Introduction to Inferential Statistics: Understanding the Need and Applications

1. Chapter 5 Overview of Inferential Statistics

2. 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

3. 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

4. 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

5. 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

6. 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.

7. 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

8. 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

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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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