Stories about crops and statistics (plus coding)
Here is data for x and y. I would like to perform regression analysis to understand how y changes with x. n x y 1 10 30 2 20 40 3 30 50 4 40 80 5 50 90 6 60 100 7 70 120 I have data for x and y as described above, … Read more
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 … Read more
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 … Read more
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 … Read more
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, … Read more
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 … Read more
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 … Read more
□ 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 … Read more
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 … Read more
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 … Read more
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 … Read more
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 … Read more
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. … Read more
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 … Read more
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. … Read more
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 … Read more
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 … Read more
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 … Read more
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 … Read more
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 … Read more
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 … Read more
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 … Read more
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 … Read more