Overview of Inferential Statistics Chapter 5 Overview of Inferential Statistics

Why do we need inferential statistics? Typically, we are interested in the population, not the sample When we study an intervention, for example, we want to be able to generalize to the larger group (the population) But we usually can’t gather the whole population of scores

Why do we need inferential statistics? Variability Remember that measurements in the sciences are variable; they change from observation to observation We need inferential statistics to assess this variability and aid in our decision making

What do we learn from inferential statistics? Inferential statistics provides us with educated guesses about quantitative characteristics of populations (“parameters”) For example, is the central tendency of one group different than the central tendency of a second group

Varieties of Inferential Procedures Parameter estimation – using data from a random sample to estimate a parameter of the population from which the sample is drawn Hypothesis testing – formulating opposing hypotheses and determining from samples which is most likely correct

Hypothesis Testing This may seem to be overly complicated, but It provides an elegant way of answering research questions For example, we may want to determine which of these two hypotheses is correct: 1. The whole language teaching method improves reading scores 2. The whole language teaching method does not improve reading scores We may be able to learn how best to teach children to read.

Parameter Estimation vs. Hypothesis Testing By using inferential procedures, we can learn from data and make decisions about important features of our world, like which method to use to teach children to read Even though we may have little interest in estimating the parameters of the population

Types of Hypothesis Testing Parametric hypothesis tests – tests about specific population parameters, usually mean or variance Since parametric tests generally require computation of mean and variance, these tests are only appropriate for interval or ratio level data

Types of Hypothesis Testing Non-Parametric hypothesis tests – tests about the shape or location of the population

Random Sampling Inferential statistical procedures will only yield accurate predictions when they are based on Random samples Inferential statistics depend on probability theory which requires random samples

Random Sample A Random Sample is one which has been obtained such that 1. each observation has an equal chance of being included in the sample, and 2. the selection of one observation does not influence the selection of any other observation

How to create a Random Sample Place all the measurements in a population into a hat, Close your eyes, reach in the hat, and Select one slip of paper Return the slip of paper to the hat, mix and Repeat But this is not very practical

Creating a Random Sample with a random number table Using a random number table, like Table H in the text book, requires that you assign every observation a number (from 1 to N) Going down the columns of Table H, your sample will use those observations associated with the numbers you encounter in the column

Creating a Random Sample with a random number generator With computers, however, Tables are no longer needed Many computer programs use algorithms for generating random numbers Excel, for example, has several functions (e.g., RAND, RANDBETWEEN) that can help you generate random numbers

Biased Samples Procedures that do not produce Random samples are those that produce Biased samples Telephone polls exclude people that do not own a telephone Magazine surveys exclude those that don’t read that magazine Website samples don’t include people that frequent that website

Overgeneralizing Inferential statistics require random samples However, inferences require care and should be restricted to the population sampled When a researcher does not adequately restrict their conclusions to the population sampled, but goes “too far” we term this problem “overgeneralizing” Or drawing an inference to a population other than the one randomly sampled