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Statistics plays a pivotal role across numerous fields including data science, business, social sciences, and more. However, many of the foundational statistical concepts can seem complex and intimidating, especially for beginners without a strong math background. This article will look at 10 foundational statistical concepts in simple, non-technical terms, with the goal of conveying these concepts in an accessible and approachable manner.
A probability distribution shows the likelihood of different outcomes occurring in a process. For example, say we have a bag with an equal number of red, blue, and green marbles. If we draw marbles randomly, the probability distribution tells us the chances of drawing each color. It would show that there’s an equal 1/3 chance or 33% probability 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 claims based on data, similar to how a courtroom trial aims to prove guilt or innocence based on available evidence. We start with a hypothesis or claim, called the null hypothesis. Then we check if the observed data supports or refutes this claim within a certain confidence level. For example, a drug manufacturer may claim their new medicine reduces pain faster than existing ones. Researchers can test this claim by analyzing results from clinical trials. Based on the data, they can either reject the claim if evidence is lacking or fail to reject the null hypothesis, indicating that there isn’t enough evidence to say the new drug 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 mean of the population lies. For example, if we state 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 mean height for all men lies between 170 cm and 174 cm. The confidence interval generally gets smaller with larger sample sizes, assuming other factors like variability remain constant.
Regression analysis helps us understand how changes in one variable impact another variable. For instance, we can analyze data to see how sales are impacted by advertising expenditure. The regression equation then quantifies the relationship, allowing us to predict future sales based on projected ad spends. Beyond two variables, multiple regression incorporates several explanatory variables to isolate their individual effects on the outcome variable.
ANOVA lets us compare means across multiple groups to see if they are significantly different. For example, a retailer might test customer satisfaction with three packaging designs. By analyzing survey ratings, ANOVA can confirm whether satisfaction levels differ across the three groups. If differences exist, it means not all designs lead to equal satisfaction. This insight helps choose the optimal packaging.
The p-value indicates the probability of getting 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. Going back to the clinical trials example, a small p-value when comparing pain relief of the new and standard drugs would indicate strong statistical evidence that the new drug does act faster.
While frequentist statistics relies solely on data, Bayesian statistics incorporates existing beliefs along with new evidence. As we get more data, we update our beliefs. For example, say the probability of actually raining today based on forecasts is 50%. If we then notice dark clouds overhead, Bayes’ theorem tells us how to update this probability to say 70% based on the new evidence. Bayesian methods, which can be computationally intensive, can be popular in aspects of data science.
The standard deviation quantifies how dispersed or spread out data is from the mean. A low standard deviation means points cluster closely around the mean, while a high standard deviation indicates 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 near 0 mean a weak correlation. For example, we can calculate the correlation between house size and price. A strong positive correlation implies larger houses tend to have higher prices. It’s important to note that while correlation measures a relationship, it does not imply that one variable causes the other to occur.
The central limit theorem is more accurate when the sample size is large and states that when we take such samples from a population and calculate sample means, these means follow a normal distribution pattern, regardless of the original distribution. For example, if we survey groups of people about 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 that we are able to make informed, evidence-based decisions. Be it in data science, business, school, or our everyday lives, statistics is a powerful set of tools that can provide us seemingly endless insight into how the world works. I hope this article has provided an intuitive yet comprehensive introduction to some of these ideas.
Matthew Mayo (@mattmayo13) holds a Master’s degree in computer science and a graduate 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 a mission to democratize knowledge in the data science community. Matthew has been coding since he was 6 years old.
