Statistics for Data Science and Business Analysis

The first step of every statistical analysis you will perform is to determine whether the data you are dealing with is a population or a sample. Furthermore, we need to know the difference between a random sample and a representative sample.

Before we can start testing we have to get acquainted with the types of variables, as different types of statistical tests and visualizations, require different types of data.

In this lecture we show the other classification of variables - levels of measurement

Following the knowledge on types of data, we look into techniques for visualizing categorical variables, namely frequency distribution tables, bar charts, pie charts and Pareto diagrams.

Exercises on visualization techniques for categorical variables.

Following the categorization through the types of data, we look into the frequency distribution table for numerical variables.

Exercise on frequency distribution table for numerical variables.

Building up on the frequency distribution table, we learn how to illustrate data with histograms.

Exercise on histograms.

Descriptive statistics.

In this lecture we explore the different ways to demonstrate relationship between variables.

Exercise on cross tables and scatter plots.

This lesson will introduce you to the three measures of central tendency - mean, median and mode.

Exercise on the measures of central tendency.

In this lesson we show the most commonly used tool to measure asymmetry - skewness, and its relationship with the mean, median, and mode.

An exercise on skewness.

We start exploring the most common measures of variablity. This lesson focuses on variance.

An exercise on variance.

We build up on variance, by introducing standard deviation and the coefficient of variation.

An exercise on standard deviation and coefficient of variation.

We continue with the most common measure of interconnection between variables: covariance.

An exercise on covariance.

Correlation coeffcient - the quantitative representation of correlation between variables.

An exercise on the correlation coefficient.

This is the practical example on descriptive statistics. 

It's a hands-on activity covering all lessons so far - types of data; levels of measurement; graphs and tables for categorical and numerical variables, and relationship between variables; measures of central tendency, asymmetry, variability, and relationship between variables.

We apply all the acquired knowledge on a real-life data for a real estate company and create business analytics from scratch.

Exercises based on the practical example.

An introductory lesson that shows what is to follow in the section inferental statistics.

We explain what a distribution is, what types of distributions are there and how this helps us to better understand statistics.

We introduce the Normal distribution and its great importance to statistics as a field.

We look into the Standard Normal distribution by deriving it from the Normal distribution, through the method of standardization. We elaborate on its use for testing.

An exercise on the Standard Normal Distribution.

The Central Limit Theorem - one of the most important statistical concepts. Definition and an example.

We introduce the standard error - an important ingredient for making predictions.

We explore the estimators and estimates, and differentiate between the two concepts.

This is the heart of the section - confidence intervals.

We see our first example of the use of confidence intervals and introduce the concept of the z-score.

An exercise on confidence intervals.

Following several questions in the Q&A sections we have decided to add a lecture which digs a bit deeper into what confidence intervals are.

A little story about the inception of the Student's T distribution - a valuable tool when working with small samples.

We combine our knowledge on confidence intervals with that on the Student's T distribution, by making inferences using a small sample.

An exercise on confidence intervals, when population variance is uknown.

A deeper dive into the drivers of confidence intervals through the margin of error.

We show real life examples of confidence intervals. In this lesson, we focus on dependent samples, which are often found in medicine.

An exercise on confidence intervals for two means (dependent samples).

We carry on with the applications. This time the example is with independent samples, where the population variance is known.

An exercise on confidence intervals for two means (independent samples).

More often than not, we do not know the population variance, as it is too costly (or impossible) to have data on the whole population. We explore how to deal with the problem, through sample variance. We start from the simpler case, where we assume that the variance of the two samples is equal.

An exercise on confidence intervals for two means (independent samples).

We conclude the section on confidence intervals with the example on independent samples, where the variance is unknown and assumed to be different. That is the most common case.

This is a practical example on inferential statistics.

We apply all the knowledge we have on descriptive statistics and inferential so far.

The data is based on purchases in a shoe shop. We explore the sales of different products and shops, and try to manage the inventory of our company better.

This is a practical example on inferential statistics.

We apply all the knowledge we have on descriptive statistics and inferential so far.

The data is based on purchases in a shoe shop. We explore the sales of different products and shops, and try to manage the inventory of our company better.

Please find an exercise file and a solution file attached to this lecture.

Hypothesis testing is the heart of statistics. We start from the very basics: what are the null and alternative hypotheses. We show different examples and explain how to form hypotheses that are later to be tested.

Whenever we do hypothesis testing, we either accept or reject a hypothesis. In this lecture, we explain the rationale behind testing.

There are two errors one can make when testing - false positive and false negative. In order to be better statisticians, we must be acquainted with those issues. 

Building on our knowledge about confidence intervals, z-scores, and the ability to state hypotheses, we test our first hypothesis.

An exercise on hypothesis testing. Test for the mean, when population variance is known.

The level of significance determines whether a hypothesis should be accepted or rejected. In real life, we prefer to use a different measure - the p-value. 

Using our new p-value notion, we perform some t-tests.

An exercise on hypothesis testing. Test for the mean when population variance is uknown.

Similar to our confidence interval examples, there are different cases for testing. We test the mean for two dependent samples. 

An exercise on hypothesis testing. Dependent samples

We get into the more common case of independent samples. We explore a dataset on university grades for two departments: engineering and management.

We conclude the topic with an apple price example. It represents two independent samples that have variances which are assumed to be equal.