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Unraveling the t-test: a deep dive into comparing means Ever wondered how scientists confidently conclude if two groups truly differ? The t-test is their go-to tool! In my latest biostatistics book chapter, we explore the t-test from the ground up, ensuring you grasp its core principles and applications. We dissect the t-statistic, unravel the mystery behind P values, and empower you with practical examples using real-world data. But that's not all! We venture beyond traditional methods and introduce you to the fascinating world of bootstrapping. Discover how this versatile technique lets you estimate P values and confidence intervals directly from your data, even when those pesky assumptions of normality aren't perfectly met. Whether you're a seasoned researcher or just starting your data analysis journey, this chapter will equip you with the knowledge and tools to confidently compare means and draw meaningful conclusions from your data. #biostatistics #statistics #ttest #bootstrapping #datanalysis #research https://lnkd.in/dY8W877C

Precision-Recall Plot - Clearly explained 🔍 The precision-recall plot is a model-wide measure for evaluating classifiers. The plot is based on the evaluation metrics of Precision and Recall. 🧐 Recall (identical to sensitivity) is a measure of the whole positive part of a dataset, whereas precision is a measure of positive predictions. The precision-recall plot uses precision on the y-axis and recall on the x-axis. You see a visual explanation in the figure. 🤔 It is easy to interpret a precision-recall plot. In general, precision decreases as recall increases. Conversely, as precision increases, recall decreases. 💡 A random classifier lies on the y-axis (precision) at y = P/( P + N ) (P: number of positive labels, N: number of negative labels). A poor classifier lies below this line, and a good classifier lies well above this line. 🌟 You can see two different plots in the figure. On the left side, you see the random line is y=0.5. The ratio of positives (P) and negatives (N) is 1:1. On the right side, you see the random line is y=0.25. There, we have a ratio of positives and negatives of 1:3. 📊 Another quality criterion in the precision-recall plot is the area under the curve (AUC) score, where the area under the curve is calculated. An AUC score close to 1 characterizes a good classifier. --- Get our FREE data science cheat sheets in high resolution by subscribing to our blog today! https://lnkd.in/egwYzbkX #MachineLearning #Statistics

Hypothesis testing is a key statistical method that allows us to draw conclusions about populations based on sample data. Choosing the right test is essential for obtaining accurate and reliable results. When the appropriate hypothesis test is selected, it ensures sound conclusions and supports data-driven decision-making. Different tests, such as t-tests, ANOVA, and chi-squared tests, are designed to address various data types and research questions, providing both flexibility and precision. However, using the wrong test can lead to misleading outcomes and incorrect conclusions, which can undermine the credibility of your analysis. Additionally, neglecting important assumptions, such as normality or equal variances, can compromise the validity of the test results. Here are some important hypothesis tests: 🔹 T-test: Used to compare the means of two groups. 🔹 Z-test: Used to determine if there is a significant difference between sample and population means when the population variance is known. 🔹 ANOVA (Analysis of Variance): Used to compare means across three or more groups. 🔹 Chi-Squared Test: Used for categorical data to assess how likely the observed distribution is, given the expected distribution. Note that there are many other tests, including the Mann-Whitney U test, Kruskal-Wallis test, Wilcoxon signed-rank test, Fisher's exact test, and McNemar's test, as well as more modern methods like Bayesian hypothesis testing, permutation tests, and bootstrap methods. Depending on your specific situation, these or other tests might be more appropriate. Interested in learning more? Check out my online course on Statistical Methods in R, starting September 9, 2024, where we dive deeper into hypothesis testing and other key statistical methods. More information: https://lnkd.in/d-UAgcYf #datascienceeducation #rstats #dataanalytics

So, just to make it simple while you are on a journey through the statistical world of data analysis, please take it slow, and try to understand in detail and without any hurry how Principal Component Analysis (PCA) distinguishes itself from Factor Analysis (FA) and Discriminant Analysis (DA). In general and without diving deeply into the technical explanation of these statistical techniques (just a guidelines), when you use PCA a kind of magic happens, where you transform your data into a new set of variables, which are known as principal components. These components are the patterns in your data containing the most variation, so it is easier for you to keep the big picture in sight. In contrast, when you use FA, you are trying to find somthing hidden, so you uncover the existence of hidden factors behind the relationships between your observed variables. The idea behind FA is to group which observed variables are related and put these related variables in one cluster, which we know as a latent factor. Here comes Discriminant Analysis commonly called DA and does a different kind of magic. DA is a classification tool. It is like a guide, showing you which observed variables are the most effective in distinguishing one group from another. While PCA and FA are about understanding the group patterns form your observed variables, DA is more about predicting the group from your observed variables. Therefore, PCA and FA are conceptually related, as they consider reducing the complexity of your observed variables data, but they differ in terms of what complexity they are simplifying. So, here it is in very simple way, PCA simplifies variance, and FA simplifies correlation, while DA is about classifying groups based on your observed variable data. Next time you are puzzled by the observed variable data hat, remember these magic tricks and think about what you want to do: simplify and show variance or solve correlation or work on the classification, however, choose wisely. If you interested, pls read this nice chapter 🙏 #statistics #datascience #datascientist #ml #researcher #rstat

🚀 **Unlocking the Power of Data Imputation: Essential Techniques for Data Scientists and Machine Learning Engineers** 📊 In the world of data analysis, missing values can pose significant challenges. How do we ensure that our datasets remain robust and reliable? 🤔 I just published a comprehensive blog exploring some of the most effective data imputation methods used in the industry, including: 🔹 **Mean/Median/Mode Imputation**: The simplest approach for handling missing values.   🔹 **Hot Deck Imputation**: Preserving data distribution using similar observations.   🔹 **Regression Imputation**: Leveraging relationships between variables for accurate predictions.   🔹 **Multiple Imputation**: Assessing uncertainty through multiple datasets.   🔹 **K-Nearest Neighbors (KNN) Imputation**: Utilizing local patterns for filling in gaps.   🔹 **Random Forest Imputation**: Capturing complex relationships with ensemble learning.   🔹 **Expectation-Maximization (EM) Algorithm**: Iterative estimates for maximum likelihood. 💡 Understanding the strengths and limitations of these techniques is crucial for data integrity and model performance. 📖 **Read the full blog** to dive deeper into each method, discover best practices, and learn how to choose the right imputation technique for your specific needs. Let’s keep the conversation going! What imputation techniques have you found most effective in your work? Share your thoughts in the comments! 💬 #DataScience #MachineLearning #DataImputation #DataAnalysis #Analytics #BigData #DataQuality #ArtificialIntelligence #DataPreparation

Day -2 of learning statistics for data analysis in easy way. Mastering descriptive statistics is essential for uncovering key insights from your data. In this post, I break down core concepts like measures of central tendency (mean, median, mode), measures of dispersion (standard deviation, variance, range, IQR), and measures of symmetricity (skewness, kurtosis). These techniques help you summarize, understand, and visualize data effectively. If you want to make sense of your data and drive data-driven decisions, this post is for you! #DataAnalytics #DescriptiveStatistics #DataAnalysis #DataScience #StatisticsForAnalysts #MeanMedianMode #StandardDeviation #DataVisualization #BusinessIntelligence #SEO #DataDriven #DataInsights

Below are the top 8 commonly used statistical tests that novices are often confused by. A brief explanation of the best time to use them: 1. Z-Test: Used to test samples of varying sizes, and a known population variance. It is used to determine if there is a distinction between two methods. 2. T-Test (Student's) smaller samples, unidentified variation in the population. Ideal for comparing mean values from two groups. It includes independent and paired tests using t-tests. 3. Welch's test for univariate variations and/or sample sizes. A modification of the t-test that doesn't assume equal variances, giving greater flexibility. 4. Chi-Squared test: categorical information, checking for independence or quality of the fit. This test is used to determine whether it is possible to establish a strong correlation between categorical variables. 5. ANOVA: Comparing means between 3 or more different groups. A great way to find out the significance of variations in the mean of several groups. 6. Mann-Whitney U test: Non-parametric alternative to the Z-test or T-test for distributions that are not normal. Comparing two groups that are independent, particularly when the data isn't normally distributed. 7. Fisher's Exact Test : Small sample sizes, specifically in contingency tables 2x2. It is used to determine the significance of the connection between two types of classifications. 8. Regression Analysis The relationship between dependent variables and one or more independent variables. To conduct more sophisticated A/B tests, which help to comprehend the impact of many variables on the outcome. To get more relevant information follow Ijtaba Hussain #datascience #datascientist #dataanalytics #dataanalysis #machinelearning #hypothesistesting #statisticalanalysis

*** Sampling Distribution: Explained *** ~ In statistics, a sampling distribution is the probability distribution of a given random-sample-based statistic. ~ If an arbitrarily large number of samples, each involving multiple observations (data points), were separately used to compute one value of a statistic (for example, the sample mean or sample variance) for each sample, then the sampling distribution is the probability distribution of the values that the statistic takes on. ~ Sampling distributions are important in statistics because they provide a significant simplification en route to statistical inference. ~ More specifically, they allow analytical considerations to be based on the probability distribution of a statistic rather than on the joint probability distribution of all the individual sample values. ~ The sampling distribution of a statistic is the distribution of that statistic, considered a random variable when derived from a random sample. ~ It may be regarded as the statistic distribution for all possible samples from the same sample size population. ~ The sampling distribution depends on the underlying distribution of the population, the statistic being considered, the sampling procedure employed, and the sample size used. ~ There is often considerable interest in whether the sampling distribution can be approximated by an asymptotic distribution, which corresponds to the limiting case either as the number of random samples of finite size, taken from an infinite population and used to produce the distribution, tends to infinity is taken of that same population. ~ For example, consider we repeatedly take samples of a given size from this population and calculate the arithmetic mean for each sample – this statistic is called the sample mean. ~ The distribution of these means, or averages, is called the "sampling distribution of the sample mean." ~ The mean of a sample from a population having a normal distribution is an example of a simple statistic taken from one of the simplest statistical populations. The formulas are more complicated for other statistics and populations and often do not exist in closed form. ~ In such cases, the sampling distributions may be approximated through Monte Carlo simulations, bootstrap methods, or asymptotic distribution theory. --- B. Noted

Real-world Data is Never Perfect. Your 3 Big Questions When Faced With Dataset Without an Output Variable 1. How can we effectively identify a target variable in a dataset with no predefined outcome, and what are the potential pitfalls of quick identification methods? ✅ Quick methods like literature review & expert consultation can guide initial identification, but may lead to errors. A more rigorous approach, using correlation matrices, visualisations, & feature importance techniques, is recommended to reduce risks. 2. In what scenarios might it be more appropriate to reframe a problem as an unsupervised learning task rather than continuing to search for a single target variable? ✅ Reframing as an unsupervised learning task is suitable when there is no clear target variable or when the goal is to discover patterns & relationships within the data. 3. What are the advantages & challenges of using multiple models with different features as target variables to explore various hypotheses? ✅ Using multiple models helps explore different hypotheses & understand data comprehensively, but it increases computational complexity & requires careful interpretation of results. 👇 Here are entries in Quora on unlabelled datasets: https://lnkd.in/gsjNdPCh 👇 Check out this article to find out more: ‘Real-world Data is Never Perfect. Your Dataset Could Come to You Without an Output Variable ’: https://lnkd.in/gCGwpcr6 👆 If you find this article useful, like & share it in your network.