Understanding Research Results: Statistical Inference Basics

Understanding Research Results: Statistical Inference Basics

1. Explain how researchers use inferential statistics to evaluate sample data

   • Inferential statistics are used to determine whether we can state that the results reflect what would happen if we were to conduct the study again and again with multiple samples from the same population
   • Allows researchers to make inferences about the true difference in the population means on the basis on the sample data

2. Distinguish between the null hypothesis and the research hypothesis

   • H0: Population means are exactly equal
   • H1: Population means are not equal

3. Discuss probability in statistical inference including the meaning of statistical significance

   • Statistical significant result: one that has a very low probability of occurring if the population means are equal
   • Probability is the likelihood of the occurrence of some event or outcome
     • Probability that the difference between means in the sample will occur if there is no actual difference in the population
     • If the probability very low, reject the possibility that chance or random error responsible for the difference in means

4. Describe the t test, and explain the difference between one-tailed and two-tailed tests

   • The t test is a statistic that allows you to determine whether the mean difference found between two groups in your sample likely came from the null hypothesis sampling distribution for that sample size
   • One tailed: specified a direction of difference between the groups
   • Two tailed: did specify a predicted direction of difference

5. Describe the F test, including systematic variance and error variance

   • F test is an extension of the t test ; when study has one independent variable with two groups
     • Also appropriate when study has more than two groups or when a factorial design is used
     • The larger the F ration, the more likely results are significant
   • Systematic variance is the deviation of the group means from the grand mean
   • Error variance is the deviation of the individual scores in each group from their respective group means

6. Distinguish between Type I and Type II errors

   • Type I error is made when we reject the null hypothesis but the null hypothesis is actually true
   • Type II error occurs when the null hypothesis is retained based on our sample sata, although in the population the null hypothesis is false

7. Discuss the reasons a researcher may obtain nonsignificant results

   • Non-significant results are more likely to be found if the researcher is very cautious in choosing the alpha level
   • A Type II error may also result from a sample size that is too small to detect a real relationship between variables
   • True effects size in the population is small. Very small effects are difficult to detect without a large sample size.

8. Define power of a statistical test

   • A sample size on the basis of a desired probability of correctly rejecting the null hypothesis, presuming it is actually false

9. Describe the criteria for selecting an appropriate statistical test