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Exhaustive events: The total number of possible outcomes of a random experiment is known as exhaustive events or cases. Example ,  In tossing of a coin there are two exhaustive cases viz, head and tail.  In tossing a die, there are 6 exhaustive cases since any one of the six faces  1,2,3,......,6 may come uppermost. Mutually Exhaustive Events: Mutually Exclusive Events: Events that cannot occur at the same time. If one event happens, the other cannot. Example Coin Toss: The events "landing heads" and "landing tails" are mutually exclusive because a coin cannot land both heads and tails at the same time. In both cases, the occurrence of both events is independent of each other. In cases

In biostatistics, data collection is a crucial step in understanding health-related phenomena and making informed decisions. Here's a simplified explanation of data collection in biostatistics: Study Design: Before collecting data, researchers design studies to address specific research questions or hypotheses. This includes deciding on the study population, sampling methods, and data collection techniques. Sampling : Biostatisticians use various sampling methods to select a representative sample from the population of interest. This ensures that the data collected is reflective of the larger group and can be generalized to make broader conclusions. Data Collection Methods: Biostatisticians collect data through various methods, including surveys, interviews, medical tests, observations, and experiments. These methods depend on the research objectives and the nature of the data being collected. Quality Control : Ensuring the quality and accuracy of data is essential in biostatisti...

Introduction Statistics is a branch of mathematics concerned with collecting, analyzing, interpreting, presenting, and organizing numerical data. It helps us make sense of numbers by organizing them and drawing conclusions. Key ideas include: Describing Data : We use measures like averages (mean, median, mode) and spread (range, standard deviation) to understand what data is telling us. Making Predictions: With inferential statistics, we can make educated guesses about bigger groups based on smaller samples. Probability : Probability is about how likely things are to happen. It helps us understand uncertainty. Sampling: Sampling is about how we pick data from a larger group. Different methods give us different insights. Experiments : When we want to study cause and effect, we design experiments to see how changing one thing affects another. Software Tools : There are programs and tools that help us crunch numbers and visualize data, making it easier to understand. Real-world Use : St...

A T-test is a statistical test that is used to compare the means of two groups. In biostatistics, the t-test is a commonly used statistical test for comparing the means of two groups. It helps researchers determine if there is a significant difference between the means of two populations based on sample data. The t-test is particularly useful in biomedical research when comparing measurements or outcomes between different groups, such as treatment groups versus control groups, or groups with different characteristics.  T-test in Biostatistics: Imagine you're a student and you have two sets of grades from two different classes. You want to know if one class generally scores higher than the other. The t-test helps you figure that out. Definition : The t-test is like a detective tool that helps you see if there's a real difference between two groups. Student's Example: Let's say you have two classes: Class A and Class B. You collect grades from both classes to compare. The...

Certainly! In hypothesis testing, there are two types of errors that can occur:  Type I error and  Type II error. Type I Error: Definition : Type I error occurs when the null hypothesis (H0) is incorrectly rejected when it is actually true. In other words, it's a false positive. Symbolically , it's denoted as α (alpha), which represents the significance level or the probability of making a Type I error. Example : Suppose a medical test is conducted to determine whether a patient has a certain disease. The null hypothesis (H0) would be that the patient does not have the disease. A Type I error would occur if the test incorrectly indicates that the patient has the disease (rejecting H0) when, in fact, they do not. Type II Error: Definition : Type II error occurs when the null hypothesis (H0) is incorrectly not rejected when it is actually false. In other words, it's a false negative. Symbolically , it's denoted as β (beta). Example : Continuing with the medical test examp...

Definition:      The alternative hypothesis is like saying, "Hey, I think something interesting is happening here!" It's a statement in statistics that suggests there is a real difference or effect in the population, and you're trying to gather evidence to support it. Example:      Imagine you are curious whether drinking coffee affects people's productivity at work. You might formulate two hypotheses: Null Hypothesis (H0): Drinking coffee has no effect on productivity. Alternative Hypothesis (Ha): Drinking coffee increases productivity.      Here, the alternative hypothesis (Ha) suggests that there is indeed a relationship between drinking coffee and productivity, specifically that coffee consumption leads to increased productivity. This is what you're trying to find evidence for through your study or experiment. Conclusion:      In simpler terms, the alternative hypothesis is like saying, "Hey, I think there's something inter...

Definition :       The null hypothesis is like saying "nothing interesting is going on" or "there's no difference" in whatever you're studying. It's the idea you're trying to test or challenge with your experiment or study. Example: Let's say you're testing a new fertilizer to see if it makes plants grow taller. The null hypothesis (H0) in this case would be: "The new fertilizer has no effect on the height of the plants."   Another example could be if you're testing whether a new drug reduces headaches. The null hypothesis (H0) would be: "The new drug has no effect on reducing headaches." Conclusion:      In simpler terms, the null hypothesis is like saying "nothing special is happening" or "there's no difference" in whatever you're studying. It's the idea you're trying to gather evidence against in your statistical analysis.      So, the null hypothesis is essentially the baseline a...

Introduction: Hypothesis Testing can be defined as a statistical tool that is used to identify if the results of an experiment are meaningful or not. It involves setting up a null hypothesis and an alternative hypothesis. These two hypothesis will always be mutually exclusive. This means if the null hypothesis is true, then the alternative hypothesis will be false and vice versa. Types : Null Hypothesis (H0): This hypothesis typically represents a statement of no effect, no difference, or no change. It is the hypothesis that researchers aim to test against. Alternative Hypothesis (Ha/H1): This hypothesis represents what the researcher is trying to provide evidence for. It's typically the opposite of the null hypothesis and suggests that there is an effect, difference, or change. Here are a few examples of statistical hypotheses from real-life scenarios: Example 1: Drug Efficacy Hypotheses: Null Hypothesis (H0) : The new drug has no effect on reducing blood pressure. A...

On this page, you will find all topics related to Immunology! Here Every Major Topic Includes Sub-Major Topics. Find the topic you want to learn! Biostatistics- Introduction to Statistics Data collection Types of data, Methods, techniques and sources Frequency distributions-Tabular and Graphical representation Descriptive statistics-  Measures of Central tendency and their applications Relationship between mean, median and mode Measures of Dispersion and their applications Probability distributions Binomial distribution and their applications  Poisson distribution and their applications Normal distribution and their applications Introduction to Correlation analysis  Bivariate data,  Covariance,  Karl Pearson’s Correlation coefficient Hypothesis testing-  Introduction to hypothesis testing Null hypothesis ,  Alternative hypothesis ,  Types of errors   Introduction to statistical tests- Student’s T-test ,  F-test,  Chi-square t...