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Statistics plays a critical role in numerous fields, including data science, business, social sciences, and more. However, many of the fundamental statistical concepts can seem complex and intimidating, especially for beginners without a strong background in mathematics. This article will discuss 10 fundamental statistical concepts in simple, non-technical terms, with the goal of conveying these concepts in an accessible and accessible manner.
A probability distribution shows the probability of different outcomes occurring in a process. For example, let’s say we have a bag with the same number of red, blue, and green marbles. If we draw marbles at random, the probability distribution tells us the chances of drawing each color. It would show that there is an equal 1/3 or 33% chance of getting red, blue or green. Many types of real-world data can often be modeled using known probability distributions, although this is not always the case.
Hypothesis testing allows us to make statements based on data, similar to how a court trial seeks to prove guilt or innocence based on the available evidence. We start with a hypothesis or statement, called the null hypothesis. We then check whether the observed data supports or refutes this claim within a certain level of confidence. For example, a drug manufacturer may claim that its new medication reduces pain more quickly than existing medications. Researchers can test this claim by analyzing the results of clinical trials. Based on the data, they may reject the claim if evidence is missing or fail to reject the null hypothesis, which indicates that there is not enough evidence to say that the new medication does not reduce pain faster.
When sampling data from a population, confidence intervals provide a range of values within which we can be reasonably sure that the true population mean lies. For example, if we claim that the average height of men in a country is 172 cm with a 95% confidence interval of 170 cm to 174 cm, then we are 95% confident that the average height of all men is It is between 170 cm and 174 cm. cm. The confidence interval generally narrows with larger sample sizes, assuming other factors such as variability remain constant.
Regression analysis helps us understand how changes in one variable impact another variable. For example, we may analyze data to see how sales are affected by advertising spending. The regression equation then quantifies the relationship, allowing us to predict future sales based on projected ad spend. Beyond two variables, multiple regression incorporates several explanatory variables to isolate their individual effects on the outcome variable.
ANOVA allows us to compare means between multiple groups to see if they are significantly different. For example, a retailer could test customer satisfaction with three packaging designs. By analyzing the survey ratings, ANOVA can confirm whether satisfaction levels differ between the three groups. If there are differences, it means that not all designs lead to the same satisfaction. This information helps you choose the optimal packaging.
The p value indicates the probability of obtaining results at least as extreme as the observed data, assuming the null hypothesis is true. A small p value provides strong evidence against the null hypothesis, so you may consider rejecting it in favor of the alternative hypothesis. Returning to the clinical trial example, a small p value when comparing the pain relief of new and standard drugs would indicate strong statistical evidence that the new drug works faster.
While frequentist statistics are based solely on data, Bayesian statistics incorporate existing beliefs along with new evidence. As we get more data, we update our beliefs. For example, let’s say the probability of rain today according to the forecast is 50%. If we then notice dark clouds above us, Bayes’ theorem tells us how to update this probability to say 70% based on the new evidence. Bayesian methods, which can be computationally intensive, may be popular in aspects of data science.
The standard deviation quantifies how dispersed or dispersed the data is from the mean. A low standard deviation means that the points are clustered closely around the mean, while a high standard deviation indicates a wider variation. For example, test scores of 85, 88, 89, 90 have a lower standard deviation than scores of 60, 75, 90, 100. Standard deviation is extremely useful in statistics and forms the basis of many analyses.
The correlation coefficient measures how strongly two variables are linearly related, from -1 to +1. Values close to +/-1 indicate a strong correlation, while values close to 0 mean a weak correlation. For example, we can calculate the correlation between house size and price. A strong positive correlation implies that larger homes tend to have higher prices. It is important to note that while correlation measures a relationship, it does not imply that one variable causes the other to occur. 10. Central limit theorem
The central limit theorem is more precise when the sample size is large and states that when we take such samples from a population and calculate the sample means, these means follow a normal distribution pattern, regardless of the original distribution. For example, if we survey groups of people about their movie preferences, plot the average for each group, and repeat this process, the averages form a bell curve, even if individual opinions vary.
Understanding statistical concepts provides an analytical lens through which to view the world and begin to interpret data so we can make informed, evidence-based decisions. Whether in data science, business, school, or our daily lives, statistics are a powerful set of tools that can give us seemingly infinite insight into how the world works. I hope this article has provided an intuitive but comprehensive introduction to some of these ideas.
Matthew May (@mattmayo13) has a master’s degree in computer science and a postgraduate diploma in data mining. As Editor-in-Chief of KDnuggets, Matthew aims to make complex data science concepts accessible. His professional interests include natural language processing, machine learning algorithms, and exploring emerging ai. He is driven by the mission to democratize knowledge in the data science community. Matthew has been coding since he was 6 years old.
