) 141 628 7445
+44 7388 619137
The money-back guarantee functions in accordance with our refund guidelines.
