Statistics is the study of collecting, analyzing, interpreting, visualizing, and organizing data. There are mainly two types of statistics: descriptive and inferential. Descriptive statistics involves analyzing, organizing, and visualizing data so that it's easy for people to understand. Inferential statistics focuses on predicting the characteristics of a population from the sample data. You will learn more about inferential statistics in this topic.
Inferential statistics
Inferential statistics is a branch of statistics where you collect part of the data from a large set to make predictions about the characteristics of overall data. It mainly focuses on drawing conclusions and predicting outcomes from the data you gather. Let's look at an example.
Imagine there is a box full of shapes; the entire box represents a population. Let us take a certain amount of shapes out of the bigger box to a smaller box. When the smaller box is later analyzed, certain information is gathered. The gathered information is later used to make predictions about the shapes in the larger box, this process is known as inferential statistics.
Population and sample
In statistics, a population is all the individuals, objects, or events that we want to study. It's the entire group we want to understand better. You define a population by specific features or criteria. For example, the population might be all college students at a certain university, all cars made by a particular company in one year, or all people registered to vote in a country. A population can be either large or unlimited, based on the situation.
A sample, however, is part of the population; it's a smaller group selected from the overall population. The sample should represent the population well so that we can learn from the sample to make conclusions about the entire group. For instance, if we want to know the average height of adults in a country, we can't measure everyone, so we choose a sample of adults from that country and measure their heights.
Introduction to hypothesis testing
Hypothesis testing is a fundamental concept in statistical inference that allows us to make decisions or draw conclusions about a population based on sample data. Hypothesis testing is a key concept in inferential statistics. It's a method used to make decisions or draw conclusions about a population based on sample data. Suppose you're a teacher and you believe that drinking coffee improves exam performance. To test this hypothesis, you could compare the exam scores of students who drink coffee with those who don't. If the coffee drinkers consistently score higher, you might conclude that coffee does indeed improve performance. But remember, correlation does not imply causation! There could be other factors at play.
Hypothetical testing is a statistical method that is used in making decisions using data from a study. It allows us to make evidence-based decisions by comparing our observed data with what we expected to happen under a specific hypothesis.
In hypothesis testing, we start with an initial claim, called the null hypothesis (denoted as H0), which typically represents a statement of no effect or no difference. For example, in the context of a drug trial, the null hypothesis might be that there is no difference in effect between the drug and a placebo.
We also have an alternative hypothesis (denoted as H1 or Ha), which is what we might believe to be true or hope to prove true. In the drug trial example, the alternative hypothesis might be that the drug has a different effect than the placebo.
Based on the test statistic, we either reject or fail to reject the null hypothesis.
For example:
Hypothesis Testing Scenario
Imagine you're working in the HR department of a large tech company. You've been hiring software engineers for a while and you've noticed that candidates who have prior experience in the tech industry tend to perform better in the technical interview compared to those who are fresh out of college.
However, you want to confirm your observation with statistical evidence before making any decisions about changing the hiring process. So, you decide to perform a hypothesis test.
Hypotheses
Null Hypothesis (H0): There is no significant difference in the performance of technical interviews between candidates with prior tech industry experience and those without it.
Alternative Hypothesis (H1): Candidates with prior tech industry experience perform significantly better on technical interviews than those without them.
Test
You would then conduct a test to gather data. This could involve looking at the interview scores of a sample of candidates who have tech industry experience and a sample of candidates who don't.
Results
After you've collected the data, you will compare the means of the two groups. If the mean score of the group with industry experience is significantly higher, you might reject the null hypothesis in favor of the alternative.
Conclusion
Inferential statistics is a very strong tool for understanding the world around us. By making educated guesses about large populations based on smaller samples, we can conclude and make decisions in a wide range of fields, from business and economics to science and healthcare. So next time you're at a party and someone asks you to guess how many jelly beans are in the bowl, you'll know what to do!