Statistics is an essential tool for making sense of and drawing meaningful conclusions from raw data. For beginners, however, there can be a lot of challenges and common mistakes when it comes to using statistics. Missteps can not only compromise the integrity of statistical analysis but also lead to incorrect conclusions being drawn from the data that can have negative repercussions when those conclusions are applied. Whether you are a student, new data analyst, or a professional refining your skills, understanding these seven common statistics mistakes beginners make can enhance the quality of your work and your confidence in your interpretations.

## 1. Misunderstanding Descriptive Versus Inferential Statistics

Broadly, there are two types of statistics techniques and being able to identify the difference between them is key to correct interpretation of statistical results. Descriptive statistics is used to summarize the features of a dataset. This includes providing information like the measures of central tendency (including mean, median, and mode) and the measures of variability (including range and standard deviation). Data visualizations largely fall under this type as well.

Inferential statistics, on the other hand, goes beyond description and attempts to make generalizations about the larger population using sample data. This type of statistics includes hypothesis testing, regression analysis, and more complex methods.

One mistake that could arise from misunderstanding the distinction between the two is trying to apply descriptive results in an inferential context. For example, assuming that the mean of a sample represents the mean of the population would not be a correct application of statistical methods.

## 2. Ignoring the Assumptions of Statistical Tests

Statistical tests are an inferential tool used to test hypotheses using the data. These tests include t-tests for comparing means between two groups, ANOVAs for comparing means across more than two groups, correlations, and more. Each statistical test comes with a set of assumptions that must be met for the results of the test to be valid. Ignoring these assumptions is a common mistake among beginners and can lead to incorrect and unreliable results.

While each test has its own list of assumptions, some common ones include using normally distributed data, having observations that are all independent of each other, and having equal variance among groups being compared. If one or more assumptions of a test are not met, alternative methods such as data transformation or using a non-parametric test should be considered.

## 3. Misinterpreting Correlation and Causation

One of the most common and misleading mistakes in statistical analysis is confusing correlation with causation. Correlation measures the strength and direction of a linear relationship between two variables. A correlation coefficient ranges from -1 to 1 with -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation.

However, correlation, even a perfect one, does not imply that the change in one variable causes the change observed in the other. Establishing causation requires more rigorous analysis or experimental designs that can account for confounding factors. These methods can also ensure that the observed effect is not due to some other variable that wasn’t included in the original analysis.

## 4. Using an Inadequate Sample Size

An important element when interpreting statistical results is the sample size of the data. A sufficiently large sample size ensures that the descriptive statistics and estimates of population parameters are accurate. Inferential statistics run with a large enough sample size also have greater power, defined as the probability that a test will correctly reject a false null hypothesis.

If the sample size of an analysis is too small, there could be too little power to properly detect an effect. There is also likely to be increased variability in the data, creating unstable and unreliable estimates of population parameters. Additionally, a sample size that is too small compared to the population size cannot accurately represent the larger population, leading to results that are not generalizable.

What counts as an adequate sample size will differ based on the hypothesis being tested and the types of analysis being conducted. There are specific formulas available for each statistical test that take into account variables like desired power, number of groups being compared, and average mean to calculate the minimum necessary sample size for a given analysis.

## 5. Neglecting Data Quality

Poor quality data can quickly undermine the reliability and validity of statistical analysis by introducing errors, biases, and inconsistencies. Ensuring high data quality involves careful collection, processing, and management of data to maintain its integrity throughout the analysis.

There are a lot of data quality issues that can be checked before working with a dataset. Missing data is a very common one. Incomplete datasets can reduce statistical power, and also lead to biased estimates if the reason why data is missing for some observations is meaningful. Other sources of poor data quality are erroneous data, variables being recorded using a mixture of units, irrelevant data, duplicate entries, and outdated data.

## 6. Forgetting Data Visualizations

Statistics is primarily a numbers driven field, driven by values like means, standard deviations, p-values, and confidence intervals. However, it is important not to neglect data visualizations as they can be powerful tools for understanding, interpreting, and communicating data.

Graphical representations make it easier to spot trends, correlations, and outliers that may not be immediately apparent in data tables or summary statistics. This makes visualizations particularly helpful in the data cleaning and analysis planning phases as they help build a stronger understanding of what the data looks like and its key characteristics.

Part of data visualizations is also ensuring the right visualization choices are made. Choosing the wrong type of chart to represent data, such as using a scatterplot on non-numeric data or a line chart for categorical data, can mislead the audience and obscure what the data truly represents.

## 7. Overgeneralizing Results

Overgeneralization is a very common beginner statistics mistakes where conclusions drawn from a specific study or dataset are inappropriately extended to broader contexts or populations. This can lead to misleading interpretations and flawed decision-making. Overgeneralization can happen in many ways, such as assuming results from a small sample apply to a larger population or extending conclusions from a controlled experiment into real world situations.

Another common mistake in this category is extrapolating beyond the data range, particularly in regression analysis interpretation. If the data used to build a regression model encompassed a certain range, such as adults between the age of 18 and 25, the model coefficients cannot be accurately used to make predictions outside of that range, such as for a 35-year-old.

## Conclusion

Understanding and avoiding these common beginner statistical mistakes is crucial for producing accurate, reliable, and meaningful analyses. Applying best practices in statistical analysis strengths the validity of your findings and also creates a deeper understanding of the data, ultimately leading to better informed decisions and impactful results.