Most professional professions nowadays rely heavily on statistical methods. In a competitive job market, insight into statistics and statistical methods offers an important advantage. But it is also important to understand statistics, even if you will never use it in your work. Understanding statistics can help you make better choices because you are bombarded every day with statistical information from news reports, advertisements, political campaigns, and surveys. A good understanding of the statistical reasoning - and in some cases statistical misconceptions - underlying these judgments will help deal with all this information.

How to use data to answer statistical questions?

Data is the information we gather with experiments and surveys.

Statistics is the art and science of designing studies and analyzing the data that those studies produce. Its ultimate goal is translating data into knowledge and understanding of the world around us. In short, statistics is the art and science of learning from data.

Researchers want to investigate questions in an objective manner. Statistical methods make that possible. Statistical problem solving is an investigative process that involves four components:

• Think of a statistical question.

• Gather data.

• Analyze the data.

• Interpret the results.

Statistics has three main components for answering a statistical question:

• Design: thinking of how to get the data necessary to answer the question.

• Description: the obtained data needs to be summarized and analyzed.

• Inference: making decisions and predictions based on the obtained data for answering the question. (Infer means to arrive at a decision or prediction by reasoning from known evidence).

Statistical description and inference are complementary to each other. Statistical description provides useful summaries and helps find patterns in your data, and to be able to make predictions and decide whether observed patterns are meaningful, it is useful to use inference.

We need to think carefully about the questions that we want to answer by analyzing data. The nature of the statistical questions has an impact on design, description and inference.

The word probability is used to refer to a framework for quantifying how likely various possible outcomes are.

What is a sample?

Subjects are the entities that are being measured in a study. These can be people, but do not have to be.

All the subjects of interest are referred to as the population. In practice, we usually have data for only some of the subjects who belong to that population. This smaller size of subjects is called a sample. We plan to gather data from the sample. The sample is often randomly selected. It is more practical to get data for a sample, because obtaining data from an entire population is often too costly and timeconsuming.

Descriptive statistics refers to methods for summarizing the collected data (where the data constitutes either a sample or a population). The summaries usually consist of graphs and numbers such as averages. The main purpose of descriptive statistics is to reduce the data to simple summaries without distorting or losing much information.

If we want to make a decision or prediction about an entire population, but we only have data for a sample, inferential statistics are used. Inferential statistics thus refers to methods of making decisions or predictions about a population, based on data obtained from a sample of that population. 

Reporting the likely precision of a prediction is an important aspect of inferential statistics.

The absolute size of the sample matters much more than the size relative to the population total.

It is crucial to distinguish between to following terms:

• Parameter: a numerical summary of the population.

• Statistic: a numerical summary of sample taken from the population.

Because the true parameter values are almost always unknown, we use sample statistics to estimate the parameter values.

A sample tends to be a good reflection of a population when each subject in the population has the same chance of being included in that sample. That’s the basis of random sampling, which is designed to make the sample representative of the population. Important to know:

• Random sampling allows us to make powerful inferences about populations.

• Randomness is also crucial to performing experiments well.

Samples do vary. The measure of the expected variability from one random sample to the next random sample is referred to as the margin of error.

Results are called statistically significant when the difference between the results for two condition groups is so large that it would be rare to see such a difference by ordinary random variation.

How do you make use of computers for statistics?

MINITAB and SPSS are two popular statistical software packages on college campuses. The TI-83+ and TI-84 graphing calculators, which have similar output, are useful as portable tools for generating simple statistics and graphs. The Microsoft Excel software can conduct some statistical methods, sorting and analyzing data with its spreadsheet program, but its capabilities are limited.

Large sets of data are organized in a data file, to make statistical analysis earlier. This file usually has the form of a spreadsheet. It is the way statistical software receives the data. 

Most studies design experiments or surveys to collect data to answer the questions of interest.

Databases are existing archived collections of data files. Sometimes it is adequate to use these databases to answer the questions of interest.