Category: Statistics

Learning statistics and data science can open the doors to a truly rewarding career. With the right level of education, you’ll have access to millions of job openings across all the top companies on Earth. Getting started is easy, too. You just have to take the best intro courses in statistics and data science to see if this is the right path for you. Here are five courses to consider as you look toward this promising career path.

Practical Statistics

In the ‘Practical Statistics’ class, the coursework will teach you how to draw accurate conclusions from data sets using key statistical techniques. To excel in this class, you’ll need to have a good understanding of SQL and Python, preferably while using NumPy or pandas libraries.

Throughout the course, you will study statistics and data science concepts for 35 hours, starting with Simpson’s Paradox. Additional modules will teach you about Bayes Rule, hypothesis testing, how to perform A/B tests, and so much more.

Data Science Specialization

John Hopkins University created its ‘Data Science Specialization’ collection to help budding professionals explore this career path in full. This collection has ten interconnected courses that introduce all the key skills you will need in this field, such as:

• R programming
• Machine learning
• Data analysis
• Debugging
• GitHub

The courses begin with ‘The Data Scientist’s Toolbox,’ which goes over all the tools, data, and questions you will use to complete your day-to-day job duties. After that, it’s time to finish the collection of courses with the ‘Data Science Capstone’ where you’ll create a useable data product that shows off your skills.

Statistics for Data Science and Business Analysis

‘Statistics for Data Science and Business Analysis’ helps you build the initial skills needed to become a successful data scientist. You will start with the fundamentals of statistics before moving on to how to plot data, estimate confidence intervals, and complete hypothesis testing.

The course introduces each concept with well-written articles, on-demand videos, and downloadable resources. By the end of the course, you’ll know how to work with many different types of data and make excellent data-driven decisions.

Data Science: Statistics and Machine Learning Specialization

For an in-depth exploration of data scientist skills, sign up to complete the ‘Data Science: Statistics and Machine Learning Specialization’ collection. In this five-course series, you will get to learn about performing regression analysis, using data to draw accurate conclusions, and building prediction functions.

The courses begin with ‘Statistical Interference,’ which teaches you how to analyze data and form reasonable conclusions. Course three dives into ‘Practical Machine Learning,’ while the fourth course is about ‘Developing Data Products.’ You’ll get to show off what you learned in the fifth course by completing a capstone project.

MicroMasters Program in Statistics and Data Science

The ‘MicroMasters Program in Statistics and Data Science’ introduces all the key statistics, data science, and machine learning concepts you’ll need in your career. This course is more than just a quick exploration of the subject. You’ll spend 10 to 14 hours a week for a little over a year completing the program.

Your educational journey will begin with a look at probability before moving on to the fundamentals of statistics. Next, you will have a chance to learn machine learning with Python using linear models and deep learning. A capstone exam completes those studies, allowing you to dive into either data analysis in social science or statistics modeling and computation in applications.

Upon completing these courses, you should have a good idea of whether you want to pursue a career in statistics and data science. If you’d like to move forward, review the job listings that interest you, and then get to work on ensuring you have the right level of education for that

In statistics, the concept of sampling is fundamental to making inferences about a population based on a subset of data. When we collect data from a sample, we want to make sure that it is representative of the larger population. One way to assess whether a sample is representative is by examining the distribution of the data. Let’s explore different types of distributions that can arise when sampling a population. 

Normal Distribution 

The normal distribution is perhaps the most well-known probability distribution. It is symmetric and bell-shaped, and many natural phenomena follow this distribution, such as the heights or weights of people, scores on standardized tests, and measurement errors. The mean and standard deviation determine the location and shape of the distribution, respectively. A normal distribution has several desirable properties, such as the 68-95-99.7 rule, which states that about 68%, 95%, and 99.7% of the data fall within one, two, and three standard deviations of the mean, respectively. 

Uniform Distribution 

A uniform distribution occurs when all values within a given range are equally likely to occur. For example, if we flip a fair coin, the probability of getting heads or tails is 0.5, so the distribution of outcomes is uniform. The uniform distribution is often used in simulation and modeling, such as in Monte Carlo methods. 

Binomial Distribution 

A binomial distribution arises when we have a fixed number of independent trials, each with a binary outcome (success or failure), and we want to know the probability of getting a certain number of successes. For example, if we flip a coin 10 times, the number of heads we get follows a binomial distribution. The distribution is determined by the number of trials, the probability of success, and the number of successes. 

Poisson Distribution 

The Poisson distribution is used to model the probability of a certain number of events occurring in a given time or space interval, assuming they occur independently of each other and at a constant rate. The distribution is characterized by a single parameter, the average rate of occurrence. It is often used in fields such as biology, finance, and engineering to model rare events, such as accidents, defects, or failures. 

Exponential Distribution 

The exponential distribution is used to model the time between two events that occur independently of each other and at a constant rate. For example, the time between customer arrivals at a store or the time between equipment failures in a factory can be modeled using the exponential distribution. The distribution is characterized by a single parameter, the rate parameter, which determines the expected time between events. 

Gamma Distribution 

The gamma distribution is a family of continuous probability distributions that generalizes the exponential distribution. It is often used to model waiting times or durations in complex systems. The gamma distribution is characterized by two parameters, the shape parameter, and the scale parameter. 

These are just a few examples of the many distributions that exist in statistics. When sampling from a population, it is important to understand the underlying distribution of the data to ensure that the sample is representative. If the data do not follow a known distribution, it may be necessary to use non-parametric methods, which do not assume a specific distribution. 

In conclusion, different types of distributions can arise when sampling a population, and each distribution has its own characteristics and applications. By understanding the properties of these distributions, we can better interpret and analyze data and make informed decisions based on the information at hand.

In statistics, the Poisson distribution is used to model the probability of a certain number of events occurring in a given time or space interval. It is particularly useful in situations where the events occur independently of each other and at a constant rate. Understanding the Poisson distribution is essential for calculating probabilities of events and making informed decisions based on data. 

The Poisson distribution is named after French mathematician Siméon Denis Poisson, who introduced it in the early 19th century. It is often used in fields such as biology, finance, and engineering to model the number of occurrences of rare events, such as accidents, defects, or failures. 

The Poisson distribution has only one parameter, λ, which represents the average rate of occurrence of the events. The probability of k events occurring in a given interval of time or space is given by the formula: P(k) = (e^(-λ) * λ^k) / k! where e is the mathematical constant approximately equal to 2.71828, and k! denotes the factorial of k. 

To use the Poisson distribution, it is important to first determine the value of λ, which represents the expected number of events in the interval of interest. For example, suppose a factory produces an average of 3 defective parts per hour. To calculate the probability of having 5 defective parts in a one-hour interval, we can use the Poisson distribution with λ = 3: P(5) = (e^(-3) * 3^5) / 5! ≈ 0.1008. This means that the probability of having 5 defective parts in a one-hour interval is approximately 10.08%. 

The Poisson distribution can also be used to calculate the expected number of events in a given interval. For example, if we know the probability of having 2 accidents per day in a certain location, we can use the Poisson distribution to estimate the expected number of accidents in a week: λ = 2 accidents per day * 7 days per week = 14 accidents per week. 

By using the Poisson distribution with λ = 14, we can calculate the probability of having a certain number of accidents in a week and make informed decisions based on the expected frequency of events. 

One important property of the Poisson distribution is that it assumes the events occur independently of each other and at a constant rate. This means that the probability of an event occurring does not depend on whether other events have occurred in the past or are expected to occur in the future. 

However, in practice, this assumption may not always hold true. For example, if a factory produces defective parts, the probability of having additional defects may increase if the root cause of the defects is not addressed. In such cases, it may be necessary to use other statistical methods to model the relationship between the events and identify potential causes. In conclusion, the Poisson distribution is a powerful tool for modeling the probability of rare events occurring in a given time or space interval. By understanding the Poisson distribution and calculating probabilities of events, we can make informed decisions based on data and identify potential areas for improvement. However, it is important to remember that the Poisson distribution assumes the events occur independently of each other and at a constant rate and that other statistical methods may be necessary in cases where this assumption does not hold true.

Correlations are a key concept in statistics that describe the relationship between two or more variables. They are used in a wide range of statistical tests, and their role is crucial for drawing accurate conclusions from data. 

A correlation coefficient is a measure of the strength and direction of the relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation. Correlations can be calculated using various methods, including Pearson’s correlation coefficient, Spearman’s rank correlation coefficient, and Kendall’s tau. 

Correlations play an important role in statistical tests because they provide information about the association between variables. For example, in a medical study, researchers might be interested in whether there is a relationship between a certain medication and a particular symptom. By calculating the correlation coefficient between the medication and the symptom, they can determine the strength and direction of the association. 

Correlations are significant in regression analysis, which is a statistical method used to model the relationship between a dependent variable and one or more independent variables. In regression analysis, the strength and direction of the correlation between the dependent variable and the independent variables are used to predict the value of the dependent variable. 

When conducting a statistical test, the presence of correlations can affect the validity of the results. For example, in a study comparing the effectiveness of two treatments for a particular condition, if the two treatments are correlated with other variables, such as age or gender, the results may be biased. To address this issue, researchers may use methods such as stratification or regression analysis to control for the effects of these variables. 

Correlations also play a role in hypothesis testing, which is a statistical method used to test whether there is a significant difference between two groups or variables. In hypothesis testing, the correlation coefficient is used to determine the strength and direction of the relationship between the two variables being compared. 

If the correlation between the variables is strong, it may indicate there is a causal relationship between them. However, it is important to remember that correlation does not imply causation. Just because two variables are strongly correlated does not necessarily mean that one causes the other. 

It is also important to note that the presence of correlations can affect the power of a statistical test. Power refers to the probability of rejecting the null hypothesis when it is actually false. If the variables being compared are highly correlated, it may be more difficult to detect a significant difference between them, even if one exists. 

In conclusion, correlations play a crucial role in statistical tests by providing information about the relationship between variables. They are particularly important in regression analysis, hypothesis testing, and controlling for the effects of confounding variables. Understanding the role of correlations in statistical tests is essential for drawing accurate conclusions from data and ensuring the validity of statistical analyses. However, it is important to remember that correlation does not imply causation and that the presence of correlations can affect the power of a statistical test.

In statistics, confidence levels are used to indicate the degree of uncertainty in a given estimate or hypothesis. They are typically represented as a percentage or a range of values, and they are based on a variety of factors, including the sample size, the level of significance, and the confidence interval. 

One important concept related to confidence levels is the alpha value, also known as the level of significance. The alpha value is a measure of how confident we want to be in our statistical test. Specifically, it represents the maximum probability of making a type I error, or rejecting a null hypothesis that is actually true. In other words, it is the probability of incorrectly concluding that there is a significant difference between two groups or variables when in fact there is no difference. 

The alpha value is typically set at 0.05, which means that we are willing to accept a 5% chance of making a type I error. This value is somewhat arbitrary, but it is widely used in many fields of research. Some researchers may choose a different alpha value depending on the nature of their study and the potential consequences of a type I error. For example, in medical research, where the consequences of a false positive can be significant, a lower alpha value may be used. 

When conducting a statistical test, the alpha value is used to determine the critical value, which is the value that separates the rejection region from the acceptance region. The rejection region is the area of the distribution where the test statistic falls when the null hypothesis is rejected, while the acceptance region is the area where the test statistic falls when the null hypothesis is accepted. 

If the test statistic falls within the rejection region, we reject the null hypothesis and conclude that there is a significant difference between the groups or variables being compared. If the test statistic falls within the acceptance region, we fail to reject the null hypothesis and conclude that there is no significant difference between the groups or variables being compared. 

It is important to note that the alpha value is not the same as the confidence level. The confidence level is the percentage of times that the true population parameter will be contained within the confidence interval, given a large number of samples. For example, if we construct a 95% confidence interval, we can say that if we were to repeat the experiment many times, 95% of the confidence intervals we construct would contain the true population parameter. 

In conclusion, the alpha value is a key concept in statistics that is used to determine the critical value in a statistical test. It represents the maximum probability of making a type I error and is typically set at 0.05. While it is an arbitrary value, it is widely used in many fields of research. Understanding the alpha value is crucial for interpreting statistical tests and drawing accurate conclusions from data.

Hypothesis testing is a crucial part of statistics, and understanding how to find the critical value is a fundamental skill for anyone studying the subject. But, if you’re struggling to make sense of it all, don’t worry—we’ve got you covered! Here are five tips to help you find that elusive critical value. 

1. Understand the Basics of Hypothesis Testing 

Before you can understand how to find the critical value, you need to understand what hypothesis testing is and why it’s important. Hypothesis testing is a method used by researchers to test whether or not a certain statement about a population is true. 

It involves setting up two different hypotheses (one null and one alternative) and then using statistical methods to determine which one is more likely to be true based on the evidence available. It’s an important tool for researchers as it allows them to draw conclusions from data without having to conduct further experiments or surveys. 

2. Know Your Alpha Level 

Your alpha level indicates how confident you are in your results. It determines how strict or lenient your test criteria will be—the higher your alpha level, the stricter your criteria will be, and vice versa. 

Most commonly, the alpha level used in hypothesis testing is 0.05, but that number can vary depending on the type of research being conducted and the researcher’s preferences. Understanding your alpha level is key when finding the critical value as it helps you decide which probability distribution chart to use when looking up values in tables (more on this below).  

3. Choose Your Distribution Chart 

Once you know your alpha level, it’s time to choose which probability distribution chart you want to use when looking up values in tables—and there are two main types: normal distribution charts and t-distribution charts. 

The normal distribution chart will be used if your sample size (n) is large enough; if n < 30 then you should use a t-distribution chart instead as this will give more accurate results for small samples of data.  

4. Calculate Your Degrees of Freedom 

The degrees of freedom (df) tell us how many values we have “freely available” for calculating our statistics given our sample size (n). In most cases df = n – 1; however, there are some exceptions so make sure you double-check before proceeding with calculations!   

5. Look Up Your Critical Value  

Once you have calculated your df and decided which chart to use, it’s just a case of looking up your critical value in either a normal or t-distribution table (depending on which one you chose above). This is usually given at two different levels—alpha/2 (for one-tailed tests) and alpha (for two-tailed tests)—but again this may vary depending on which type of research you are conducting so make sure you double-check before proceeding!   

In conclusion, finding the critical value in hypothesis testing can seem like an overwhelming task but with these five tips under your belt, it doesn’t have to be! By understanding what hypothesis testing is all about, knowing your alpha level, choosing between normal and t-distribution charts correctly, calculating degrees of freedom accurately, and finally looking up values in tables appropriately; finding that elusive critical value has never been easie.