Introductory Statistics

The field of statistics is vast and utilized by professionals in many disciplines. Statistics has a place in science, technology, engineering, medicine, psychology and many other fields. Results from statistical analysis underlying both scientific and heuristic reasoning, and therefore, it is important for everyone to grasp basic statistical methods and operations. A brief overview of common statistical methods and analytical techniques is provided herein to be used as a reference and reminder material for professionals in a broad array of disciplines. 

Data captured during analysis can be easily summarized using visual techniques such as graphing. Graphing is utilized to both summarize and convey information in a clear and readable format. Graphing techniques discussed in this chapter include frequency distributions, histograms, box plots and Pareto charts.

A commonly used statistical measure is the measurement of probability. Probability is governed by both additive and multiplicative rules. These rules determine if events are independent of one another or dependent on previous or related outcomes. Conditional probability governs events that are not independent of one another and helps researchers to better make predictions about future datasets. 

Discrete random variables are variables that can only take on a countable number of discrete or distinct variables. Only a finite number of values can be obtained for the result to be a discrete random variable. Discrete variables can be visualized or understood as a binomial distribution. The outcome of a binomial distribution is how often a particular event occurs in a fixed number of times or trials.

Distributions of data give important information about the dataset, both to researchers and to analysts. Continuous random variables are those variables whose outcomes are measured instead of random variables that are counted. These variables can be handled using probability density functions and cumulative distribution functions. Both have appropriate times and usage cases. 

Sampling of a distribution and as well as how to treat the sampling distribution of the sample mean is an important topic for understanding statistics. The central limit theorem, when applied to this type of dataset can allow researchers to make predictions about future datasets as well as to better understand current datasets. Normally distributed populations are important to correctly treating the data occurring within the dataset

It is critically important for researchers to select the correct sample size to determine the population means. By understanding the difference between small and large sample sets, researchers can then construct intervals of confidence that assist in determining the population means. Confidence intervals are the margins of the error present within the dataset and are included to show the confidence of the researcher in the integrity of their dataset. Common confidence intervals are 90%, 95%, and 99%. The Z confidence level is calculated to show where the mean is likely to fall, and the T confidence level is used only when the sample size is smaller than 30 samples.

Hypothesis testing is a simple way to construct information about a dataset and to determine if that information is true or false. Another method to think about hypothesis testing is to use it as a way to decide whether an assumption about a dataset succeeds and is supported or fails and is not supported. It is used frequently in science and medicine to better understand the effects of drugs and treatments.

Researchers use correlation and regressions to show the relationships between factors or scenarios in a dataset. These types of analyses are important to all aspects of statistical analysis and are a common way to report connections between factors in a data set. This section will address basic linear correlation and regression techniques.

Ethical behavior by researchers, analysts and statisticians is paramount to the creation and reporting of data in all fields. Without ethics, data obtained and analyzed cannot be relied upon. A short discussion of ethical standards for all involved in data handling, research and statistical analysis is included, as this important aspect of the field cannot be understated.