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Introduction to Hypothesis Testing <ul><li>Chapter 5 </li></ul>Copyright © 2011 by Pearson Education, Inc. All rights rese...
Chapter Outline <ul><li>A Hypothesis-Testing Example </li></ul><ul><li>The Core Logic of Hypothesis Testing </li></ul><ul>...
Hypothesis Testing <ul><li>Theory </li></ul><ul><ul><ul><li>A set of principles that attempts to explain one or more facts...
Hypothesis Testing <ul><li>A systematic procedure for deciding whether the results of a research study supports a hypothes...
Hypothesis Testing <ul><li>Researchers want to draw conclusions about a particular population. </li></ul><ul><ul><li>e.g.,...
The Core Logic of Hypothesis Testing <ul><li>Research is usually designed to answer a specific question </li></ul><ul><ul>...
The Core Logic of Hypothesis Testing  <ul><li>ISSUES!! </li></ul><ul><ul><li>Karl Popper (1902-1994) </li></ul></ul><ul><u...
The Core Logic of Hypothesis Testing <ul><li>Null Hypothesis (H 0 ) </li></ul><ul><ul><li>The hypothesis predicting that n...
Null Hypothesis <ul><li>The purposes of the null hypothesis </li></ul><ul><ul><li>Acts as a  starting point </li></ul></ul...
The Hypothesis-Testing Process <ul><li>Step 1: Restate the question as a research hypothesis and a null hypothesis about t...
Hypothesis Testing: Step 1 <ul><li>Restate the question as a research hypothesis and a null hypothesis about the populatio...
Hypothesis Testing: Step 2 <ul><li>Determine the characteristics of the comparison distribution </li></ul><ul><ul><li>Comp...
Hypothesis Testing: Step 3 <ul><li>Set a cutoff sample score or critical value </li></ul><ul><ul><li>This is a target agai...
Hypothesis Testing: Step 3 (cont.) <ul><li>Researchers use Z scores and percentages to set the cutoff scores. </li></ul><u...
Hypothesis Testing: Step 3 (cont.) <ul><li>Generally, researchers in the social and behavioral sciences use conventional l...
Hypothesis Testing: Step 4 <ul><li>Determine your samples score on the comparison distribution. </li></ul><ul><ul><li>Figu...
Hypothesis Testing: Step 5 <ul><li>Decide Whether to Accept or Reject the Null Hypothesis. </li></ul><ul><ul><li>Compare y...
Implications of Rejecting of Failing to Reject the Null Hypothesis <ul><li>When you reject the null hypothesis, all you ar...
Implications of Rejecting of Failing to Reject the Null Hypothesis <ul><li>When the results are not extreme enough to reje...
Another Example
Another Example
Another Example
Another Example
Another Example -1.64
Another Example
Another Example
Another Example
Another Example
One-Tailed and Two-Tailed Hypothesis Tests <ul><li>Directional Hypothesis </li></ul><ul><ul><li>focuses on a specific dire...
Determining Cutoff Scores with Two-Tailed Tests <ul><li>For a two-tailed test, you have to divide the significance percent...
When to Use One-Tailed or Two-Tailed Tests <ul><li>Use a one-tailed test when you have a clearly directional hypothesis. <...
Decision Errors <ul><li>When the right procedures lead to the wrong decisions </li></ul><ul><li>In spite of calculating ev...
Type I Error <ul><li>Rejecting the null hypothesis when the null hypothesis is true   </li></ul><ul><ul><li>You find an ef...
Type I Error <ul><li>The chance of making a Type I error is the same as the significance level. </li></ul><ul><ul><li>If t...
Type II Error <ul><li>With a very extreme significance level, there is a greater probability that you will not reject the ...
Relationship Between Type I and Type II Errors <ul><li>Decreasing the probability of a Type I error increases the probabil...
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Aron chpt 5 ed revised

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  1. 1. Introduction to Hypothesis Testing <ul><li>Chapter 5 </li></ul>Copyright © 2011 by Pearson Education, Inc. All rights reserved
  2. 2. Chapter Outline <ul><li>A Hypothesis-Testing Example </li></ul><ul><li>The Core Logic of Hypothesis Testing </li></ul><ul><li>The Hypothesis-Testing Process </li></ul><ul><li>One-Tailed and Two-Tailed Hypothesis Tests </li></ul><ul><li>Decision Errors </li></ul>Copyright © 2011 by Pearson Education, Inc. All rights reserved
  3. 3. Hypothesis Testing <ul><li>Theory </li></ul><ul><ul><ul><li>A set of principles that attempts to explain one or more facts, relationships, or events </li></ul></ul></ul><ul><ul><ul><li>Usually gives rise to various specific hypotheses that can be tested in research studies </li></ul></ul></ul><ul><li>Hypothesis </li></ul><ul><ul><li>A specific prediction intended to be tested in a research study </li></ul></ul><ul><ul><li>Can be based on informal observation or theory </li></ul></ul>Copyright © 2011 by Pearson Education, Inc. All rights reserved
  4. 4. Hypothesis Testing <ul><li>A systematic procedure for deciding whether the results of a research study supports a hypothesis that applies to a population </li></ul>Copyright © 2011 by Pearson Education, Inc. All rights reserved
  5. 5. Hypothesis Testing <ul><li>Researchers want to draw conclusions about a particular population. </li></ul><ul><ul><li>e.g., babies in general </li></ul></ul><ul><li>Conclusions will be based on results of studying a sample. </li></ul><ul><ul><li>e.g., one baby </li></ul></ul>Copyright © 2011 by Pearson Education, Inc. All rights reserved
  6. 6. The Core Logic of Hypothesis Testing <ul><li>Research is usually designed to answer a specific question </li></ul><ul><ul><li>Do students who attend an after-school program that is academically oriented (math, writing, computer use) score higher on an intelligence test than students who do not attend such a program? </li></ul></ul><ul><li>Researcher forms a hypothesis </li></ul><ul><ul><li>Children in academic after-school programs will have higher IQ scores than children in the general population. </li></ul></ul><ul><li>Researcher sets criteria and runs experiment </li></ul>Copyright © 2011 by Pearson Education, Inc. All rights reserved
  7. 7. The Core Logic of Hypothesis Testing <ul><li>ISSUES!! </li></ul><ul><ul><li>Karl Popper (1902-1994) </li></ul></ul><ul><ul><ul><li>Philosophy of Falsification </li></ul></ul></ul><ul><ul><ul><li>Can only falsify a hypothesis-cannot prove a hypothesis </li></ul></ul></ul><ul><ul><ul><ul><li>Need only one case to disprove something </li></ul></ul></ul></ul><ul><ul><ul><ul><li>e.g. –”All birds are blue” </li></ul></ul></ul></ul><ul><ul><li>It is impossible statistically to demonstrate something is true. </li></ul></ul><ul><ul><ul><li>Statistical techniques are better at demonstrating that something is not true </li></ul></ul></ul>Copyright © 2011 by Pearson Education, Inc. All rights reserved Confusing but Important
  8. 8. The Core Logic of Hypothesis Testing <ul><li>Null Hypothesis (H 0 ) </li></ul><ul><ul><li>The hypothesis predicting that no difference exists between groups being compared. </li></ul></ul><ul><ul><ul><li>Children in academic after-school programs will not have higher IQ scores than children in the general population. </li></ul></ul></ul><ul><li>Research Hypothesis (Alternative Hypothesis) (H a ) </li></ul><ul><ul><li>The hypothesis that the researcher wants to support predicting that a significant difference exists between the groups being compared. </li></ul></ul><ul><ul><ul><li>Children in academic after-school programs will have higher IQ scores than children in the general population. </li></ul></ul></ul>Confusing but Important
  9. 9. Null Hypothesis <ul><li>The purposes of the null hypothesis </li></ul><ul><ul><li>Acts as a starting point </li></ul></ul><ul><ul><ul><li>Until researchers can verify that there is a difference between two groups, it must be assumed that there is no difference </li></ul></ul></ul><ul><ul><li>Provides a benchmark </li></ul></ul><ul><ul><ul><li>The null hypothesis helps define a range within any observed differences between groups can be attributed to chance or are due to something other than chance </li></ul></ul></ul>
  10. 10. The Hypothesis-Testing Process <ul><li>Step 1: Restate the question as a research hypothesis and a null hypothesis about the population. </li></ul><ul><li>Step 2: Determine the characteristics of the comparison distribution. </li></ul><ul><li>Step 3: Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected. </li></ul><ul><li>Step 4: Determine your sample’s score on the comparison distribution. </li></ul><ul><li>Step 5: Decide whether to reject the null hypothesis. </li></ul>Copyright © 2011 by Pearson Education, Inc. All rights reserved
  11. 11. Hypothesis Testing: Step 1 <ul><li>Restate the question as a research hypothesis and a null hypothesis about the populations </li></ul><ul><ul><li>Research hypothesis </li></ul></ul><ul><ul><ul><li>Children in academic after-school programs will have higher IQ scores than children in the general population. </li></ul></ul></ul><ul><ul><li>Null hypothesis </li></ul></ul><ul><ul><ul><li>Children in academic after-school programs will not have higher IQ scores than children in the general population. </li></ul></ul></ul><ul><ul><li>. </li></ul></ul>
  12. 12. Hypothesis Testing: Step 2 <ul><li>Determine the characteristics of the comparison distribution </li></ul><ul><ul><li>Comparison distribution (sampling distribution) </li></ul></ul><ul><ul><ul><li>distribution used in hypothesis testing </li></ul></ul></ul><ul><ul><ul><li>represents the population distribution if the null hypothesis is true </li></ul></ul></ul><ul><ul><ul><li>distribution to which you compare the score based on your sample’s results </li></ul></ul></ul><ul><ul><li>Find out the key information about the comparison distribution </li></ul></ul><ul><ul><ul><li>e.g., population mean, population SD, shape of the distribution (does it follow a normal curve?) </li></ul></ul></ul><ul><ul><ul><li>M = 100, SD = 15 </li></ul></ul></ul><ul><ul><li>If the null hypothesis is true: </li></ul></ul><ul><ul><ul><li>Population 1 and Population 2 are the same. </li></ul></ul></ul>
  13. 13. Hypothesis Testing: Step 3 <ul><li>Set a cutoff sample score or critical value </li></ul><ul><ul><li>This is a target against which you will compare the results of your study </li></ul></ul><ul><ul><li>By setting a cutoff score, you are deciding how extreme a sample score would need to be in order to be too unlikely to get such an extreme score if the null hypothesis were true. </li></ul></ul>
  14. 14. Hypothesis Testing: Step 3 (cont.) <ul><li>Researchers use Z scores and percentages to set the cutoff scores. </li></ul><ul><ul><li>For instance, a researcher might decide that if a result was less likely than 5%, she would reject the null hypothesis </li></ul></ul><ul><ul><li>In this case, researchers would look at the normal curve table and find the Z score cutoff for scores in the top 5% of a normal curve, which is 1.64 </li></ul></ul>
  15. 15. Hypothesis Testing: Step 3 (cont.) <ul><li>Generally, researchers in the social and behavioral sciences use conventional levels of significance, which are cutoff scores of either 5% or 1%. </li></ul><ul><li>When a sample score is at least as extreme as the cutoff score, then the result is considered statistically significant. </li></ul>
  16. 16. Hypothesis Testing: Step 4 <ul><li>Determine your samples score on the comparison distribution. </li></ul><ul><ul><li>Figure the Z score for the sample’s raw score based on the comparison distribution’s mean and standard deviation </li></ul></ul><ul><ul><ul><li>If your sample’s raw score = 125, the population mean = 100, and the population standard deviation = 15 </li></ul></ul></ul><ul><ul><ul><li>The Z score for your sample would be: </li></ul></ul></ul>
  17. 17. Hypothesis Testing: Step 5 <ul><li>Decide Whether to Accept or Reject the Null Hypothesis. </li></ul><ul><ul><li>Compare your sample’s Z score to the cutoff Z score </li></ul></ul><ul><ul><ul><li>Cutoff Z = 1.64 </li></ul></ul></ul><ul><ul><ul><li>Sample Z = 1.67 </li></ul></ul></ul><ul><ul><li>Reject Null Hypothesis </li></ul></ul><ul><ul><ul><li>“ Children in academic after-school programs will not have higher IQ scores than children in the general population.” </li></ul></ul></ul><ul><ul><li>Found Support for Research Hypothesis </li></ul></ul><ul><ul><ul><li>“ Children in academic after-school programs will have higher IQ scores than children in the general population.” </li></ul></ul></ul>
  18. 18. Implications of Rejecting of Failing to Reject the Null Hypothesis <ul><li>When you reject the null hypothesis, all you are saying is that your results support the research hypothesis. </li></ul><ul><ul><li>The results never prove the research hypothesis or show that your hypothesis is true. </li></ul></ul><ul><ul><li>Research studies and their results are based on the probability or chance of getting your result if the null hypothesis were true. </li></ul></ul>
  19. 19. Implications of Rejecting of Failing to Reject the Null Hypothesis <ul><li>When the results are not extreme enough to reject the null hypothesis, you do not say that the results support the null hypothesis. </li></ul><ul><ul><li>You say that the results are not statistically significant, or that the results are inconclusive. </li></ul></ul><ul><ul><li>We are basing research on probabilities, and the fact that we did not find a result in this study does not mean that the null hypothesis is true. </li></ul></ul>
  20. 20. Another Example
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  22. 22. Another Example
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  24. 24. Another Example -1.64
  25. 25. Another Example
  26. 26. Another Example
  27. 27. Another Example
  28. 28. Another Example
  29. 29. One-Tailed and Two-Tailed Hypothesis Tests <ul><li>Directional Hypothesis </li></ul><ul><ul><li>focuses on a specific direction of effect </li></ul></ul><ul><ul><ul><li>e.g., that reading levels would be greater in students participating in a reading program </li></ul></ul></ul><ul><ul><li>one-tailed test </li></ul></ul><ul><ul><ul><li>To reject the null hypothesis, a sample score needs to be in a particular tail of the distribution (e.g., the top 1% of the distribution). </li></ul></ul></ul><ul><li>Non-Directional Hypothesis </li></ul><ul><ul><li>a hypothesis that predicts an effect, but does not specify whether the score will be high or low </li></ul></ul><ul><ul><li>The null hypothesis would be that there would be no change, or that the scores would not be extreme at either tail of the comparison distribution. </li></ul></ul>Copyright © 2011 by Pearson Education, Inc. All rights reserved
  30. 30. Determining Cutoff Scores with Two-Tailed Tests <ul><li>For a two-tailed test, you have to divide the significance percentage between two tails. </li></ul><ul><li>For a 5% significance level, the null hypothesis would be rejected if the sample score was in either the top 2.5% or the bottom 2.5% of the comparison distribution. </li></ul>
  31. 31. When to Use One-Tailed or Two-Tailed Tests <ul><li>Use a one-tailed test when you have a clearly directional hypothesis. </li></ul><ul><li>Use a two-tailed test when you have a clearly non-directional hypothesis. </li></ul><ul><li>With a one-tailed test, if the sample score is extreme—but in the opposite direction—the null cannot be rejected. </li></ul><ul><li>Often researchers will use two-tailed tests even if the hypothesis is directional. </li></ul>Copyright © 2011 by Pearson Education, Inc. All rights reserved
  32. 32. Decision Errors <ul><li>When the right procedures lead to the wrong decisions </li></ul><ul><li>In spite of calculating everything correctly, conclusions drawn from hypothesis testing can still be incorrect. </li></ul><ul><li>This is possible because you are making decisions about populations based on information in samples. </li></ul><ul><ul><li>Hypothesis testing is based on probability. </li></ul></ul>Copyright © 2011 by Pearson Education, Inc. All rights reserved
  33. 33. Type I Error <ul><li>Rejecting the null hypothesis when the null hypothesis is true </li></ul><ul><ul><li>You find an effect when in fact there is no effect. </li></ul></ul><ul><li>A Type I error is a serious error as theories, research programs, treatment programs, and social programs are often based on conclusions of research studies. </li></ul>
  34. 34. Type I Error <ul><li>The chance of making a Type I error is the same as the significance level. </li></ul><ul><ul><li>If the significance level was set at p < .01, there is less than a 1% chance that you could have gotten your result if the null hypothesis was true. </li></ul></ul><ul><ul><li>To reduce the chance of making a Type I error, researchers can set a very stringent significance level (e.g., p < .001). </li></ul></ul>
  35. 35. Type II Error <ul><li>With a very extreme significance level, there is a greater probability that you will not reject the null hypothesis when the research hypothesis is actually true. </li></ul><ul><ul><li>e.g. concluding that there is dangerous drug effects when there is actually no dangerous effect </li></ul></ul><ul><ul><ul><li>The probability of making a Type II error can be reduced by setting a very lenient significance level (e.g., p < .10). </li></ul></ul></ul>
  36. 36. Relationship Between Type I and Type II Errors <ul><li>Decreasing the probability of a Type I error increases the probability of a Type II error. </li></ul><ul><ul><li>The compromise is to use standard significance levels of p < .05 and p < .01. </li></ul></ul>  Real Situation H 0 True H a True H a Supported (H 0 Rejected) Error Type I Correct Decision Inconclusive (H 0 Not Rejected) Correct Decision Error Type II
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