Posts

Zero Residual Sum of Square in ANOVA

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 Summary: This blog explains case when the residual sum of square is zero for two way ANOVA (RBD Design in terms of DoE). A sample data set is shared for detailed explanation. The goal is to share the observation.  Reading time 5 mins Introduction In the field of Design of Experiments (DoE) , the Randomized Block Design (RBD) is a commonly used layout where treatments are tested across blocks or replications. Typically, the ANOVA table in RBD presents some residual (error) variation that captures the unexplained variance. However, there are rare instances when the residual sum of squares (SS) turns out to be zero . In this blog, we demonstrate one such case using a small dataset and provide insights into why this occurs , backed by observations. Data set used in demonstration: The data is of 6 treatments T1, T2, T3, T4, T5 and T6 with three replications R1, R2 and R3. When we perform two way ANOVA the results is shown below: As we can observe that difference between R1...

Bernoulli and Binomial Distribution Quiz

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Probability Quiz (Bay's Theorem)

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Understanding the p-Value: A Guide for Statisticians

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  Summary: This blog explains the role of p-values in statistical analysis, highlighting their significance in testing hypotheses and understanding evidence against the null hypothesis. It also emphasizes the need to consider sample size and effect size when interpreting p-values, cautioning against arbitrary significance thresholds. Reading Time: Approximately 7–10 minutes. When we test something in science, we start with a basic assumption called the null hypothesis (H₀) —it usually says "nothing is happening" or "there's no effect." Then, we collect data and calculate a number (called a test statistic ) to see how unusual our data is compared to what we'd expect if the null hypothesis were true. The p-value tells us the chance of getting a result as surprising (or even more surprising) than what we observed, assuming the null hypothesis is true. A small p-value (like less than 0.05) means our result is really surprising, so we might reject the null hyp...

Understanding Bartlett's Test: Assessing Homogeneity of Variances in Combined Experiment Analysis

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Summary: This blog delves into the importance of Bartlett's test for validating homogeneity of error variances in pooled/combined experiments. It explains the test's significance, provides step-by-step calculations, and highlights its application in agricultural research. Practical examples and code snippets for various software are included for comprehensive understanding. Estimated Reading Time: ~12 minutes.   Introduction In experimental research, especially in fields like agriculture, researchers often conduct experiments under varying conditions such as different times, locations, or environments. To draw more comprehensive and robust conclusions, combining or pooling the data from these experiments into a single analysis is a common practice. Pooled analysis offers several benefits: Increased Statistical Power : Pooling data increases the total sample size ( n n ) and the degrees of freedom for error, thereby reducing the Mean Square Error (MSE). This leads to a smalle...

F test: Theory, Solved Example and Demonstration in Agri Analyze

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 The blog discuss in details about theory of F test, its use cases, solved example (manually) and a demonstration using online tool Agri Analyze (Reading time 10 min)  Introduction The F-test is a statistical method used to compare the variances of two samples or the ratio of variances across multiple samples. It assesses whether the data follow an F-distribution under the null hypothesis, assuming standard conditions for the error term (ε). The test statistic, denoted as F, is commonly used to compare fitted models to determine which best represents the underlying population. F-tests are frequently employed in models fitted using least squares. The test is named after Ronald Fisher, who introduced the concept as the "variance ratio" in the 1920s, with George W. Snedecor later naming the test in Fisher’s honor. Definition An F-test uses the F-statistic to evaluate whether the variances of two samples (or populations) are equal. The test assumes that the population follows an ...