Outliers: Extreme values, known as outliers, can distort the shape of the distribution. Outliers can stretch the tails of the distribution, making it positively or negatively skewed. In some cases, they can lead to heavy-tailed distributions (leptokurtic).
Sample Size: Small sample sizes are more likely to produce distributions that diverge from normality due to sampling error. Larger sample sizes tend to provide more reliable estimates that resemble the normal distribution due to the Central Limit Theorem.
Measurement Errors: If the data collection process includes errors (e.g., faulty instruments or biases in measurement), it can cause the data to diverge from normality. These errors might introduce skewness, kurtosis, or other distortions in the distribution.
Non-homogeneity: If the population from which the sample is drawn is heterogeneous (diverse or varied), it may lead to a bimodal or multimodal distribution. Different subgroups in the data can have different distributions, leading to divergence from normality.
Time and Contextual Factors: In longitudinal studies or research involving real-world phenomena, changes over time (e.g., seasonality in sales data, cyclical economic factors) can cause the data to deviate from normality.
The Nature of the Data: Certain types of data, such as categorical data or count data, inherently cannot follow a normal distribution. For example, data on the number of occurrences of an event often follows a Poisson distribution, not a normal one.
