Lecture Conducting and reading research in health and human performance (4/e): Chapter 14 - Ted A. Baumgartner, Larry D. Hensley

Chapter 14 - Inferential data analysis. This chapter includes contents: Inferential statistics, uses for inferential statistics, sampling error, hypothesis testing, hypothesis testing procedures, statistical significance, parametric statistics, t-tests, types of t-test,...

Chapter 14 Inferential Data Analysis Inferential Statistics   Techniques that allow us to study samples and then make generalizations about the population Inferential statistics are a very crucial part of scientific research in that these techniques are used to test hypotheses Uses for Inferential Statistics    Statistics for determining differences between experimental and control groups in experimental research Statistics used in descriptive research when comparisons are made between different groups These statistics enable the researcher to evaluate the effects of an independent variable on a dependent variable Sampling Error  Differences between a sample statistic and a population parameter because the sample is not perfectly representative of the population Hypothesis Testing  The purpose of the statistical test is to evaluate the null hypothesis (H0) at a specified level of significance (e.g., p < 05)  In other words, the treatment effects differ significantly so that these differences would be attributable to chance occurrence less than times in 100? Hypothesis Testing Procedures  State the hypothesis (H0)  Select the probability level (alpha) Determine the value needed for significance Calculate the test statistic Accept or reject H0    Statistical Significance  A statement in the research literature that the statistical test was significant indicates that the value of the calculated statistic warranted rejection of the null hypothesis  For a difference question, this suggests a real difference and not one due to sampling error Parametric Statistics  Techniques which require basic assumptions about the data, for example:      normality of distribution homogeneity of variance requirement of interval or ratio data Most prevalent in HHP Many statistical techniques are considered robust to violations of the assumptions, meaning that the outcome of the statistical test should still be considered valid t­tests  Characteristics of t-tests     requires interval or ratio level scores used to compare two mean scores easy to compute pretty good small sample statistic Types of t­test  One-Group t-test   Independent Groups t-test   t-test between a sample and population mean compares mean scores on two independent samples Dependent Groups (Correlated) t-test   compares two mean scores from a repeated measures or matched pairs design most common situation is for comparison of pretest with posttest scores from the same sample Overview of Multivariate Tests  Univariate statistic –   used in situations where each participant contributed one score to the data analysis, or in the case of a repeated measures design, one score per cell Multivariate statistic –  used in situations where each participant contributes multiple scores Example Multivariate Tests     MANOVA Canonical correlation Discriminant analysis Factor analysis Multiple Analysis of Variance     MANOVA Analogous to ANOVA except that there are multiple dependent variables Represents a type of multivariate test Prediction and Regression Analysis   Correlational technique Simple prediction    Predicting an unknown score (Y) based on a single predictor variable (X) Y’ = bX + c Multiple prediction   Involves more than one predictor variable Y’ = b1X1 + b2X2 + c Multiple Regression/Prediction    a.k.a multiple correlation Determines the relationship between one dependent variable and or more predictor variables Used to predict performance on one variable from another   Y’ = b1X1 + b2X2 + c Standard error of prediction is an index of accuracy of the prediction Statistical Power  The probability that the statistical test will correctly reject a false null hypothesis   it is effectively the probability of finding significance, that the experimental treatment actually does have an effect a researcher would like to have a high level of power Statistical Power   alpha = probability of a Type I error    beta = probability of a Type II error   rejecting a true null hypothesis this is your significance level failing to reject a false null hypothesis Statistical power = - beta Factors Affecting Power     Alpha level Sample size Effect size One-tailed or two-tailed test Alpha level  Reducing the alpha level (moving from 05 to 01) will reduce the power of a statistical test This makes it harder to reject the null hypothesis Sample size   In general, the larger the sample size the greater the power This is because the standard error of the mean decreases as the sample size increases One­tailed versus two­tailed tests  It is easier to reject the null hypothesis using a one-tailed test than a two-tailed test because the critical region is larger Effect size     This is an indication of the size of the treatment effect, its meaningfulness With a large effect size, it will be easy to detect differences and statistical power will be high But, if the treatment effect is small, it will be difficult to detect differences and power will be low Effect Size   Numerous authors have indicated the need to estimate the magnitude of differences between groups as well as to report the significance of the effects One way to describe the strength of a treatment effect, or meaningfulness of the findings, is the computation of “effect size” (ES) ES =  M1 ­ M2 SD Note: SD represents the standard deviation of the control group or the pooled standard  deviation if there is no control group Effect Size  Interpretation of ES by Cohen (1988)     0.2 represents a small ES 0.5 represents a moderate ES 0.8 represents a large ES Researchers using experimental designs are advised to provide post hoc estimates of ES for any significant findings as a way to evaluate the meaningfulness A Priori Procedures  Calculate the power for each of the statistical procedures to be applied   requires three indices - alpha, sample size, effect size Estimate the sample size needed to detect a certain effect (ES) given a specific alpha and power  may require an estimation of ES from previous published studies or from a pilot study ... observed frequencies and expected frequencies for a questionnaire item in agreement with each other? Independent Groups Chi­Square    a.k.a two-way chi-square or contingency table chi-square Used... hypotheses Uses for Inferential Statistics    Statistics for determining differences between experimental and control groups in experimental research Statistics used in descriptive research when... extension of the t-test     requires interval or ratio level scores used for comparing or more mean scores maintains designated alpha level as compared to experimentwise inflation of alpha