Please enable JavaScript.

Coggle requires JavaScript to display documents.

Chapter 8 Introduction to Hypothesis Testing, The values in the sample…

- - - - Use the hypothesis to predict the characteristics that the sample should have.
        
        Obtain a random sample from the population
        
        Compare the obtained sample data with the prediction that was made from the hypothesis.
        
        calculate a z-score that identifies where our sample mean is located in this hypothesized distribution.
        
        The hypothesis is wrong, if there is a big discrepancy between the data and the prediction
        
        The hypothesis is reasonable, if the sample mean is consistent with the prediction
        
        test statistic simply indicates that the sample data are converted into a single, specific statistic that is used to test the hypotheses.
        
        collected after the researcher has stated the hypotheses and established the criteria for a decision. Ensures that a researcher makes an honest, objective evaluation of the data
      - Null hypothesis states that in the general population there is no change, no difference, or no relationship.
        
        use the null hypothesis to predict the kind of sample mean that ought to be obtained
        
        Sample means that are likely to be obtained if null hypothesis is true
        
        located in the center of the distribution
        
        Sample means that are very unlikely to be obtained if null hypothesis is true
        
        located in the extreme tails of the distribution
        
        the level of significance, or alpha level is a probability value that is used to define the concept of “very unlikely” in a hypothesis test.
        
        The critical region is composed of the extreme sample values that are very unlikely (as defined by the alpha level) to be obtained if the null hypothesis is true.
        
        If sample data fall in the critical region, the null hypothesis is rejected.
      - Alternative hypothesis states that there is a change, a difference, or a relationship for the general population.
- - - - The primary concern when selecting an alpha level is to minimize the risk of a Type I error.
      - alpha levels tend to be very small probability values
  - - - impossible to determine a single, exact probability for a Type II error.
        
        the probability of a Type II error is represented by the Greek letter beta.
- - - - size of the z-score is also influenced by the standard error
        
        number of scores in the sample
        
        determine whether the z-score will be large enough to reject the null hypothesis
        
        increasing the number of scores in the sample produces a smaller standard error and a larger value for the z-score.
        
        variability of the scores
        
        increasing the variability of the scores produces a larger standard error and a smaller value (closer to zero) for the z-score.
- - - - Cohen’s d is a standard measure of effect size computed by dividing the sample mean difference by the sample standard deviation.
        
        measures the distance between two means and is typically reported as a positive number even when the formula produces a negative value.
      - alternative approach to determining the size or strength of a treatment effect is to measure the power of the statistical test.
        
        The power of a statistical test is the probability that the test will correctly reject a false null hypothesis.
        
        Researchers typically calculate power as a means of determining whether a research study is likely to be successful.
        
        usually calculate the power of a hypothesis test before they actually conduct the research study.
        
        As the size of the treatment effect increases, statistical power increases.
        
        Increasing the alpha level increases power.
        
        A one-tailed test has greater power than a two-tailed test.
        
        A large sample results in more power than a small sample