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▪ Without measuring the entire population, the results can be inaccurate due to sampling error▪ The larger the proportion of the population that is sampled,
the lower the sampling error; the smaller the proportion of the population that is sampled, the higher the sampling error
▪ A sample of 99% of a population is likely to show results that are very, very similar to those that would have been found if everyone in the population was measured
▪ A sample of 1% is likely to show results that are different from those in the population - the question is how different are the sample results
▪ Need to estimate the level of sampling error relative to the inferences being drawn
Hypothesis testing exemplified with an experimental control group comparison The five stages of the process
▪ State the null hypothesis - no difference between the mean scores for the experimental and control groups
▪ Assume the null hypothesis is true to establish a base from which the statistician can work▪ The base is actually the sampling distribution of the test statistic,
in this case the sampling distribution of the difference between two means, t
▪ Through statistical theory we can establish the characteristics of this sampling distribution (i.e., mean; standard deviation, known as the standard error in this situation; and shape)
Issues related to statistical and practical significance▪ Statistical significance
▪ The typical or atypical nature of the comparison of the observed difference to the sampling distribution can be estimated using statistical theory The estimate is the probability of being wrong in
rejecting the null hypothesis It is stated as p = x where x is the specific
probability of the comparison (e.g., p = .001, p = .042, p = .56) or as p < y where y is the alpha level (e.g., .10, .05, .01)
▪ There is always the possibility of making a mistake given that this is based on a probability model▪ Type I error - deciding to reject the null hypothesis when in
reality it is true▪ Type II error - accepting the null hypothesis when it in reality it
is false
▪ Typical levels of significance in education - .10, .05, and .01
▪ Factors affecting the level of significance▪ The actual differences between the groups▪ The degree to which sampling and measurement errors exist▪ The size of the sample
Each consumer of the research must judge the balance between the statistical significance and the practical significance of the statistical results given the context in which the results might be used
▪ Are students’ affective traits (e.g., attitudes, self-esteem, preferences, etc.) predictive of their knowledge (i.e., test scores) and skills (i.e., performances)?