The goal of this platform is to automate the statistical processes for studying the differences between multiple groups. Before explaining the tests performed, we will review the basic concepts needed to interpret these tests.
Initially, the selected tests are:
ANOVA is a parametric test used to determine if there is a significant difference between two or more groups for a given measurement. Group formation is done using categorical variables. The null hypothesis (H0) for this test is the equality of all groups (no significant difference), while the alternative hypothesis (H1) is that at least one group differs from the others. If the p-value is below our significance level, we reject the null hypothesis, and we can perform a Tukey test (Emmeans) to estimate the means of each group and determine which ones are different.
In a study measuring PIE, the dependent variable would be PIE, and the explanatory variables could be the product and time (0H, 6H, etc.).
The Tukey test is used after rejecting the null hypothesis in an ANOVA. It helps determine which groups differ from each other.
Mixed models combine ANOVA and the Tukey test, allowing us to detect if there are differences between multiple groups within a population and measure those differences if they exist. Unlike ANOVA, it relies on two types of effects:
We assume that fixed effects react similarly across all individuals, while variations are captured by random effects.
In a study measuring PIE, the dependent variable would be PIE. The fixed effects could be the product and time (0H, 6H, etc.), and the panelist would be a random effect. In a test studying the cellular response to different products, the dependent variable could be collagen production, the product concentration could be a fixed effect, and the cell line could be a random effect.
The Kaplan-Meier method is used to estimate survival probabilities over time. It allows for visualizing survival data and helps determine if different groups (e.g., treatment vs. control) exhibit different survival patterns over time.
This method is widely applied in clinical studies where the outcome of interest is time to event (such as time to death, disease recurrence, or other outcomes). The Kaplan-Meier curve provides an intuitive representation of survival data and can be compared across different groups.
In a study measuring the longevity of lipstick wear, the event could be defined as the point when the lipstick wears off. Different curves can represent different lipstick products, allowing for comparison.
The Cox regression model, also known as the proportional hazards model, is used to assess the effect of multiple variables on survival time. Unlike Kaplan-Meier, which focuses on one group or treatment at a time, Cox regression allows for the inclusion of covariates and the examination of their influence on survival while adjusting for other factors.
This model assumes proportional hazards, meaning the effect of the covariates on the hazard (risk of event occurrence) is constant over time.
In a study on the long-lasting effect of lipstick, factors such as product type, application technique, and environmental conditions could be included in the model to assess their effect on how long the lipstick stays on.
The Log Rank test is used to compare the survival distributions of two or more groups. It is a non-parametric test and can be used alongside Kaplan-Meier curves to determine whether there is a statistically significant difference between the survival curves of different groups.
The null hypothesis for the Log Rank test is that the survival curves are equal across the groups being compared.
In a comparison of different lipstick brands, the Log Rank test could be used to determine if there is a significant difference in the longevity of wear across the different brands.
The Chi-square test is a non-parametric test used to determine if there is a significant association between categorical variables. It compares observed and expected frequencies of events to assess whether distributions differ significantly across groups.
In a study assessing customer preferences for different lipstick colors, the Chi-square test could determine if preferences vary significantly by age group.
The Student’s t-test is a parametric test used to compare the means of two groups to see if they differ significantly. It assumes normally distributed data with equal variances across groups.
In a cosmetic study comparing the average time it takes for different foundations to wear off, a t-test could assess if the mean wear times differ significantly between two specific products.
The Shapiro-Wilk test is a normality test used to assess whether a sample is drawn from a normally distributed population. It is commonly used as a prerequisite check before applying parametric tests.
In a study on foundation wear time, the Shapiro-Wilk test could confirm if wear time data follows a normal distribution, thus validating the use of parametric tests.
Pearson correlation measures the strength and direction of the linear relationship between two continuous variables. It assumes both variables are normally distributed.
In a study of customer satisfaction and repurchase rate for a skincare product, Pearson correlation could reveal if higher satisfaction is associated with increased repurchase rates.
PCA is a technique used to reduce the dimensionality of large datasets while retaining as much variability as possible. By transforming variables into a new set of uncorrelated components, PCA helps identify the main features driving data variation.
In a study with many product characteristics (color, durability, texture), PCA could reduce the dimensions to a few principal components that summarize the main variation in product properties.
MCA is similar to PCA but is designed for categorical data. It allows for the exploration of relationships between multiple categorical variables by reducing data dimensionality and creating easily interpretable visualizations.
In a survey study, MCA could reveal relationships between customer demographics (age, gender) and preferences for specific product features.
t-SNE is a non-linear dimensionality reduction technique used for visualizing high-dimensional data in two or three dimensions. It excels at preserving local structures in the data, making it suitable for identifying clusters and patterns.
In a dataset containing customer reviews of multiple products, t-SNE could help visualize groups of similar reviews, revealing patterns in customer feedback.
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