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Category: Statistics

What is logistic regression (feat. odds, odds ratio and model equation)?

What is logistic regression (feat. odds, odds ratio and model equation)?

Logistic regression is a type of statistical analysis used to model the relationship between a binary (yes/no) dependent variable and independent variables. The goal of logistic regression is to find a relationship between the independent variables (x) and the probability of a particular outcome for the dependent variable (y). The logistic regression model calculates the probability of a certain outcome by applying a logistic function to the linear combination of the independent variables. Here is one example. Sulphur improves plant…

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What is split-split-plot design in agronomy research (feat. using R and SAS)?

What is split-split-plot design in agronomy research (feat. using R and SAS)?

In my previous post, I explained what split-plot design and the statistical model is, and also how it is different RCBD. What is split-plot design in agronomy research? I explained the main difference between split-plot design and RCBD is that in split-plot design, error is divided into two (error a and b), increasing the significance of interaction between the main plot and sub-plot. Now our interest lies in cases where we have three factors. In a split-plot design, we typically…

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An Introduction to Residual Analysis in Simple Linear Regression Models

An Introduction to Residual Analysis in Simple Linear Regression Models

Sample No. x y 1 10 30 2 20 40 3 30 50 4 40 80 5 50 90 6 60 100 7 70 120 Here is a dataset that allows us to analyze the relationship between x and y and obtain the model equation, y= β0 + β1x. Although statistical programs can provide us with results in just 10 seconds, it is more important to understand the principles behind the calculations than to simply know how to run the…

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What is odds, log odds and logit (feat. Slam Dunk story)?

What is odds, log odds and logit (feat. Slam Dunk story)?

Odds and logit is the basic concept to understand logistic regression. Today I’ll explain what it is as much as easily. Do you know a comic book, ‘Slam Dunk’? I’ll explain odds with this story. 1) Odds Now, Shohoku high school is playing games with other high schools in the tournament. In the first round, Shohoku high school won 4 games and lost 6 games out of 10 games. Now the winning odds of Shohoku high school is 4/6 ≈…

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How to analyze linear plateau model in R Studio?

How to analyze linear plateau model in R Studio?

When we talk about regression, it’s usually about simple linear regression model. This is about the relationship between two variables. FYI□ Simple linear regression (1/5)- correlation and covariance□ Simple linear regression (2/5)- slope and intercept of linear regression model Linear plateau model is similar with simple linear model, but linear plateau model is a segmented model, and this statistical model is interested in the critical value (the x-value above which there is no further increase in y), indicating the plateau value (the statistically highest value…

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Simple linear regression (4/5)- t value on the slope and intercept    

Simple linear regression (4/5)- t value on the slope and intercept    

Simple Linear Regression Series 1) Simple linear regression (1/5)- correlation and covariance 2) Simple linear regression (2/5)- slope and intercept of linear regression model 3) Simple linear regression (3/5)- standard error of slope and intercept 4) Simple linear regression (4/5)- t value on the slope and intercept 5) Simple linear regression (5/5)- Coefficient of determination In my previous post, I explained how to calculate standard error of slope and intercept in simple linear regression model. Now, I’ll explain how to calculate t…

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Simple linear regression (3/5)- standard error of slope and intercept

Simple linear regression (3/5)- standard error of slope and intercept

Previous post!!□ Simple linear regression (1/5)- correlation and covariance□ Simple linear regression (2/5)- slope and intercept of linear regression model In my previous post, I explained how to calculate slope (β1) and intercept (β0) of linear regression model. If you well followed my previous posts, you will get the above result, y= 89.0 + 1.5x  Now our interest is how to calculate standard error in the intercept and slope (Red box). Here is the equation to obtain standard error of…

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Simple linear regression (2/5)- slope and intercept of linear regression model

Simple linear regression (2/5)- slope and intercept of linear regression model

□ Simple linear regression (1/5)- correlation and covariance In my previous post, I explained about correlation and covariance. Now, I’ll explain about slope (β1) and intercept (β0) of linear regression model. In the whole picture to explain a linear regression model, β1 is calculated as β1 = r * Sy / Sx We already know how to calculate correlation (r), and only we need to calculate the ratio between standard deviation of x and y. Let’s go back to the…

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Simple linear regression (1/5)- correlation and covariance

Simple linear regression (1/5)- correlation and covariance

Since today, I’ll explain simple linear regression model. There are lots of information about linear regression on websites, but I believe I’ll tell you about what most people don’t mention. My philosophy on data analysis and statistics is to fully understand the concept, not simply follow what software programs say. Therefore I usually calculate statistical concepts by hand, and only my hand calculation is exactly same as the software programs provide, I say I understand the concept. In this context,…

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What is Probability Density Function (PDF) and Cumulative Distribution Function (CDF): How to calculate using Excel and R ?

What is Probability Density Function (PDF) and Cumulative Distribution Function (CDF): How to calculate using Excel and R ?

When we analyze data, we may need to show graphs depicting normal distributions. These graphs differ from density graphs as they convey various concepts that simple bar graphs cannot. While it is easy to draw these graphs in Excel, understanding the underlying concepts is crucial. In this article, I will explain what the Probability Density Function (PDF) is, and I will show how we can calculate it in both Excel and R. Here is a dataset of 1,000 individual wheat…

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R-Squared in ANOVA: A Practical Approach to Calculation and Interpretation

R-Squared in ANOVA: A Practical Approach to Calculation and Interpretation

Every time we discuss R2, we typically associate it with regression models. However, R2 also has a significant role in ANOVA. There seems to be less information available on how to calculate and interpret R2 in ANOVA, so today’s topic will focus on how to interpret this measure in the context of ANOVA. Let’s consider an example dataset. Suppose we measured the final yield at varying nitrogen levels. We established three replicates as a block. Consequently, this model will be…

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What is Wilcoxon Rank-Sum Test?

What is Wilcoxon Rank-Sum Test?

The reason why we use t-test, not z-test is because we don’t know the variance (σ2) of the population. The sample mean (x̅) is an unbiased estimator for the population mean (μ), and therefore we can estimate μ from x̅ (E(x̅) = μ). How about variance? If we know σ2, sample variance could be estimated by dividing σ2 by sample size (n); σ2x̄ = σ2/n. However, if we don’t know σ2, we should use standard deviation (s) of samples; s2x̄ = s2/n…

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What is Finlay-Wilkinson Regression Model?

What is Finlay-Wilkinson Regression Model?

The genotype is dependent on environmental changes. One genotype may strongly respond to certain environmental conditions, while another genotype may weakly respond to the same conditions. If some genotypes strongly respond under better conditions, they would be adaptable to the environment. Adaptability refers to the flexibility of a genotype in its response to improved environments. If a certain genotype exhibits high performance across a wide range of environmental conditions, it would be considered to have broad adaptation. To achieve this…

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What is a nested model in statistics?

What is a nested model in statistics?

One tomato farmer is growing tomato seedlings, and all of sudden he wants to investigate the amount of calcium in leaves. So, he selected four tomato seedlings, and he randomly chose three leaves in each seedling and investigated the amount of calcium. He measured twice in each leaf. This experimental design would be explained by below table. y111 means the amount of calcium in the 1st seedling – 1st leaf – 1st replicate. Then, y432 will mean the outcome of…

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In agronomy research, how to estimate a missing value in collected field data?

In agronomy research, how to estimate a missing value in collected field data?

Here is an example of missing data. There are four different cultivars and I would like to determine if there is a difference in yield among them. I have five replicates as blocks, so the experimental design is a Randomized Complete Block Design (RCBD), and we can analyze the data using one-way ANOVA with blocks. You can download the data using R by copying and pasting the code below into your R script. After running the code, an Excel file…

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How to calculate pooled variance when including block in the experimental design?

How to calculate pooled variance when including block in the experimental design?

New equation I suggest!! You might be already familiar with how to calculate pooled variance. This story is about pooled variance when blocks exist. If you run statistics programs, you’ll simply obtain pooled variance (also known as MSE), but you’ll never understand the concept of pooled variance if you just run software programs. Here is an example data. Let’s say this is a yield data. Cultivar A Cultivar B 120 70 130 90 110 50 Mean: 120Variance (s2): 100 Mean:…

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How to calculate the optimum sample size for 2-Sample t test (using R and G*Power program)?

How to calculate the optimum sample size for 2-Sample t test (using R and G*Power program)?

When we set up our experimental design, it is not easy to decide the sample size because we don’t know exactly how many samples are required for our experiments. Of course the more, the better. However, eventually, we need to decide appropriate sample size according to our time and resources. For example, if we want to know the average height of students in University of Guelph, the best way is to measure all students’ height. According to Wikipedia, total number…

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What is ANCOVA (2/3)? How to interpret Parameter Estimates

What is ANCOVA (2/3)? How to interpret Parameter Estimates

Previous post□ What is ANCOVA (1/3)? The basic concept In previous post, I explained how to interpret ANCOVA table (red box in below tables). In this post, I’ll explain how to interpret Parameter Estimates (blue box in below table) in ANCOVA analysis. Let’s check the ‘Parameter Estimates’ table. Most statistical programs set up one level of an experimental factor as “zero” and estimate the results based on that level. This concept is known as the Generalized Linear Model (GLM). If you…

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What is ANCOVA (1/3)? The basic concept

What is ANCOVA (1/3)? The basic concept

Today, I will explain Analysis of Covariance (ANCOVA). ANCOVA is a statistical technique that involves including covariates, which are additional variables that may impact the dependent variable (y) in addition to the independent variable (x). I have a dataset as shown below, and I would like to analyze crop yield based on different fertilizer types (Control, Slow-release, and Fast-release). The experimental design is a Completely Randomized Design (CRD) with 10 replicates. Rep Fertilizer Yield Fertilizer Yield Fertilizer Yield 1 Control…

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What is ANCOVA (3/3)? The common slope and adjusted mean

What is ANCOVA (3/3)? The common slope and adjusted mean

Previous post□ What is ANCOVA (1/3)? The basic concept□ What is ANCOVA (2/3)? How to interpret Parameter Estimates In the previous posts, I explained the basic concept of ANCOVA and how to interpret statistical results. Now, I will discuss the most important concept that is not commonly mentioned. The statistical program provided the following model in the previous posts. Control: y= 9.53 + 0.0558 xFast: y= 6.39 + 0.0558 xSlow: y= 13.10 + 0.0558 x Then, if we apply the mean…

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[데이터 칼럼] 회귀모델의 절편을 0 으로 조정 했을때 결정계수는 어떻게 변할까?

[데이터 칼럼] 회귀모델의 절편을 0 으로 조정 했을때 결정계수는 어떻게 변할까?

과거에 저는 밀 종자의 면적을 구하기 위해 밀 종자를 이미지 스캔하고, 그 다음에는 각 밀 종자의 면적에 해당하는 무게를 측정하였습니다. 다음 회귀 분석은 밀 종자의 면적과 무게 간의 관계를 보여줍니다. # Data download https://www.kaggle.com/datasets/agronomy4future/wheat-grain-area-vs-weight 위 데이터를 제 Github 에서 R 로 업로드 하겠습니다. 그리고 통계 분석을 해 보겠습니다. 회귀모형 y= 3.3333x – 13.7155 을 Excel 과 R을 사용하여 얻었습니다. 여기서 y 는 밀 종자 무게(mg) 이고, x 는 밀 종자 면적(mm2) 입니다. 그러나 이 모델에서, x 값이 작아지는 어느 시점부터…

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단순선형 회귀분석에서 결정계수 (R², Coefficient of Determination) 를 가장 쉽게 설명해 보자

단순선형 회귀분석에서 결정계수 (R², Coefficient of Determination) 를 가장 쉽게 설명해 보자

여기 x 와 y 에 대한 데이터가 있습니다. x 가 변화함에 따라 y 는 어떻게 달라지는지를 알고 싶어 회귀분석을 해 보겠습니다. x y 1 10 30 2 20 40 3 30 50 4 40 80 5 50 90 6 60 100 7 70 120 저는 SAS 를 이용합니다. 먼저 데이터 데이블을 생성합니다. 그리고 단순선형 회귀분석을 해 보겠습니다. 통계 프로그램은 회귀방정식 y= 11.429 + 1.5357x 를 제공해 주었습니다. 즉, x 가 1 증가할 때 y 는1.5357 배로 증가합니다. 그리고 이 회귀모형의…

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How to conduct Least Significant difference (LSD) test using R STUDIO?

How to conduct Least Significant difference (LSD) test using R STUDIO?

For the mean comparison among variables, Least Significant difference (LSD) test is the most common method. Today I’ll introduce LSD test using R Studio. Here is one data. This data is about the yield difference of CV1 in response to 4 different nitrogen fertilizer (N0 ,N1, N2, N3). First of all, let’s check the mean per each nitrogen fertilizer. It seems that yield is different from nitrogen fertilizers, but we need to confirm it statistically. First, I’ll run One-Way ANOVA…

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