Chapter 10 Hypothesis Testing and the Sign Test

Experimental Design � Purpose – ◦ Allows a scientist to test the influence of

Experimental Design � Conclusions ◦ Primary question – “How reasonable are these results if

Experimental Design � Repeated Measures Design ◦ One of several commonly used designs ◦

Experimental Design � Two Experimental Groups ◦ Experimental – Receives treatment ◦ Control Group

Hypothesis � Directional Hypothesis ◦ Specifies the direction of the effect of the independent

Null Hypothesis (H 0) � Logical counterpart of alternative hypothesis ◦ Nondirectional – the

Mutually Exhaustive and Exclusive � The alternative hypothesis and the null hypothesis are mutually

Decision Rule � The null hypothesis is evaluated directly because it is possible to

Decision Rule � Chance – the probability of the results is compared to that

Decision Rule Level of alpha is dependent upon the particular experiment

Decision Errors � Type I – Null hypothesis is rejected when it is actually

Evaluating the Tail of the Distribution � Directional Hypothesis – determine the probability of

Evaluating the Tail � Two-tailed probability – without valid basis for directional hypothesis, indirectional

Sign Test � Used only in replicated measures ◦ 1. Null and alternative hypothesis

Sign Test � Difference between control group and experimental calculated ◦ ◦ Sign of

Sign Test � Calculate ◦ Probability of getting results and more extreme results ◦

Size of Effect � Results that are statistically significant are reliable � Yet statistically

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Chapter 10 Hypothesis Testing and the Sign Test James A. Van Slyke Azusa Pacific University

Experimental Design � Purpose – ◦ Allows a scientist to test the influence of the independent variable upon the dependent variable ◦ Controls for the influence of other variables

Experimental Design � Conclusions ◦ Primary question – “How reasonable are these results if chance alone were responsible? ” ◦ If the results are not due to chance, then the results are attributed to the experimental manipulation

Experimental Design � Repeated Measures Design ◦ One of several commonly used designs ◦ Replicated Measures Design or Correlated Groups Design �Subjects are paired prior to conducting experiment �Difference between paired scores is analyzed

Experimental Design � Two Experimental Groups ◦ Experimental – Receives treatment ◦ Control Group – No Treatment (placebo) � Alternative Hypothesis (H 1) ◦ Claims that difference in results between the two conditions is due to the independent variable

Hypothesis � Directional Hypothesis ◦ Specifies the direction of the effect of the independent variable � Nondirectional Hypothesis ◦ The independent variable has an effect but the direction is not specified

Null Hypothesis (H 0) � Logical counterpart of alternative hypothesis ◦ Nondirectional – the independent variable has no effect on the dependent variable ◦ Directional – the independent variable has no effect in that specific direction on the dependent variable

Mutually Exhaustive and Exclusive � The alternative hypothesis and the null hypothesis are mutually exclusive and exhaustive � If one is true the other must be false and vice versa � The experiment attempts to show that the null hypothesis is false � Obviously if the null hypothesis is false, the alternative hypothesis can be accepted as true

Decision Rule � The null hypothesis is evaluated directly because it is possible to calculate the probability of chance events � But, there are no mathematics for the alternative hypothesis � The focus in on the null hypothesis to support accepting the alternative hypothesis

Decision Rule � Chance – the probability of the results is compared to that of chance � Alpha level – If the probability is less then or equal to the value of alpha, the null hypothesis is rejected � When the null hypothesis is rejected, the results are thought to be significant or reliable

Decision Rule Level of alpha is dependent upon the particular experiment

Decision Errors � Type I – Null hypothesis is rejected when it is actually true ◦ Probability of Type I error set by alpha � Type II – Null hypothesis is retained when it is actually false ◦ Probability of making a Type II error is called beta � Increasing alpha decreases beta and vice versa � Setting alpha and beta depends upon the cost of making either type of error

Evaluating the Tail of the Distribution � Directional Hypothesis – determine the probability of getting an outcome or an even more extreme score ◦ Evaluate the tail of the distribution � Nondirectional hypothesis – probability of obtaining an extreme score in both direction ◦ Evaluate both tails of the distribution

Evaluating the Tail � Two-tailed probability – without valid basis for directional hypothesis, indirectional used � One-tailed probability – Used for directional hypothesis ◦ If there is a good theoretical basis ◦ If there is other data supporting the conclusion

Sign Test � Used only in replicated measures ◦ 1. Null and alternative hypothesis generated ◦ 2. Directional or nondirectional ◦ 3. Alpha level set

Sign Test � Difference between control group and experimental calculated ◦ ◦ Sign of the difference recorded Magnitude of difference ignored Ties are ignored Assumptions of binomial distribution must be present

Sign Test � Calculate ◦ Probability of getting results and more extreme results ◦ Use one or two-tailed binomial distribution depending on hypothesis ◦ Compare probability to alpha � Draw appropriate conclusions and generalizations

Size of Effect � Results that are statistically significant are reliable � Yet statistically significant does not mean a large effect � Effects are dependent upon their particular size and their reliability

Homework � 4, 5, 7, 9, 10