Analysis of Variance (ANOVA) is a statistical model developed by statistician and evolutionary biologist Ronald Fisher (Ronald Fisher) to analyze the differences between organizational methods and related procedures (such as between groups And differences between groups).
If your postgraduate statistical training is like mine, you will learn one type of analysis of variance, and the other is linear regression. My professor often said that "ANOVA is only a special regression situation", but will give vague answers when pressed.
It was not until I started consulting that I realized that ANOVA and regression are closely related. They are not only related, they are the same thing. Not a quarter and the same coin with different aspects of nickel.
So here is a very simple example to show why. When someone shows me this, even I already know about the analysis of variance (ANOVA) and multiple linear regression (very simple), and I already have my statistics! I believe that understanding this small concept is the key to my understanding of the overall linear model, and its application range is very wide.
The employment category model with a single categorical independent variable has three categories: management, clerical, and guardianship. The dependent variable is the experience of the previous few months. (The data set is employment. sav, which is one of the data sets that comes with SPSS ).
We can run it as ANOVA or regression. In an analysis of variance, categorical variables are effectively coded, which means that the average of each category is compared with the large average. In regression, the categorical variable is a dummy code**, which means that the intercept of each category is compared with the intercept of the reference group. Since the intercept is defined as the average value when all other predicted values are 0, and there are no other predicted values, the three intercepts are just averages.
Someone asked me to explain the difference between regression and analysis of variance. This is challenging because regression and analysis of variance are like two sides of the same coin. They are different, but they have more in common, which you might see at first glance.
A very simple explanation is that regression is a statistical model that you use to predict continuous outcomes based on one or more continuous predictor variables. In contrast, ANOVA is a statistical model that you use to predict continuous outcomes based on one or more categorical predictor variables. Most people will draw a big exception to the "one or more categorical variables" declaration. If you have a single categorical variable with only two levels (in other words, binary categories), then most people will describe the method/method as a two-sample t-test. A single categorical predictor with three or more levels or two plus categorical predictors with any number of levels will be considered an ANOVA model.
Therefore, if you want to use the mother's age as a predictor variable to predict the duration of breastfeeding, then you will use a regression model. If you want to use the mother's marital status (single, married, divorced, widowed) to predict the duration of breastfeeding, you will use the ANOVA model. If you want to use prenatal smoking status (smoking during pregnancy, not smoking during pregnancy) to predict the duration of breastfeeding, then you will use a two-sample t-test. If you add the delivery type (vaginal/part c) to prenatal smoking status, use the ANOVA model to analyze two binary predictor variables.
What if you have two predictors, one continuous and one categorical? For example, suppose you want to use your mother's age and type of delivery to predict the duration of breastfeeding in a few weeks? Is it a regression model, ANOVA model, or t-test? Some people use a brand new term to describe this model, ANCOVA (Analysis of Covariance). Others may use this term to ridicule. Generally speaking, the language of statistics is not as standardized as you would like, and sometimes different people will use different terminology to essentially the same model
But you should always remember that regression and analysis of variance have a lot in common. First, these two models are only applicable when you have a continuous outcome variable. Categorical outcome variables will exclude the use of regression models or ANOVA models.
Second, you can use regression algorithms based on the principle of least squares to fit the ANOVA model. You do not need to use the principle of least squares, because there are other ways to generate an analysis of the variance model. However, because the basis of the least-squares regression model is also applicable to the analysis of the variance model, some people think that the regression model is a more general model. You can incorporate categorical prediction values into the regression model by using indicator variables. The indicator variable is equal to 1 for a particular category, and zero for the remaining categories. If you have k-level categorical predictor variables, you can enter k-1 indicator variables in the regression program (the last indicator is always redundant), and effectively obtain the same results as the ANOVA model.
Third, in the ANOVA model, the concept of decomposing the variance into the sum of squares (SS) also provides a good way to test complex regression models. In the ANOVA model, total variation (total SS) is divided into variation between groups (SS) and variation within groups (within SS). You can do the same with regression models, decomposing the overall change into changes due to changes in the model (model SS) and ambiguous by the model (error SS).
Fourth, regression models and analysis of variance models share many of the same diagnostic procedures (procedures for checking potential hypotheses). In particular, you can calculate the residuals in both models, and graphs involving these residuals are often very useful.
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If your postgraduate statistical training is like mine, you will learn one type of analysis of variance, and the other is linear regression. My professor often said that "ANOVA is only a special regression situation", but will give vague answers when pressed.
It was not until I started consulting that I realized that ANOVA and regression are closely related. They are not only related, they are the same thing. Not a quarter and the same coin with different aspects of nickel.
So here is a very simple example to show why. When someone shows me this, even I already know about the analysis of variance (ANOVA) and multiple linear regression (very simple), and I already have my statistics! I believe that understanding this small concept is the key to my understanding of the overall linear model, and its application range is very wide.
The employment category model with a single categorical independent variable has three categories: management, clerical, and guardianship. The dependent variable is the experience of the previous few months. (The data set is employment. sav, which is one of the data sets that comes with SPSS ).
We can run it as ANOVA or regression. In an analysis of variance, categorical variables are effectively coded, which means that the average of each category is compared with the large average. In regression, the categorical variable is a dummy code**, which means that the intercept of each category is compared with the intercept of the reference group. Since the intercept is defined as the average value when all other predicted values are 0, and there are no other predicted values, the three intercepts are just averages.
Someone asked me to explain the difference between regression and analysis of variance. This is challenging because regression and analysis of variance are like two sides of the same coin. They are different, but they have more in common, which you might see at first glance.
A very simple explanation is that regression is a statistical model that you use to predict continuous outcomes based on one or more continuous predictor variables. In contrast, ANOVA is a statistical model that you use to predict continuous outcomes based on one or more categorical predictor variables. Most people will draw a big exception to the "one or more categorical variables" declaration. If you have a single categorical variable with only two levels (in other words, binary categories), then most people will describe the method/method as a two-sample t-test. A single categorical predictor with three or more levels or two plus categorical predictors with any number of levels will be considered an ANOVA model.
Therefore, if you want to use the mother's age as a predictor variable to predict the duration of breastfeeding, then you will use a regression model. If you want to use the mother's marital status (single, married, divorced, widowed) to predict the duration of breastfeeding, you will use the ANOVA model. If you want to use prenatal smoking status (smoking during pregnancy, not smoking during pregnancy) to predict the duration of breastfeeding, then you will use a two-sample t-test. If you add the delivery type (vaginal/part c) to prenatal smoking status, use the ANOVA model to analyze two binary predictor variables.
What if you have two predictors, one continuous and one categorical? For example, suppose you want to use your mother's age and type of delivery to predict the duration of breastfeeding in a few weeks? Is it a regression model, ANOVA model, or t-test? Some people use a brand new term to describe this model, ANCOVA (Analysis of Covariance). Others may use this term to ridicule. Generally speaking, the language of statistics is not as standardized as you would like, and sometimes different people will use different terminology to essentially the same model
But you should always remember that regression and analysis of variance have a lot in common. First, these two models are only applicable when you have a continuous outcome variable. Categorical outcome variables will exclude the use of regression models or ANOVA models.
Second, you can use regression algorithms based on the principle of least squares to fit the ANOVA model. You do not need to use the principle of least squares, because there are other ways to generate an analysis of the variance model. However, because the basis of the least-squares regression model is also applicable to the analysis of the variance model, some people think that the regression model is a more general model. You can incorporate categorical prediction values into the regression model by using indicator variables. The indicator variable is equal to 1 for a particular category, and zero for the remaining categories. If you have k-level categorical predictor variables, you can enter k-1 indicator variables in the regression program (the last indicator is always redundant), and effectively obtain the same results as the ANOVA model.
Third, in the ANOVA model, the concept of decomposing the variance into the sum of squares (SS) also provides a good way to test complex regression models. In the ANOVA model, total variation (total SS) is divided into variation between groups (SS) and variation within groups (within SS). You can do the same with regression models, decomposing the overall change into changes due to changes in the model (model SS) and ambiguous by the model (error SS).
Fourth, regression models and analysis of variance models share many of the same diagnostic procedures (procedures for checking potential hypotheses). In particular, you can calculate the residuals in both models, and graphs involving these residuals are often very useful.
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