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Aron chpt 5 ed Aron chpt 5 ed Presentation Transcript

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