*14/01/2024*

First post in 2024. Happy new year to you all.

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Operating as usual

First post in 2024. Happy new year to you all.

A very important certificate in Medical Research.

Predict and win MK5000. It's a London derby today at 6:30PM.

I will give MK5000 to the first person who predicts correctly on the match between Chelsea vs Arsenal.

It starts now, and ends 10 min before kick off.

All the best.

Errors in statistical decision-making

Let’s review the steps for conducting a hypothesis test:

1. State the null hypothesis and the alternative hypothesis.

2. Choose a significance level.

3. Find the p-value.

4. Reject or fail to reject the null hypothesis.

When you decide to reject or fail to reject the null hypothesis, there are four possible outcomes–two represent correct choices, and two represent errors. You can:

• Reject the null hypothesis when it’s actually true (Type I error)

• Reject the null hypothesis when it’s actually false (Correct)

• Fail to reject the null hypothesis when it’s actually true (Correct)

• Fail to reject the null hypothesis when it’s actually false (Type II error)

Example: Clinical trial

Let’s explore an example to get a better understanding of Type I and Type II errors. Hypothesis tests are often used in clinical trials to determine whether a new medicine leads to better outcomes in patients. Imagine you’re a data professional who works for a pharmaceutical company. The company invents a new medicine to treat the common cold. The company tests a random sample of 200 people with cold symptoms. Without medicine, the typical person experiences cold symptoms for 7.5 days. The average recovery time for people who take the medicine is 6.2 days.

You conduct a hypothesis test to determine if the effect of the medicine on recovery time is statistically significant, or due to chance.

In this case:

• Your null hypothesis (H0) is that the medicine has no effect.

• Your alternative hypothesis (Ha) is that the medicine is effective.

Type I error

A Type 1 error, also known as a false positive, occurs when you reject a null hypothesis that is actually true. In other words, you conclude that your result is statistically significant when in fact it occurred by chance.

For example, in your clinical trial, if the null hypothesis is true, that means the medicine has no effect. If you make a Type I error and reject the null hypothesis, you incorrectly conclude that the medicine relieves cold symptoms when it’s actually ineffective.

The probability of making a Type I error is called alpha (α). Your significance level, or alpha (α), represents the probability of making a Type I error. Typically, the significance level is set at 0.05, or 5%. A significance level of 5% means you are willing to accept a 5% chance you are wrong when you reject the null hypothesis.

Reduce your risk

To reduce your chance of making a Type I error, choose a lower significance level.

For instance, if you want to minimize the risk of a Type I error, you can choose a significance level of 1% instead of the standard 5%. This change reduces the chance of making a Type I error from 5% to 1%.

Type II error

However, reducing your risk of making a Type I error means you are more likely to make a Type II error, or false negative. A Type II error occurs when you fail to reject a null hypothesis which is actually false. In other words, you conclude your result occurred by chance, when in fact it didn’t.

For example, in your clinical study, if the null hypothesis is false, this means that the medicine is effective. If you make a Type II error and fail to reject the null hypothesis, you incorrectly conclude that the medicine is ineffective when it actually relieves cold symptoms.

The probability of making a Type II error is called beta (β), and beta is related to the power of a hypothesis test (power = 1- β). Power refers to the likelihood that a test can correctly detect a real effect when there is one.

P-Value in Statistical Inference

The p-value in statistical inference is a measure that helps you determine the strength of evidence against a null hypothesis. It indicates the probability of observing the data, or more extreme data, under the assumption that the null hypothesis is true. A low p-value (typically ≤ 0.05) suggests that the observed data is unlikely under the null hypothesis, which may lead you to reject the null hypothesis in favor of an alternative hypothesis.

To calculate a p-value, you need to perform a statistical test based on the type of data and hypothesis you're dealing with. Common methods include t-tests, ANOVA, chi-squared tests, and regression analysis. The specific calculation depends on the chosen test and the statistical software or tools you're using.

It's important to note that interpreting p-values requires caution, as they don't provide information about the practical significance or the magnitude of an effect. Other factors, such as effect size and sample size, should also be considered when making conclusions from statistical analyses.

What is VLOOKUP in excel?

Regression is a statistical method used to find the relationship between two or more variables. It helps us understand how changes in one variable (often called the "independent" or "predictor" variable) are related to changes in another variable (known as the "dependent" or "outcome" variable). The goal of regression is to create a mathematical model that allows us to make predictions or estimate values of the dependent variable based on the values of the independent variable(s).

Types of regression

• Simple Linear Regression: Involves two variables, with one being the predictor and the other the outcome. It helps us draw a straight line to understand how a change in the predictor affects the outcome.

• Multiple Linear Regression: Similar to simple linear regression, but here we have more than one predictor variable, allowing us to consider the combined effects of multiple predictors on the outcome.

• Polynomial Regression: This type of regression accommodates curved relationships between the predictor and outcome variables, using polynomial equations (e.g., quadratic or cubic) instead of straight lines.

• Logistic Regression: Used when the outcome variable is categorical (e.g., yes/no or pass/fail). It helps us understand the probability of an event occurring based on the predictor variables.

• Ridge Regression and Lasso Regression: Variants of linear regression that help prevent overfitting (a model fitting too closely to the data) by introducing penalties for large coefficients of predictor variables.

These are just some of the common types of regression. Each type has its own strengths and applications depending on the nature of the data and the research question.

A very good tool to test reliability in research.

For example, if u have developed a questionnaire and one variable is measuring happiness, and u want to see if all the questions are testing happiness.. Cronbach's alpha Must be used. It means that if u use it for the first, second or third time, it will still give u the same result.

A very important aspect in Research. Learn more on how to develop and differentiate between Conceptual Framework and Theoretical framework.

Keep it on grinding.

Very important in Research.

Basics.

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