EPPP - Statistics and Research Design - Inferential Statistics Overview, Tests

An inferential statistical test enables an investigator to determine the probability of obtaining a sample with a particular value by comparing the obtained sample value to an appropriate _________ distribution. When the sample value of interest is a mean, the comparison distribution is the sampling distribution of the __________, which is the distribution of means that would be obtained if a larger number of equal-sized random samples were drawn from the same _________ and the mean of each sample was calculated. While many sample means would equal the population mean, because of the effects of _________, some means would be lower than the population mean and some would be higher.

In inferential statistics, a sampling distribution is not actually constructed by obtaining a large number of samples. Instead, a theoretical sampling distribution is derived from probability theory. According to the ________ theorem, the sampling distribution of the mean is ________ shaped; its mean equals the _________; and its standard deviation, the _________ of the mean, is equal to the population ________ divided by the square root of the ___________.

Hypothesis testing involves first translating the verbal research hypothesis into two competing statistical hypotheses: The __________ hypothesis is stated in a way that implies that the independent variable does not have an effect on the dependent variable and that any observed effect is the result of __________. In contrast, the __________ hypothesis states the opposite of the null hypothesis and is expressed in a way that implies that the independent variable does __________ the dependent variable. The alternative hypothesis can take one of two forms. A ________ alternative hypothesis predicts whether the population value will be greater or ________ the population value specified in the null hypothesis; while a _________ alternative hypothesis states only that the population value is not equal to the value stated in the null hypothesis.

The results of an inferential statistical test indicate whether the obtained sample value falls within the region of likely values or unlikely values in the _________ distribution. When the results of the statistical test indicate that the obtained sample values fall in the region of unlikely values, the null hypothesis is __________ and the alternative hypothesis is _________.  Coversly, when the results indicate that the sample value falls in the region of likely values, the null hypothesis is ______ and the alternative hypothesis is ________.

The size of the ______ region (region of unlikely values) is defined by alpha. A researcher sets alpha before collecting or analyzing the data. In psychological research, alpha is usually set at .01 or _______. When alpha is .01, this mean that ________% of the sampling distribution is the region of unlikely values, while the remaining ______% is the region of likely values.  The region of unlikely values is always placed in one or both __________ of the sampling distribution so that it contains the sample values that are least likely to occur as the result of sampling error.

When a researcher makes the decision to retain or reject the ________ hypothesis, there is no way to know with certainty if the decision is correct or in error. There are two kinds of decision errors: A type I error is made when a true null hypothesis is ________. This occurs when a researcher concludes that an independent variable has had an effect on the dependent variable, but the observed effect was actually due to _________. The probability of making a type I error is equal to _________. For example, when ________ is set to .05 and the researcher has rejected the null hypothesis, there is a _____% chance that a type I error has been made.

A type II error is made when a false null hypothesis is ________. This occurs when the researcher decided that an independent variable has had no effect on the dependent variable when it actually did. A type II error might occur when the ________ variable was not administered in sufficient intensity or for a long enough period of time, when the sample size was too _______, or when alpha is too _______

A researcher can, of course, make a correct decision. One kind of correct decision is to _______ a true null hypothesis. In this situation, the researcher correctly concludes that any observed effected of an IV is actually due to ________. The other correct decision is to ________ a false null hypothesis. In this situation, the researcher correctly decided that the ________ had an effect on the DV. When a statistical test enables a researcher to make this kind of correct decision, the test is said to have statistical power. Power is increased as alpha _________, as sample size _________, and as the magnitude of the effect of the independent variable increases. Power is also maximized when a one-tailed test is used (when appropriate) and when the data are analyzed using a t-test, ANOVA, or other _________ statistical test.

The inferential statistical tests are categorized as parametric or nonparametric. Both types of test share the assumptions that the sample has been ________ from the population and that observations are __________.

A ______ test is used when the data being analyzed represent a(n) ________ or ratio scale of measurement and when two assumptions have been met. The first assumption is that, in the population from which the sample was drawn, scores on the variable are _______ distributed. The second assumption is that there is "homoscedasticity" which means that the _______ of the populations that the different groups represent are equal

If the data to be analyzed do not meet the assumptions for a parametric test or if they represent a(n) ________ or ordinal scale of measurement, a _______ test is used. The major limitation of the nonparametric tests is that they are less ________ than parametric tests, which means that, when using these tests, it is more difficult to detect a false ________ hypothesis.

Parametric and nonparametric test both yield a test statistic that the researcher compares to a critical value, which is the cutoff point that divides the ______ into the regions of likely or unlikely values. The critical value for a particular research study is determined by two factors: _______ and the degrees of freedom.

A chi-square test is used to analyze data collected on a nominal variable (or other variable that is being treated as a nominal variable). The _____ sample chi-square test is used when a study includes only one _______ and data on that variable are reported in terms of ________. It would be the appropriate statistical test when a researcher asks a sample of 40 students to indicate which of five textbooks they prefer for an introductory clinical psychology class. The degrees of freedom for this study are equal to _________.

The ______ sample chi-square test is used when a study includes _______ or more variables and the data to be analyzed are frequencies in each nominal category. It would be the appropriate statistical test when a hospital director wants to compare the number of current adult male, adult female, adolescent male, and adolescent female in-patients who have received primary diagnoses for either MDD, BPI, BPII or Mood Disorder. The degrees of freedom for this study are equal to _________.

A Mann-Whitney U test and the Wilcoxon matched-pairs test are used to analyze data when a study includes one _______ variable with two levels and the data to be analyzed are reported in terms of _________. The Mann-Whitney U test is appropriate when the two groups are ________, while the Wilcoxon test is used when the groups are __________.

The various forms of the t-test are all used to compare two ________. Although they can be used to analyze data from studies involving more than two means, this is problematic because it increases the ______ error rate which refers to the chance of make a type ______ error.

The t-test for a single sample is appropriate for comparing an obtained _______ to a known _________. the degrees of freedom for a t-test for a single sample are equal to _________, where N is the number of subjects in the sample.

The t-test for _______ samples is used to compare the means obtained by subjects in two unrelated groups. The degrees of freedom for this t-test are equal to ______, where N is the total number of subjects in the study.

Finally, the t-test for ______ samples is used to compare two means when groups are related. Related groups are obtained in several ways. One way is by matching subjects in pairs on the basis of their status on a(n) _________ variable. Another way is for subjects to act as their own ________ (comparison) group. The degrees of freedom for this t-test equal _______, where N is the number of _________

If a psychologist conducts a study to compare the effects of two weight reduction programs, and he matches subjects in pairs in terms of their initial weight and assigns members of each pair to a different program, the t-test for _______ is the appropriate statistical test. If the sample consists of 26 subjects, the degrees of freedom for this study are ________.

The two main forms of the analysis of variance are the one-way ANOVA and the factorial ANOVA. The _____ ANOVA is used when a study includes one _______ variable and two or more _________ groups. It yields a single F-ratio, which is calculated by dividing the MSB by MSW. MSB is a measure of variability that reflects _______, and MSW is a measure of variability that reflects ________ only

When MSB is _______ than MSW, the F-ratio is greater than ______, suggesting that the independent variable has had an effect on the dependent variable.

The factorial ANOVA is the appropriate statistical test when a research study includes _______ independent variables. It provides a separate F-ratio for the _______ effects of each independent variable and for the _______ between independent variables.

If a psychologist conducts a study to compare the effects of four different weight loss programs for males and females, the study's independent variable(s) are ________. Assuming that the dependent variable is measured on a(n) ________ or ration scale, the appropriate statistical test be be the _____ ANOVA