What are the best ways to check statistical test assumptions?

When comparing performance between two or more groups given any type of metric, the numbers will never identically resemble each other between the groups that you are studying. We NEED to check assumptions because you never know if there difference in behavior you are seeing between these groups is due to random chance or if there is an actual trend that can be extracted here to give us insights on how a certain initiative will behave in the future with different data points. Equally as important is to ensure proper testing methodology.

The importance of checking statistical assumptions cannot be overstated, it sets the stage for trustworthy analytics. If your data is skewing away from normality or violating any other assumptions, your analytics tool, no matter how sophisticated, is going to generate misleading results. I remember a project where we used machine learning models to optimize marketing campaigns. The statistical assumptions weren't thoroughly checked in the initial runs, and the model recommended over-investing in channels that were actually underperforming. It was an expensive lesson that reinforced the need for rigorous assumption checks before deploying any model into production.

It’s important look for anomalies and subtleties during data visualisation. The validity and reliability of data assumption should be tested if it’s non linear to avoid false positive .

Checking the assumptions of a statistical test is essential because these tests rely on mathematical models that assume specific properties of the data, like normality, independence, homogeneity, or linearity. Failing to meet these assumptions can lead to inaccurate or unreliable results. For instance, using a t-test to compare group means with non-normally distributed or heteroscedastic data can yield erroneous outcomes. Thus, validating assumptions is a critical step to uphold the accuracy and dependability of your analysis.

The specific assumptions vary depending on the type of statistical test you are conducting, but here are some common ways to check these assumptions: -There is a linear relationship between X and Y -Error terms are normally distributed with mean zero(not X, Y) -Error terms are independent of each other Error terms have constant variance (homoscedasticity) -Outlier Detection

Sometimes it's hard to test your assumptions if the distribution of the dataset doesn't follow the common distributions. You can also check the data using historical data collected in your company and use it as a baseline. In my experience, data can look different than text book examples and it's also important to ask the business team to help interpret the data to see whether it makes sense from a product or marketing perspective.

Data visualization is indeed a brilliant tool for checking assumptions. Evaluating the robustness of data pipelines routinely has been a crucial part of my responsibilities. We integrate visual checks right into our data dashboards. For example, we used scatterplots to visually check the linearity assumption between marketing spend and revenue generated. It's not just about looking at the numbers; it's about seeing the numbers. When you see a scatterplot diverging from a straight line, it’s a red flag that can be immediately investigated.

Following are the data assumptions and tests commonly found in statistical research: ? Assumptions of normality: Most of the parametric tests require that the assumption of normality be met. - Skewness and Kurtosis - Shapiro-Wilk’s W test - Kolmogorov-Smirnov test - Q-Q plot(Graphical method) ? Assumptions of homogeneity of variance - Levene’s test ? Homogeneity of variance-covariance matrices assumption - Box’s M test ? Randomness: Most of the statistics assume that the sample observations are random. Run Test is used to test the assumption of randomness. ? Multicollinearity: VIF and Condition indices can be used, especially in regression analyses. A value of VIF >10 indicates multicollinearity is present and the assumption is violated.

To assess statistical test assumptions effectively, utilize data visualization techniques. Data visualization involves creating graphical data representations to reveal patterns and insights. It offers an intuitive way to inspect data for adherence to test assumptions. For example, employ histograms, boxplots, or density plots to assess normality, scatterplots or residual plots to evaluate linearity and independence, and Q-Q plots or Shapiro-Wilk tests to check normality and homogeneity. These visual tools assist in spotting outliers, skewness, heteroscedasticity, or non-linearity within your data. Consequently, you can make informed decisions about whether data transformation, removal, or adjustments are necessary before test conduction.

Excel and SPSS are great, but as someone who works intensively with data, I can vouch for the adaptability and extensiveness of Python libraries like cufflinks (plotly), matplotlib and seaborn. For a project involving real-time data analytics, we employed Python due to its compatibility with real-time data streams and extensive libraries. We used cufflinks for visually appealing and informative plots, ensuring not only that our assumptions were being met but also that we could instantly communicate these to stakeholders in an intuitive manner.

While the initial premise of this question is correct, a significant part of this question's answer depends on the sanctioned tech stack used by your organization and stakeholders. I like to use R for any statistics-heavy task because of its sheer number of specialized packages. Subjectively speaking, I've found ggplot2 a tad easier and more intuitive than Matplotlib, and with Shiny integrations, the sky is the limit. Also, remember that Excel is a very dynamic tool, and Excel Data Analysis Toolpak is dynamic enough to help you in most cases. Last but not least, Excel is excellent for some initial EDA. P.S. However, Be careful with Excel if your row count> 1M rows.

The choice between Python, R, and Excel depends on the specific needs, and complexity of the analysis. I prefer Python and R most of the time, as they have a wide range of libraries and can handle both small and large data. However, for those who are new to Python and R, they may experience a steeper learning curve. On the other hand, Microsoft Excel is user-friendly and suitable for small datasets. However, its statistical functions and tools are limited compared to programming languages.

Tool selection is critical for validating statistical assumptions through visualization. Options like Excel, SPSS, R, and Python offer unique strengths. Excel employs Data Analysis Toolpak or Analysis ToolPak - VBA for various plots. SPSS provides similar capabilities. R offers versatility with base graphics and ggplot2. Python has libraries like matplotlib, seaborn, and plotly. Your choice depends on project needs, software familiarity, and data complexity. Effective data visualization is essential for insightful, assumption-validating analyses.

To perform data visualizations checks for statistical test assumptions, you'll require software or a programming language capable of handling data analysis and visualization. Popular choices include Excel, SPSS, R, and Python. Each tool offers its own strengths and drawbacks but comes equipped with functions or libraries for generating diverse plots and charts to assess these assumptions. For instance, in Excel, you can utilize the Data Analysis Toolpak or Analysis ToolPak - VBA for histograms, boxplots, scatterplots, or Q-Q plots. SPSS offers the Explore or Graphs menus for similar plots. R provides options like base graphics and ggplot2 package, while Python offers libraries such as matplotlib, seaborn, and plotly for data visualizations.

In your visualizations, the devil is in the details. For instance, you might have a bell-shaped curve in a histogram, but the tails could be heavier, indicating potential outliers that can skew results. While working on customer segmentation, we scrutinized Q-Q plots for each segment. A slight deviation at the tails forced us to reconsider our initial segmentation criteria. Always look for subtleties that could be pivotal in your analysis.

I would like to share my experience with correlation analysis. It's important to note that, unlike some parametric tests, correlation analysis does not assume that the data follow a normal distribution. Instead, one of the key assumptions is the presence of a linear relationship between the variables being correlated. To assess this assumption, one should construct a scatterplot to examine the connection between variables. But remain vigilant for any potential outliers within the data, which require careful consideration. Subsequently, confirm that the scatterplot demonstrates a linear relationship between the variables. If this linear assumption is not met, it may be worthwhile to explore alternative approaches, such as nonlinear models.

When using data visualizations to assess statistical test assumptions, understand what to observe and how to interpret them. The specific features or patterns to look for can vary depending on the assumption and test type. For instance, when examining the normality assumption, seek a bell-shaped curve, symmetric distribution, or similar quantiles in histograms, boxplots, density plots, or Q-Q plots. To evaluate independence, aim for randomly or evenly dispersed points in scatterplots or residual plots. To assess homogeneity, watch for consistent variances, shapes, or ranges in boxplots, Q-Q plots, or through Levene's test. For the linearity assumption, scrutinize scatterplots or residual plots for a linear relationship or a straight line.

Once you’ve validated or invalidated your assumptions, the next steps are critical. I once worked on a project where the data violated normality and homogeneity assumptions. Instead of scrapping the model, we used a Box-Cox transformation to stabilize variances and used bootstrapping techniques for normalizing. This adaptability allowed us to still gain valuable insights without starting from scratch.

If an outlier is identified, investigate why these outliers exist, whether they are a result of data entry errors or genuine values. If the outliers are due to data entry errors or measurement errors, consider removing them from the dataset. But if they're representing genuine data points, data transformation may be a suitable approach. Alternatively, conducting sensitivity analyses by comparing results with and without outliers can provide insights into how outliers impact your findings. If you believe that outliers contain meaningful information, document them and clearly outline the steps you've taken to address them. Transparency in handling outliers is vital for the integrity and reproducibility of your research.

After creating data visualizations to assess statistical test assumptions, you'll either confirm their satisfaction or identification of violations. If met, proceed with the test confidently. For violations, consider actions like data transformation to improve normality, homogeneity, or linearity, handling outliers, opting for a different test that doesn't demand the same assumptions, or choosing a non-parametric test that doesn't rely on distributional assumptions. Your decision hinges on the extent of the violation, data nature, research goals, and hypothesis. Data visualization serves as a powerful tool for assumption checks, aiding in error prevention and result validity, ensuring your analysis's reliability.

One contributor correctly pointed out how messy real-world data can be. So, many of your presupposed notions of the nature of the data gained from visualization may need to be adjusted. Case in point, Time-series data has a few standard plots concerning stationarity, seasonality, and its inherent, additive or multiplicative, nature. However, hierarchical time-series datasets may only sometimes stick to such desired observations. Hence, these are the times when statistical tests like ADF are helpful and serve as the requisite verification tool.

Consider using non-parametric tests when the data significantly deviates from parametric assumptions, as they make fewer distributional assumptions. Additionally, if you have a relatively large sample size, you may also explore the use of machine learning models. In this case, perform cross-validation to assess the model's generalization performance and check for overfitting.