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Chapter 13

chapter 13 notes

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Anna Nagy

CHAPTER 13: UNDERSTANDING RESEARCH RESULTS- STATISTICAL INFERENCE SAMPLES AND POPULATIONS Inferential statistics are necessary because the results of a given study are based on data obtained from a single sample of research participants. If researchers ever study entire populations; their findings are based on sample data. In addition to describing sample data, we want to make statements about populations. o Would the results hold up if the experiment were conducted repeatedly, each time with a new sample? Definition of Inferential Statistic: statistics designed to determine whether results based on sample data are generalizable to a population Used to determine whether we can, in fact, make statements that the results reflect what would happen if we were to conduct the experiment again and again with multiple samples. o Whether we can infer that the difference in the sample means reflects a true difference in the population means. Example: People in one state might tell you that 57% prefer the Democratic candidate and that 43% may favor the Republican candidate for office. Reports say that these results are accurate to within 3 percentage points, with a 95% confidence level. The researchers are very confident that if they were able to study the entire population rather than a sample, the actual percentage who preferred the Democratic candidate would between 60% and 54% The percentage preferring the Republican would be 46% and 40% Researcher could predict with a great deal of certainty that the Democratic candidate will win because there is no overlap in the projected population values. INFERENTIAL STATISTICS Equivalence of groups is achieved by experimentally controlling all other variables or by randomization. The assumption is that if the groups are equivalent, any differences in the dependent variable must be due to the effect of the independent variable. (usually valid) It is also true that the difference between any two groups will almost never be zero. o There will be some difference in the sample means, even when all of the principles of experimental designs are utilized; this happens because we are dealing with samples rather than populations. Random or chance error will be responsible for some difference in the means even if the independent variable had no effect on the dependent variable. THE POINT IS THAT THE DIFFERENCE IN THE SAMPLE MEANS REFLECTS ANY TRUE DIFFERENCEIN THE POPULATION MEANS, PLUS ANY RANDOM ERROR. www.notesolution.com Inferential statistics give the probability that the difference between means reflects random error than a real difference. NULL AND RESEARCH HYPOTHESIS Statistical inference begins with a statement of the null hypothesis and a research (or alternative) hypothesis. Null Hypothesis: The hypothesis used for statistical purposes that the variables under investigation are not related in the population, that any observed effect based on sample results is due to random error. (null hypothesis) : the population mean of the no-model group is equal to the population mean of the model group Independent variable had no effect Used because it is very precise o The population means are exactly equal o Permits us to know precisely the probability of the outcome of the study occurring if the null hypothesis is correct. o The null hypothesis is rejected when there is a low probability that the obtained results could be due to random error. This is what is meant by statistical significance. Statistical significance: Rejection of the null hypothesis when an outcome has a low probability of occurrence (usually .05 or less) if, in fact, the null hypothesis is correct. Significance is a matter of probability. Research Hypothesis: The hypothesis that the variables under investigation are related in the population- that the observed effect based on sample data is true in the population. (research hypothesis): The population mean of the no-model group is not equal to the population mean of the model group Independent variable did have an effect. LOGIC OF THE NULL HYPOTHESIS If we can determine that the null hypothesis is incorrect, then we accept the research hypothesis as correct. Acceptance of the research hypothesis means that the independent variable had an effect on the dependent variable. PROBABILITY AND SAMPLING DISTRIBUTIONS Probability- The likelihood that a given event (among a specific set of events) will occur. We all use probabilities frequently in everyday life. o Example: the weather forecaster says there is a 10% chance of rain today; this means that the likelihood of rain is very low. Probability in statistical inference is used in much the same way. www.notesolution.com
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