What is Statistics ?
Statistics can be a difficult subject to wrap your head around, but it’s important to have at least a basic understanding of the concepts . This guide will introduce you to the basics of statistics and help you Demystify some of the jargon :
- Statistical models :
A statistical model is a mathematical model that is used to describe or predict data . There are many different types of statistical models, but they all have one thing in common : they are all based on probabilities .
- Parameters :
Parameters are the variables in a statistical model that can be estimated from data . For example, in a linear regression model, the parameters are the slope and intercept .
- Estimators :
An estimator is a statistic that is used to estimate a population parameter . For example, the sample mean is an estimator of the population mean .
- Bias :
Bias is the difference between an estimator’s expected value and the true value of the population parameter being estimated . An estimator is biased if its expected value is not equal to the true value of the population parameter .
- Variance :
Variance is a measure of how spread out the values of an estimator are . An estimator with high variance is less reliable than one with low variance
- Central limit theorem :
The Central Limit Theorem states that the sampling distribution of a statistic will be approximately normally distributed, regardless of the underlying distribution of the population . This means that, even if the data come from a non-normal population, you can assume that it is normally distributed when estimating parameters .
- Confidence intervals :
A confidence interval is a range of values that is calculated from a sample of data, where the true population parameter is thought to lie within . These intervals are computed by taking the mean of the sample and adding/subtracting a certain number of standard errors . The larger the sample size, the narrower the confidence interval will be .
- Hypothesis testing :
Hypothesis testing is a method used to test whether a null hypothesis can be rejected or not . It involves calculating a test statistic from sample data and comparing it with the values from a known distribution . If the test statistic falls outside of the expected range, then we can reject the null hypothesis and accept an alternative hypothesis .
These are just a few of the common terms used in Statistics . It’s important to become familiar with these concepts so that you can understand and make use of statistical models and methods .
What Are The Types of Data Used In Statistics ?
There are two types of data : qualitative and quantitative . Qualitative data is descriptive and deals with non-numerical information, such as words or labels . It can be further divided into categorical and ordinal data . Categorical data is divided into a limited number of categories, such as hair color (blonde, brunette, red, etc .), while ordinal data has a defined order, such as 1st, 2nd, 3rd place in a race . Quantitative data is numerical and can be further divided into discrete and continuous data . Discrete data consists of whole numbers (no decimal places) while continuous data includes decimal places .
Examples of qualitative data include gender, race, opinions, education level, hair color and subjective labels such as “good” or “bad .” Examples of quantitative data include weight, height, age and number of siblings .
Qualitative data can be manipulated and analyzed using qualitative methods such as statistical analysis, correlation, non-parametric testing and regression analysis . Quantitative data can be manipulated and analyzed using quantitative methods such as mean, median and mode analysis, correlation, parametric tests and regression analysis .
The type of data used for a particular study or analysis will depend on the purpose and goals of the study . Both qualitative and quantitative data can be useful in providing insights into a problem . However, it is important to choose the most appropriate type of data given the objectives of the study .
No matter which type of data is used, it is important to ensure that it is reliable, valid and free from bias . It should be collected in a systematic and detailed manner and interpreted and analyzed accurately . Data accuracy is essential to ensure that the results are both meaningful and helpful .
What Are The Measures of Central Tendency and Dispersion (Mean, Median, Mode, Range) ?
There are three main measures of central tendency : the mean, the median and the mode . The mean is the arithmetic average of a set of numbers and is the most commonly used measure of central tendency . The median is the middle value in a set of numbers and is less affected by outliers than the mean . The mode is the most frequently occurring value in a set of numbers .
The range is a measure of dispersion and is simply the difference between the largest and smallest values in a set of numbers . Other measures of dispersion include standard deviation and variance .
What About Probability Theory and Rules ?
In mathematics, probability theory is the study of random phenomena . Probability theory is used to describe the behavior of systems that are governed by chance . In other words, it’s the math of luck .
There are two types of probability : classical and empirical . Classical probability is based on theoretical models, such as a coin toss or a deck of cards . Empirical probability is based on observed data, such as from a poll or an experiment .
Probability can be expressed in terms of proportions, percentages or odds . For example, the proportion of times an event occurs over the number of trials is the probability of that event occurring . The percentage is simply the proportion multiplied by 100% . Odds are a ratio of the number of ways an event can occur divided by the number of events that cannot occur .
There are four basic rules of probability : addition, multiplication, generalization and Bayes’ theorem . These rules allow us to calculate probabilities for various events happening simultaneously .
The addition rule says that if there are two possible outcomes (A and B) and we want to know the probability that either A or B will happen, we simply add the individual probabilities together :
P(A or B) = P(A) + P(B) – P(A and B ) .
The multiplication rule says that if there are two possible outcomes (A and B) and we want to know the probability that both A and B will happen, we need to multiply the individual probabilities together :
P(A and B) = P(A) * P(B) .
The generalization rule says that if there are more than two possible outcomes (A, B and C), we need to add all the individual probabilities together :
P(A or B or C) = P(A) + P(B) + P(C) .
Finally, Bayes’ theorem is a formula for calculating conditional probabilities . This states that if we know the probability of an event B given another event A has occurred (P(B\A)) and we know the prior probability of event A occurring (P(A)), then we can calculate the posterior probability of event B occurring (P(B)) . This can be expressed as follows :
P(B\A)=P(A and B)/P(A)
What Are The Different Types of Statistics ?
There are four different types of statistics :
- Descriptive Statistics :
This type of statistic summarizes data from a sample using tools such as means, medians and mode .
- Inferential Statistics :
This type of statistic uses a smaller sample to make predictions about a larger population . It employs techniques such as estimation and hypothesis testing .
- Predictive Statistics :
This type of statistic uses historical data to build models that predict future events . It is used in fields such as weather forecasting and stock market analysis .
- Prescriptive Statistics :
This type of statistic combines predictive and inferential techniques to recommend actions that can be taken to achieve desired outcomes . It is used in fields such as operations research and decision analysis .
These are the four main types of statistics but there may be many more within these categories as well .
What Are The Key Points To Know About Descriptive Statistics ?
Descriptive statistics are a branch of mathematics that deals with the collection, analysis, interpretation, presentation and organization of data . It is all about describing data .
There are two main types of descriptive statistics : univariate and bivariate . Univariate statistics deal with data that can be quantified or categorized into one variable, while bivariate statistics deal with two variables .
Common descriptors used in univariate statistics include mean, median, mode, range, IQR (Interquartile Range) and standard deviation . Mean is the arithmetic average of a set of numbers, while median is the middle value of a set of numbers . Mode is the most frequently occurring value in a set of numbers . Range is the difference between the largest and smallest values in a set of numbers . IQR is used to measure dispersion and is calculated by subtracting the 25th percentile from the 75th percentile . Standard deviation measures how far a set of numbers are spread out from the mean .
In bivariate statistics, common descriptors include correlation and regression . Correlation measures the strength and direction of the relationship between two variables, while regression predicts the value of one variable based on the other variable .
Both univariate and bivariate statistics can be used to describe data sets; however, they each have their own strengths and weaknesses . It is important to choose the appropriate type of descriptive statistic based on what information you are trying to learn from your data .
Descriptive statistics are helpful for transforming data into useful information . They help to summarize and make sense of large amounts of data, enabling researchers to draw meaningful conclusions about their findings .
What Are The Key Points To Know About Inferential Statistics (Chi-Square Test, ANOVA) ?
In order to understand inferential statistics, it is important to first understand some basic concepts . Central tendency measures, such as the mean and median, give us a way to describe the "center" of our data . Variability measures, such as the range and standard deviation, give us a way to describe how spread out our data is . Correlation and regression allow us to measure the relationship between two variables .
With this understanding of basic statistics, we can move on to inferential statistics . The most common types of inferential statistical tests are the chi-square test and ANOVA .
The chi-square test is used to determine if there is a significant difference between two or more categorical variables . For example, we might use a chi-square test to compare the proportion of males and females in a population who are left-handed .
ANOVA is used to compare the means of two or more groups . For example, we might use ANOVA to compare the average SAT scores for students in different grades .
Both the chi-square test and ANOVA require that certain assumptions be met in order for the results to be reliable . These assumptions include things like homogeneity of variance and normality of data . It is important to check for these assumptions before running any inferential statistical tests .
Overall, inferential statistics give us the tools to draw conclusions from data . They allow us to make conclusions about populations when we only have sample data available . This is an incredibly powerful tool for researchers and statisticians alike .
What Are The Key Points To Know About Predictive Statistics ?
Predictive statistics encompass a wide variety of methods used to identify patterns and relationships in data and then use those patterns to make predictions about future events . The key points to know about predictive statistics include :
- Predictive analytics is not a crystal ball, but rather a tool that can help organizations make more informed decisions .
- Predictive analytics is used extensively in a variety of industries, including healthcare, insurance, retail and manufacturing .
- Predictive analytics can be used for both short-term predictions (such as what product a customer is likely to buy next) and long-term predictions (such as which patients are at risk for developing certain diseases) .
- There are many different techniques that fall under the umbrella of predictive analytics, including regression analysis, time series analysis, machine learning and artificial intelligence .
- Data is key when using predictive analytics – the more data you have, the better your predictions will be .
- It’s important to use a mix of techniques and tools when leveraging predictive analytics, depending on the problem that needs to be solved .
- Predictive analytics can help organizations improve efficiency, reduce costs and make better decisions .
- Ethical considerations should always be kept in mind when using predictive analytics .
What Are The Key Points To Know About Prescriptive Statistics ?
When it comes to statistics, there is a lot of information out there that can be confusing . But, don’t let that stop you from learning about this important topic ! Prescriptive statistics is a branch of math that deals with making predictions and recommendations based on data . Here are the key points to know about prescriptive statistics :
- Prescriptive statistics uses mathematical models to make predictions and recommendations .
- The predictions and recommendations made by prescriptive statistical models are based on past data .
- There are different types of prescriptive statistical models, each with its own strengths and weaknesses .
- It is important to understand the limitations of prescriptive statistical models before using them to make decisions .
- Prescriptive statistical models can be used in any field or industry and provide valuable insights to decision makers .
- In order to accurately analyze data with prescriptive statistics, it is essential to have a strong understanding of the data and the underlying assumptions behind the models .
- It is important to be aware of potential biases in the data or the modeling assumptions when creating or using prescriptive statistical models .
- It is also important to consider any ethical implications of the predictions or recommendations made with prescriptive statistical models .
What Are Correlation and Regression ?
The concepts of correlation and regression are closely related and are used to measure the strength of the relationship between two variables . Correlation is a measure of how well two variables are linearly related, while regression is a technique used to predict the value of one variable based on the value of another .
Both correlation and regression can be used to understand the relationships between different variables in a data set . For example, you might use correlation to understand the relationship between height and weight or use regression to predict someone’s weight based on their height . In both cases, you would be measuring the strength of the linear relationship between the two variables .
Correlation is measured using a statistic called the correlation coefficient, which takes on values between -1 and 1 . A positive correlation coefficient indicates that as one variable increases, the other variable also increases; a negative correlation coefficient indicates that as one variable increases, the other decreases . The magnitude of the correlation coefficient indicates how strong the linear relationship is between two variables . For example, a small correlation coefficient (close to 0) would indicate a weak linear relationship, while a large coefficient (close to -1 or 1) would indicate a strong linear relationship .
Regression is a more complex statistical technique that can be used to predict the value of one variable based on the values of other variables . For example, you might use regression to predict someone’s weight based on their height and age . This type of prediction is called predictive modeling and it can be used to make predictions about future events or trends . regression models can also be used to understand the relationships between different variables in a data set, as well as to identify which variables are most important for predicting a particular outcome . In general, regression is a powerful tool for analyzing and understanding data .
Overall, correlation and regression are two closely related techniques used to measure the strength of linear relationships between two or more variables . Both can be used to understand the relationships between different variables in a data set, as well as to make predictions about future events or trends .
What Are The Statistical Software Packages ?
There are many different types of statistical software packages available on the market today . Some are designed for specific types of data analysis, while others are more general purpose . When choosing a statistical software package, it is important to consider what type of analyses you will be performing and whether the package has the required functionality .
The most popular statistical software packages are SAS, SPSS and R . SAS is a commercial package that is widely used in industry and academia . It is a powerful tool for data analysis but can be expensive to purchase . SPSS is another commercial package that is also widely used . It has a user-friendly interface and offers many features for data analysis . R is a free and open-source software package that is becoming increasingly popular in both industry and academia . It offers a wide range of capabilities for data analysis and is freely available to anyone .
When choosing a statistical software package, it is important to consider your budget, the type of data you will be analyzing and the type of analyses you will be performing . SAS, SPSS and R are all excellent choices for statistical software packages and offer different advantages depending on your needs .
Conclusion
Statistics can be a daunting and intimidating concept, but with the right knowledge and understanding, it doesn’t have to be . This article has aimed to demystify statistics by illustrating what statistical concepts are and providing an overview of some common tools used in data analysis .
With these basics under our belts, we can now confidently use basic analytical techniques on datasets that will give us important insights into business decisions or research questions that may come our way !
