Introduction to statistics with MySQL

Introduction

In 2002, baseball manager Billy Bean decided to form a team not from the point of view of the players' star status, but with mathematically calculated strengths and weaknesses of players. As a result, they were able to win 20 consecutive games for the first time in the history of the league. The MIT Blackjack Team used to beat the house at blackjack in various casinos by card counting and using various other math-based techniques. This story is written in the book "Bringing Down the House" and in 2008 it turned into the film "21" with Jim Sturgess and Laurence Fishburne. What unites these two separate stories is that they show how people applied the use of statistics to search for insights into the data for their benefit. Unfortunately, we can't just open a large table with statistics and obtain useful and necessary information, so we need some tools to work with. One of the best and most convenient is – SQL.

In this article, we will embark on a journey to explore the essentials of statistics and its integration with SQL, highlighting its significance and providing practical examples.

Intro to statistics: some fundamentals

In nowadays world, statistics is playing a vital role in giving insights from data. If you apply statistical techniques to your data, you can identify patterns and trends, and uncover hidden relationships. Analyzing data to find insight is widely spread in completely different spheres such as business, healthcare, finance, and social sciences.

Here are some key reasons why statistics is crucial in data analysis:

• Data Interpretation: Statistics is a tool by which you can interpret data accurately. It helps you organize and summarize large datasets, making it easier to comprehend and draw conclusions from complex information.

• Data Validation: Statistics plays a crucial role in data analysis by helping analysts validate the quality and reliability of datasets. By utilizing statistical techniques, it becomes possible to identify outliers and anomalies, thus ensuring that the analysis is conducted using reliable and trustworthy data.

• Pattern Recognition: Statistics allows us to understand the past and predict the future by analyzing patterns and trends within data. By analyzing historical data, we can identify recurring patterns, forecast future trends, and make informed predictions.

• Decision Making: No CEO will make a crucial decision if their thoughts are not backed up by statistics. By examining statistical measures and drawing comparisons, analysts can evaluate different scenarios, weigh the risks, and make informed choices.

Now, let's explore some basic concepts that are essential in statistical data analysis:

1. Data Types: In statistics, data is categorized into several types: numerical (continuous or discrete) and categorical.

For instance, height and temperature are Numeric(continuous) data types. The number of children or quantity of products sold is a Numeric(discrete) data type. There cannot be 1.5 children. Examples of Categorical data types can be marital status (Single, Married, Divorced) or gender(male/female/other), you name it.

2. Variables: Variables are the characteristics or attributes that are being measured or observed in a study. They can be independent or dependent variables, and their analysis helps in understanding relationships and making predictions.

An example of an independent variable could be – Advertising Expenditure: The amount of money spent on advertising campaigns. For dependent variable – Sales Revenue: The total revenue generated from product sales.

3. Measures of Central Tendency: These measures provide information about the central or average value of a dataset.

Common measures include the mean (average), median (middle value), and mode (most frequently occurring value). These measures help in understanding the typical or representative value of the data.

4. Measures of Dispersion: Dispersion measures describe the spread or variability of data points within a dataset.

Common measures include the range, variance, and standard deviation. They provide insights into the distribution of data and the degree of variability.

By mastering these basic concepts of statistics, you as a data analyst can lay a solid foundation for analysis skills. These concepts form the building blocks for more advanced statistical techniques and enable analysts to extract meaningful insights from complex datasets.

SQL for data analysis

SQL for Data Analysis: Unleashing the Power of Statistical Measures

Structured Query Language (SQL) is not only a great tool for managing and manipulating databases but also an invaluable asset for data analysis. With SQL, you can leverage its rich set of functions and capabilities to calculate basic statistical measures, enabling them to gain insights into datasets and make informed decisions. Let's explore how SQL can be used to calculate these fundamental statistical measures.

You can use this data to create tables if you want to try this at home.

• Mean (Average): The mean is a standard statistical measure that represents the average value of a dataset. In SQL, you can utilize the AVG() function to calculate the mean. For example:

SELECT AVG(mark) AS average_mark
FROM mark;

This query calculates the average mark from the "mark_data" table and aliases the result as "average_mark."

• Median: The median is the middle value in a dataset when it is sorted in ascending or descending order. In SQL, the median can be computed using various techniques, such as using the PERCENTILE_CONT() or PERCENTILE_DISC() functions. Here's an example using PERCENTILE_CONT()

SELECT PERCENTILE_CONT(0.5) WITHIN GROUP (ORDER BY mark) AS median_mark
FROM mark;

This query calculates the median mark from the "mark_data" table using the PERCENTILE_CONT() function with a percentile value of 0.5.

• Mode: The mode represents the value(s) that occur most frequently in a dataset. SQL does not have a built-in function specifically for calculating the mode, but it can be derived using aggregation functions and grouping. For example:

SELECT subject_type, COUNT(*) AS frequency
FROM mark
JOIN subject_type ON subject_type.id = mark.subject_id
GROUP BY subject_type
HAVING COUNT(*) = (SELECT MAX(cnt) 
                   FROM (SELECT COUNT(*) AS CNT
                         FROM mark 
                         JOIN subject_type ON subject_type.id = mark.subject_id 
                         GROUP BY subject_type) AS subquery);

This query identifies the mode by grouping the data based on a specific column and selecting the value(s) with the highest count.

• Standard Deviation: The standard deviation measures the dispersion or variability of values in a dataset. SQL provides the STDDEV() function to calculate the standard deviation. Here's an example:

SELECT STDDEV(mark) AS mark_std_dev
FROM mark;

This query calculates the standard deviation of marks from the "marks" table.

By leveraging SQL's capabilities to perform mathematical calculations and aggregations, analysts can easily compute these basic statistical measures. These measures provide essential insights into the central tendency, variability, and distribution of data, enabling analysts to better understand their datasets.

Putting it all together

If you combine statistical concepts with SQL knowledge, you will be able to look deeper into data and get meaningful insights about a subject. By analyzing datasets, using statistical concepts and SQL, you could gain a comprehensive understanding of the data and be possible to make essential conclusions.

Let's see how we can put it all together.

Combining statistical concepts and SQL to analyze data

1. Hypothesis Testing: Hypothesis testing is a form of statistical inference that uses data from a sample to conclude a population parameter or a population probability distribution. (Source)

Hypothesis testing allows us to make probabilistic statements about population parameters. SQL can be employed to analyze data and perform hypothesis testing. For example, consider a scenario where you want to determine if there is a significant difference in sales between two faculties. You can use SQL to calculate the average mark for each faculty, perform a t–test or other relevant statistical tests, and draw conclusions about the significance of the difference.

Scenario: We want to determine if there is a significant difference in the average marks between two faculties: Gryffindor and Hufflepuff.

Null Hypothesis (H0): There is no significant difference in the average marks between Gryffindor and Hufflepuff.

Alternative Hypothesis (HA): There is a significant difference in the average marks between Gryffindor and Hufflepuff.

To test this hypothesis, we can use a two-sample t-test.

-- Calculate the average marks for Gryffindor faculty
SELECT AVG(m.mark) AS avg_mark_gryffindor
FROM mark m
JOIN students s ON m.student_id = s.id
JOIN faculty_name f ON s.faculty_id = f.id
WHERE f.name = 'Gryffindor';

-- Calculate the average marks for Hufflepuff faculty
SELECT AVG(m.mark) AS avg_mark_hufflepuff
FROM mark m
JOIN students s ON m.student_id = s.id
JOIN faculty_name f ON s.faculty_id = f.id
WHERE f.name = 'Hufflepuff';

-- Perform t-test
WITH gryffindor_marks AS (
  SELECT mark
  FROM mark m
  JOIN students s ON m.student_id = s.id
  JOIN faculty_name f ON s.faculty_id = f.id
  WHERE f.name = 'Gryffindor'
), hufflepuff_marks AS (
  SELECT mark
  FROM mark m
  JOIN students s ON m.student_id = s.id
  JOIN faculty_name f ON s.faculty_id = f.id
  WHERE f.name = 'Hufflepuff'
)
SELECT
  t.test_result,
  t.p_value
FROM (
  SELECT
    t.test_result,
    t.p_value,
    ROW_NUMBER() OVER (ORDER BY t.p_value) AS row_num
  FROM (
    SELECT
      t.test_result,
      t.p_value
    FROM (
      SELECT
        (avg(gm.mark) - avg(hm.mark)) / sqrt(variance(gm.mark) / count(gm.mark) + variance(hm.mark) / count(hm.mark)) AS test_result,
        (2 * (1 - abs(two_sided_p_value(avg(gm.mark) - avg(hm.mark), variance(gm.mark) / count(gm.mark) + variance(hm.mark) / count(hm.mark), count(gm.mark), count(hm.mark))))) AS p_value
      FROM gryffindor_marks gm, hufflepuff_marks hm
    ) t
  ) t
  WHERE row_num = 1;

This query calculates the average marks for Gryffindor and Hufflepuff faculties separately. Then, it performs a two-sample t-test to compare the means of the two groups. The result includes the test result (the difference in means divided by the standard error) and the p-value.

Note: The two_sided_p_value function in the query is a custom function that calculates the p-value for a two-sided t-test. You may need to define this function separately in your database.

2. Regression Analysis: Regression analysis allows us to understand the relationship between variables and make predictions. SQL can be used to build regression models and analyze data to identify the impact of independent variables on the dependent variable. For instance, using our dataset, you can use SQL to fit a linear regression model to predict an average mark based on factors such as faculty, minimal/maximal mark, and sex.

3. Data Visualization: Visualizing data is vital for gaining insights and communicating findings effectively. SQL can be combined with statistical concepts to create insightful visualizations. For example, you can use SQL to aggregate data, calculate summary statistics, and then visualize the results. With these visual results, you can produce new insights and make crucial conclusions.

By combining statistical concepts and SQL, analysts can conduct sophisticated data analysis, uncover patterns and relationships, and make informed decisions. These examples demonstrate the practical application of statistical concepts within the SQL framework, showcasing the versatility and power of this combination.

Conclusion

In this article, we explored the importance of statistics in data analysis and how to leverage SQL for basic statistical measures. We also discussed how statistical concepts and SQL can be combined to analyze data and provided case studies and examples to illustrate their practical application.

In conclusion, the fusion of statistics and SQL empowers data analysts to explore and derive insights from datasets. By strengthening your understanding of statistical concepts, and expanding your SQL skills, you can become a proficient data analyst capable of tackling complex data analysis tasks.