Statistical Concepts for Excelling Using Data Science

Data Science is based on statistical and probability theory notions that have been around for a long time. Having a firm grasp on the ten concepts and strategies discussed here is critical to your success in the field, and it’s also a popular topic for concept tests during interviews.

1) P-values

The supreme technical and precise definition of a p-value is the likelihood of getting a result that is equally or more extreme than the result assuming the null hypothesis is also extreme.

That makes logic when you think about it. In practice, if the p-value is smaller than the alpha, say 0.05, we’re implying that the outcome is less than 5% likely to have occurred by chance. Similarly, a 0.05 p-value is equivalent to saying, “5% of the time, we would see this by chance.”

2) Confidence Intervals and Hypothesis Testing

The association between confidence intervals and hypothesis testing is very strong. The confidence interval proposes a range of values for an unknown parameter and is then linked to a level of assurance that the true parameter is within the indicated range. In medical research, confidence intervals are frequently used to give researchers a more solid foundation for their estimates.

To present an example, a confidence interval can be written as “10 +/- 0.5” or [9.5, 10.5].

3) Z-tests vs. T-tests

Understanding the distinctions between z-tests and t-tests, as well as when and how to employ each of them, is essential in statistics.

A Z-test is a hypothesis test that employs the z-statistic and uses a normal distribution. When you know the population variance or don’t know the population variance but have a high sample size, a z-test is utilized.

A T-test is a hypothesis test that uses a t-statistic and a T-distribution. When you don’t know the population adjustment and have a small sample size, you’ll utilize a t-test.

You can use the graphic below as a guide to help you decide which test to use:

4) Linear regression and its assumptions

One of the most basic methods for estimating relationships between a dependent variable and one or more independent variables is linear regression. In plain terms, it entails determining the ‘best-fit line’ between two or more variables.

Reducing the squared distances between the points and the line of best fit is known as minimizing the sum of squared residuals, and it is used to find the line of best fit. A residual is just the difference between the predicted and actual values.

Consider the image above if you’re still not convinced. When comparing the green and red lines of greatest fit, notice how the green line’s vertical lines (residues) are significantly larger than the red line’s. This is understandable because the green line is so distant from the points that it isn’t an accurate representation of the data!

5) Logistic regression

The likelihood of a discrete quantity of events, often two, is modeled using logistic regression, which is comparable to linear regression. You might, for example, want to know whether a person is alive or dead based on their age.

Logistic regression appears to be much more sophisticated than linear regression at first appearance, yet it only has one more step.

To begin, you must first generate a score using an equation similar to that of the line of best fit in linear regression.

The extra step is to pass the score you calculated before into the sigmoid function below to receive a probability back. After that, the probability can be transformed to a binary output of 1 or 0.

Methods such as gradient descent or maximum likelihood are used to identify the weights of the initial equation in order to calculate the score. I won’t go into much more depth because it’s beyond the scope of this essay, but you now know how it works!

6) Sampling techniques

Simple random, systematic, convenient, cluster and Stratified sampling are the five basic approaches to sample data.

Simple Random Sampling

To choose a sample, simple random sampling involves the use of randomly generated integers. A sample frame, or a list or database of all individuals of a population, is required at first. Then, using Excel, for example, generate a random integer for each element and take the first n samples you need.

Systematic Sampling

Sampling in a systematic manner is significantly simpler. Simply select one element from your sample, skip a predetermined number of elements (n), and then select the next element. Returning to our example, every fourth name on the list might be taken.

Convenience Sampling

Convenience sampling involves taking a sample from a population that is simple to reach, such as people outside a shopping mall. You merely take samples from the first persons you meet. This strategy is frequently seen as poor practice because your data may be viewed as biased.

Cluster Sampling

The first step in cluster sampling is to divide a population into groups or clusters. The fact that each cluster must be representative of the population distinguishes this method from stratified sampling. After that, you sample complete clusters at random.

If an elementary school has five different grades, eight classes, cluster random sampling may be employed, with only one class picked as a sample.

7) Central Limit Theorem

The central limit theorem asserts that the distribution of sample means approaches that of a normal distribution.

Take a section from a data set and calculate the mean of that sample, for example. Once you’ve done this several times, you’ll be able to plot all of your means and frequencies on a graph and notice that a bell curve, also known as a normal distribution, has formed.

This distribution’s mean will be very similar to the original data. By enchanting larger samples of data and more samples overall, you can improve the accuracy of the mean and minimize the standard deviation.

8) Combinations and Permutations

Permutations and combinations are two somewhat different approaches of selecting objects from a set to generate a subset. Permutations take the order of the subset into account, whereas combinations do not.

If you’re operating on network security, pattern analysis, operations research, or anything else, combinations and permutations are crucial. Let’s take a closer look at each one.

Permutations

Definition: A permutation of n elements is any specified order in which those n elements are arranged. There is n factorial (n!) ways to put n components together.

The number of r-tuples that may be taken from n different items is defined as the number of permutations of n objects taken r-at-a-time and is equal to the following equation:

Dr. Nancy Agnes, is the author of this guest blog, Technical head operation to the Tutors India #1 Academic writing company. Past 20+ years, they are offering research guidance to bachelor, master and Ph.D. students