Chapter 17- Inferential Statistics

Inferential statistics, which are based on laws of probability, allow researchers to make inferences about a population based on data from a sample; they offer a framework for deciding whether the sampling error that results from sampling fluctuations is too high to provide reliable population estimates. - answer- The sampling distribution of the mean is a theoretical distribution of the means of an infinite number of samples drawn from a population. The sampling distribution of means follows a normal curve, so the probability that a specified sample value will be obtained can be ascertained. - answer- The standard error of the mean (SEM) -- the standard deviation of this theoretical distribution-- indicates the degree of average error of a sample mean; the smaller the SEM, the more accurate are the same estimates of the population mean. - answer- Statistical inference consists of two approaches estimating parameters and testing hypotheses. Parameter estimation is used to estimate a population parameter. - answer- Point estimation provides a single descriptive value of the population estimate (e.g. a mean or odds ration). Interval estimation provides the upper and lower limits of a range of values-- the confidence interval (CI)-- between which the population value is expected to fall, at a specified probability. Researchers establish the degree of confidence that the population value lies within this range. A 95% CI indicates a 95% probability that the true population value lies between the upper and lower confidence limits. - answer- Hypothesis testing through statistical procedures enables researchers to make objective decisions about the validity of their hypotheses. - answer- The null hypothesis states that there is no relationship between research variables, and that any observed relationship is due to chance. Rejection of the null hypothesis lends support to the research hypothesis. - answer- A Type I error occurs when a null hypothesis is incorrectly rejected (a false positive). A Type II error occurs when a null hypothesis is wrongly accepted (a false negative). - answer- Researchers control the risk of a Type I error by establishing a level of significance (or alpha level), which is the probability that such an error will occur. The .05 level means that in only 5 out of 100 samples would the null hypothesis be rejected when it should have been accepted. - answer- In testing hypotheses, researchers compute a test statistic and then determine whether the statistic falls at or beyond the critical region on the relevant theoretical distribution. If the value of the test statistic indicates that the null hypothesis is "improbable," the result is statistically significant (i.e. obtained results are not likely to result from chance fluctuations at the specified level of probability). - answer- Most hypothesis testing involves two-tailed tests, in which both ends of the sampling distribution are used to define the region of improbable values; a one-tailed test may be appropriate if there is a strong rationale for an a priori directional hypothesis. - answer- Parametric tests involve the estimation of at least one parameter, the use of interval- or ratio-level data, and assumptions of normally distributed variables; nonparametric tests are used when the data are nominal or ordinal or when a normal distribution cannot be assumed- especially when samples are small. - answer- Tests for independent groups compare separate groups of people, and tests for dependent groups compare the same group of people over time or conditions (within-subjects designs). - answer- Two common statistical tests are the t-test and analysis of variance (ANOVA), both of which are used to test the significance of the difference between group means; ANOVA is used when there are three or more groups (one-way ANOVA) or when there is more than one independent variable (e.g. two-way ANOVA). Repeated measures ANOVA (RM_ANOVA) is used when there are multiple means being compared over time. - answer- Nonparametric analogs of t-tests and ANOVA include the Mann-Whitney U Test and the Wilcoxon signed-rank test (two-group situation), and the Kruskal-Wallis and Friedman tests (three-group or more situations). - answer- The chi-square test is used to test hypotheses about differences in proportions. For small samples or small cell sizes, Fisher's exact test should be used. - answer- Statistical tests to measure the magnitude of bivariate relationships and to test whether the relationship is significantly different from zero include Pearson's r for interval-level data, Spearman's rho and Kendall's tay for ordinal-level data, and the phi coefficient and Cramer's V for nominal-level data. - answer- Confidence intervals can be constructed around almost any computed statistic, including differences between means, differences between proportions, and correlation coefficients. CI information is valuable to clinical decision-makers, who need to know more than whether differences are probably real. - answer- Power analysis is a method of estimating either the likelihood of committing a Type II error or sample size requirements. Power analysis involves four components: desired significance level (alpha), power (1-beta), sample size (N), and estimated effect size (ES). Effect size estimates convey important information about the magnitude of effects in a study and are a useful supplement to p values and CI values. Cohen's d is a widely used effect size index summarizing mean-difference effects between two groups. - answer- inferential statistics (p.404) - answer-statistics that permit inferences about whether results observed in a sample are likely to be found in the larger population laws of probability (p.404) - answer- sampling error (p.404) - answer-the fluctuation of the value of a statistic form on sample to another drawn from the same population sampling distribution of the mean (p.404) - answer-a theoretical distribution of a statistic, using the values of the statistic, using the values of the statistic (e.g., the means) computed from an infinite number of samples as the data poin