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How best to analyze likely depends on your specific aims. If what you wish to do is model the relationship, then clearly you'd need to include not just the value of the IV

(speed, in your example), but a function of the squared IV as well (whether centered or not is up to you) as a second IV, as the relationship appears quadratic in form. Logistic regression could work (with the DV being the dichotomous outcome of success).

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https://www.researchgate.net/deref/http%3A%2F%2Fpsychologicalstatistics.blogspot.com%2F2021%2F01%2Fa-brief-introduction-to-logistic.html

I have been thinking to write a paper about MANOVA (and in particular why it should be avoided) for some time, but never got round to it. However, I recently discovered an excellent article by Francis Huang that pretty much sums up most of what I'd cover. In this blog post I'll just run through the main issues and refer you to Francis' paper for a more in-depth critique or the section on MANOVA in Serious Stats (Baguley, 2012)

I have three main issues with MANOVA:

1) It doesn't do what people think it does

2) It doesn't offer Type I error protection for subsequent univariate tests (even though many text books say it does)

3) There are generally better approaches available if you really are interested in multivariate research questions

Logistic regression is therefore (on its surface) rather like simple or multiple linear regression

(which I’m assuming you have some familiarity with). In a simple regression we have a contin-

uous outcome variable and a linear model that takes this form:

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In this simple example we just have the outcome y predicted by a single predictor x. Most importantly this outcome is considered continuous and could (in principle) take any value from −∞ to +∞. This matters in practice because if our outcome is bounded between say 0 and 100 or 0 and 1 the model can’t take account of this and that might cause problems (especially predicting impossible values.

This simple model has two coefficients: b0, the intercept, and b1, the slope of the predictor x. If x is a categorical grouping variable anddummy coded (0 or 1) then b1 turns out to be the difference between the two groups and b0 the mean of the group coded

The e term are the residuals in the model (the differences between the predicted values and the data) and we assume all the residuals are sampled from a Normal distribution with unknown but constant variance: σ 2(the error variance).

The model uses the variation in the residuals to estimate the error variance. The probability distribution is important for deriving inferences such as significance tests (and p values). We can add predictors to the model and complicate

It in other ways, but these basic ideas are helpful to understand how logistic regression is both similar and different from more familiar regression

models.

While we could use multiple regression with a y variable that only takes the values 0 and 1, this has two main issues.2 First, it is bounded and this means that we would like a model that doesn’t predict impossible values such as 1.23 or - 0.3.

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The basic concepts of hypothesis testing and explained the need for performing these tests. In this post, I’ll build on that and compare various types of hypothesis tests that you can use with different types of data,

A hypothesis test uses sample data to assess two mutually exclusive theories about the properties of a population. Hypothesis tests allow you to use a manageable-sized sample from the process to draw inferences about the entire population.

Cover common hypothesis tests for three types of data—continuous, binary, and count data. Recognizing the different types of data is crucial because the type of data determines the hypothesis tests you can perform and, critically, the nature of the conclusions that you can draw. If you collect the wrong data, you might not be able to get the answers that you need.

There are an infinite number of possible values between any two values. You often measure a continuous variable on a scale. For example, when you measure height, weight, and temperature, you have continuous data. With continuous variables, you can use hypothesis tests to assess the mean, median, and standard deviation.

Suppose we have two production methods and our goal is to determine which one produces a stronger product. To evaluate the two methods, we draw a random sample of 30 products from each production line and measure the strength of each unit.

Before performing any analyses, it’s always a good idea to graph the data because it provides an excellent overview. Here is the CSV data file in case you want to follow along

Histograms suggest that Method 2 produces a higher mean strength while Method 1 produces more consistent strength scores. The higher mean strength is good for our product, but the greater variability might produce more defects.

Graphs provide a good picture, but they do not test the data statistically.

https://statisticsbyjim.com/hypothesis-testing/comparing-hypothesis-tests-data-types/#:~:text=If%20the%20observed%20differences%20are%20due%20to%20random%20error%2C%20it%20would%20not%20be%20surprising%20if%20another%20sample%20showed%20different%20patterns.

The goal of learning a linear model from training data is to find the coefficients, β, that best explain the data. In frequentist linear regression, the best explanation is taken to mean the coefficients, β, that minimize the residual sum of squares (RSS).

It can be a costly mistake to base decisions on “results” that vary with each sample. Hypothesis tests factor in random error to improve our chances of making correct decisions.

Keep this graph in mind when we look at binary data because they illustrate how much more information continuous data convey.

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Dear Ca Dr. Gaurav Bhambri . See the following useful RG link: Article The use of continuous data versus binary data in MTC models:...

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Neter et al. (1996) describe a study of 54 patients undergoing a certain kind of liver operation in a surgical unit. The data set Surg contains survival time and certain covariates for each patient.

Measurements of continuous variables are made in all branches of medicine, aiding in the diagnosis and treatment of patients.

In clinical practice it is helpful to label individuals as having or not having an attribute, such as being “hypertensive” or “obese” or having ”high cholesterol,” depending on the value of a continuous variable.

Categorisation of continuous variables is also common in clinical research, but here such simplicity is gained at some cost.

Though grouping may help data presentation, notably in tables, categorisation is unnecessary for statistical analysis and it has some serious drawbacks.

Here we consider the impact of converting continuous data to two groups (dichotomising), as this is the most common approach in clinical research.1

A common argument is that it greatly simplifies the statistical analysis and leads to easy interpretation and presentation of results. A binary split—for example, at the median—leads to a comparison of groups of individuals with high or low values of the measurement, leading in the simplest case to a t test or χ2 test and an estimate of the difference between the groups (with its confidence interval)

Dichotomising leads to several problems. Firstly, much information is lost, so the statistical power to detect a relation between the variable and patient outcome is reduced. Indeed, dichotomising a variable at the median reduces power by the same amount as would discarding a third of the data.2,3 Deliberately discarding data is surely inadvisable when research studies already tend to be too small. Dichotomisation may also increase the risk of a positive result being a false positive

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Establish the code's foundation on essential principles such as trust and integrity.

Confirmatory factor analysis (CFA) and exploratory factor analysis (EFA) are similar techniques, but in exploratory factor analysis (EFA), data is simply explored and provides information about the numbers of factors required to represent the data.

Confirmatory factor analysis (CFA) is the method for measuring latent variables (Hoyle 1995; 2011; Kline 2010; Byrne 2013).

https://www.researchgate.net/deref/https%3A%2F%2Fwww.cs.princeton.edu%2F~ken%2Fdynamiconline00.pdf

But in confirmatory factor analysis (CFA), researchers can specify the number of factors required in the data and which measured variable is related to which latent variable.  Confirmatory factor analysis (CFA) is a tool that is used to confirm or reject the measurement theory.

Confirmatory factor analysis estimates latent variables based on the correlated variations of the dataset (e.g., association, causal relationship) and can reduce the data dimensions, standardize the scale of multiple indicators, and account for the correlations inherent in the dataset (Byrne 2013)

Defining individual construct: First, we have to define the individual constructs. The first step involves the procedure that defines constructs theoretically. This involves a pretest to evaluate the construct items, and a confirmatory test of the measurement model that is conducted using confirmatory factor analysis (CFA), etc.

Constant imputation methods impute a constant value in the replacement of missing data in an observation.

The measurement model deals with the relationship between a latent variable and its indicators.

Designing a study to produce the empirical results: The measurement model must be specified.  Most commonly, the value of one loading estimate should be one per construct.  Two methods are available for identification; the first is rank condition, and the second is order condition.

But in contrast, a structural model defines the relationship between the various constructs in a model.

the two measurement model becomes a structural model when they are linked together as shown below. Thus, specifying how latent variables directly or indirectly affect other latent variables in the model.

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