Inferential statistics Modules

inferential statistics to estimate population parameters from sample data, inferential statistics allow investigators to answer questions about relationships that might exist between two or more variables of interest (bivariate analyses). Inferential statistics help test initial hypotheses about “guessed at” relationships between study variables. In other words, investigators infer answers to quantitative research questions about populations from what was observed in sample data. In prior modules, you learned about study design options that maximize the probability of drawing accurate conclusions about the population based on sample data. Now we examine how to use inferential statistics to test bivariate hypotheses.

To understand our level of confidence in the conclusions drawn from these statistical analyses, we first need to explore the role played by probability in inferential statistics.

In this chapter, you will learn about:

• probability principles and the role of probability in inferential statistics
• principles of hypothesis testing and the “null” hypothesis
• Type I and Type II error.

Understanding Probability Principles

You think about and calculate probability often during the course of daily living—what are the chances of being late to class if I stop for coffee on the way, of getting a parking ticket if I wait another half hour to fill the meter, of getting sick from eating my lunch without washing my hands first? While we generally guess at these kinds of probability in daily living, statistics offers tools for estimating probabilities of quantitative events. This is often taught in terms of the probability of a coin toss being heads or tails, or the probability of randomly selecting a green M&Ms® candy from a full bag.

Let’s see what happens when we consider the probability of drawing a blue card from a deck of 100 Uno® cards—Uno® game card decks have equal numbers of Blue, Yellow, Red, and Green cards: 25 each (ignoring the un-numbered action and wild cards). In drawing one card from the deck, we have 100 possible outcomes—our draw could be any of the 100 cards. You may intuitively see that we have a 1 in 4 probability of blue being drawn (25%).