Life is a struggle to overcome unseen and unexpected obstacles at the end of which the traveler will find illumination and enlightenment. Replicate this quest in your home by moving light switches away from doors and over to the far side of each room.* ~ Wisdom of Wrong Shui.

What is Statistics?

The term statistics refers to a set of mathematical procedures for organizing, summarizing, and interpreting information.

Representing information using facts and figures to inform and save time.

Statistics are used to organize and summarize information so that the researcher can see what happened in the research study and can communicate the results to others.

A population is the set of all the individuals of interest in a particular study.

A Sample is a set of individuals selected from a population, usually intended to represent the population in a research study.

A Variable is a characteristic or condition that changes or has different values for different individuals.

The measurement obtained from each individual is called a datum, or more commonly, a score or raw score. The complete set of scores is called the data set or simply the data.

Data are measurements or observations. A data set is a collection of measurements or observations.

A parameter is a value, usually a numerical value, that describes a population usually derived from measurements of the individuals in the population.

A statistic is a value, usually a numerical value, that describes a sample and derived from measurements of individuals in the sample.

A comparison between descriptive and inferential statistical methods

Descriptive statistics are statistical procedures used to summarize, organize, and simplify data. Common practices include summaries using tables or graphs to visualize entire set of scores, computing average to summarize a set of scores using a single descriptive value.

Inferential statistics consists of techniques that allow us to study samples and then make generalizations about the populations from which they were selected.

Although samples are generally representative, it is naturally impossible to achieve samples that perfectly and accurately reflect the entire population. A Sampling Error is a naturally occurring error between a sample statistic and the corresponding population parameter.

A Frequency distribution is an organized tabulation pf the number of individuals located in each category on the scale of measurement. A frequency distribution can be structured using a table or a graph, either of which present a set of categories and the participants per category measured/observed.

Introduction to Hypothesis Testing

Hypothesis testing is an inferential procedure that uses the data from a sample to draw a general conclusions about a population.

The process of hypothesis testing begins with a hypothesis about an unknown population. Then a sample is selected, and the sample data provided evidence that either supports or refutes the hypothesis.

Consider a hypothesis testing illustration where the mean of a sample is used to test a hypothesis about an unknown mean of a population. This assumes that the sample is extracted from the population. We begin with an unknown population, generally a population that has received a treatment. The question is to determine whether the treatment has an effect on the population mean.

The 4 Steps Process of Hypothesis Testing

1. State the null hypothesis (H0) and select the alpha level (p-value). The null hypothesis states there is no effect or no change. In this case, H0 states that the mean for the treated population is the same as the mean before treatment. The alpha level, usually α = .05 or α = .01, provides a definition of the term very unlikely and determines the risk of a Type I error. Also state an alternative hypothesis (H1), which is the exact opposite of the null hypothesis.