Summary of Chapter 13
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| inferential statistics | deal with inferences about populations based on the behavior of samples
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| inferential statistics are | used to determine how likely it is that results based on a sample or samples are the same results that would have been obtained for the entire population
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| the degree to which the results of a sample can be generalized to a population is | always expressed in terms of probabilities not in terms of proof
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| expected, chance variation among means | referred to as sampling error
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| The question that guides inferential statistics is | whether observed differences are real or only the result of sampling error
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| Useful characteristic of sampling errors | usually normally distributed
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| if a sufficiently large number of equal sized large samples are | randomly selected from a population, the means of those samples will be normally distributed around the population mean
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| the smaller the standard of error of the mean | the less sampling error
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| as the size of the sample increases | the standard of error of the mean decreases
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| standard error | can also be calculated for other measures of central tendency as well as for measure of variability, relationship, and relative position
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| standard error | can also be determined for the difference between the means
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| hypothesis testing | process of decision making in which researchers evaluate the results of a study against their original expectations
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| hypothesis testing | process of determining whether to reject the null hypothesis (i.e., no meaningful differences only those due to sampling error) in favor of the research hypothesis (i.e., groups are meaningfully different; one treatment is more effective than another)
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| test of significance | statistical procedure in which we determine the likelihood (i.e., probability) that results from our sample are just due to chance
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| significance | refers to a selected probability level that indicates how much risk we are willing to take if the decision we make is wrong
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| the standard preselected probability level used by educational researchers | is usually 5 out of 100 chances that the observed difference occurred by chance
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| tests of significance can be | either one tailed or two tailed
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| tails | refers to the extreme ends of the bell shaped curve of a sampling distribution
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| one tailed test | assumes that a difference can occur only in one direction; the research hypothesis is directional; the researcher should be quite sure that the results can occur only in the predicted direction
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| two tailed test | assumes that the results can occur in either direction; the research hypothesis is non-directional
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| one tailed test has one major advantage | it is statistically easier to obtain a significant difference when using a one tailed tests
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| type I error | occurs when the null hypothesis is true, but the researcher rejects it, believe incorrectly, that the results from the sample are not simply due to chance. (you think you are pregnant but you are not, false positive
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| type II error | occurs when the null hypothesis is false, but the researcher fails to reject it, believing incorrectly, that the results from the sample are simply due to chance (you think you are not pregnant, but you are, false negative)
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| parametric tests | more powerful and appropriate when the variable measured is normally distributed in the population and the data represent an interval or ratio scale of measurement
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| non parametric tests | makes no assumptions about the shape of the distribution and are used when the data represent an ordinal or nominal scale
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| t test | used to determine whether two groups of scores are significantly different at a selected probability level
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| basic strategy of a t test | compare the actual difference between the means of the groups, with the difference expected by the chance if the null hypothesis (i.e., no difference) is true. This ratio is known as the t value
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| t value | is equal or greater than the value statistically established for the predetermined significance level, we can reject the null hypothesis
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| Simple or one way analysis of variance (ANOVA) | used to determine whether scores from two or more groups are significantly different at selected probability level
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| ANOVA | total variance of scores is attributed to two sources variance between groups (variance caused by the treatment or other independent variables) and variance within groups (error variance)
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| Analysis of covariance (ANCOVA) | form of ANOVA used for controlling extraneous variables
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| ANCOVA | adjusts posttest scores for initial differences on some variable and compares adjusted scores
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| ANCOVA | used as a means of increasing the power of a statistical test
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| power | refers to the ability of a significance test to identify a true research finding, allowing the experimenter to reject a null hypothesis that is false
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| multiple regression | combines variables that are known individually to predict the criterion into a multiple regression equation
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| chi square | is a nonparametric test of significance appropriate when the data are in form of frequency counts or percentages and proportions that can be converted to frequencies in different categories or groups
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