Exploring+Inferential+Statistics+and+their+Discontents


 * ** EDU7006-8 ** ||  ||
 * ** Quantitative Research Design ** || ** 2 Exploring Inferential Statistics and Their Discontents ** ||
 * Stephen: Thank you for your work on this assignment! I have made comments throughout your document so please see them for specific feedback on the problems and essay responses. A couple of your calculations were slightly off, but overall I think you are on the right track! I hope that you will take the time to revisit those few calculations after you read my feedback since that is where some additional learning can occur. Thanks! **
 * Stephen: Thank you for your work on this assignment! I have made comments throughout your document so please see them for specific feedback on the problems and essay responses. A couple of your calculations were slightly off, but overall I think you are on the right track! I hope that you will take the time to revisit those few calculations after you read my feedback since that is where some additional learning can occur. Thanks! **

=Exploring Inferential Statistics and Their Discontents=

Jackson (2012) Chapter Exercises
=2.015; //t//(5) obt = 2.739; //p// < 0.05, one-tailed test =t 2 / t 2 + //df =// 2.739 2 / (2.739 2 + 5)= 7.502 / (7.502 + 5) = 7.502 / 12.502 = __r__ 2 __= 0.60 for a large effect size__.* =39; W(n1= 7, n2 = 7) = 43, //p// = 0.05, one-tailed test.
 * 2a.** This is a one-tailed test. We are interested in the product preventing cavities.
 * 2b**. H 0 : μ new TP ≥ μ oth ; H a : μ new TP < μ oth
 * 2c.** Z obt =** 1.591 ** *
 * 2d.** Z cv = 1.645
 * 2e.** H 0 should not be rejected. The difference in cavities between other brands and the new toothpaste are not significant enough to support the claim.
 * 2f.** CI = M ± Z * SEM, M = 1.5, Z = ± 1.96, SEM = 1.12 / √ 60 = 1.12 / 7.746 = 0.145 = 1.5 ± 19.6*0.145 = 1.5 ± 2.834 = __CI = -1.334 to 4.334__. Since you can’t have negative cavities, I would assume that the confidence interval would be from 0 to 4.334 cavities.
 * 4.** As the degrees of freedom increase the critical value decreases. By comparing //t// obt with his //t// cv with //df// = 13 there is a larger percentage that he will fail to reject the null hypothesis even though it should be rejected; a Type II error.
 * 6a.** This is a two-tail test; hypothesis is that there is a difference, but no direction is indicated.
 * 6b.** μ cm = μ pop ; Ha: μ cm ≠ μ pop
 * 6c.** //t// = ( M – μ) / SEM; //t// obtvv (59 – 58) / 1.016 = __0.984__
 * 6d.** //t//(13) cv = ±2.160
 * 6e.** H0 should not be rejected. The difference demonstrated in spatial ability between those who listen to classical music and those in the general population who do not listen to classical music is not large enough to reject the null hypothesis.
 * 6f.** CI = M ± t cv * SEM = 59 ± 2.160*1.016 = 59 ± 2.195 = __CI = 56.805 to 61.195__
 * 8a.** χ 2 Σ ( O – E) 2 / E = (31-24) 2 / 24 + (89 – 96) 2 / 96 = 72 / 24 – 72 / 96 = 49 / 24 + 49 / 96 = 2.042 + 0.510 = χ 2 obt = 2.552
 * 8b.** //df// = 1
 * 8c.** χ 2 cv = 3.841
 * 8d.** The null hypothesis is rejected if χ 2 obt is greater than χ 2 cv ; this is not the case. The researcher will __fail to reject the null hypothesis__, because the number of people exercising in California is not significantly larger than the number of people exercising in the United States.
 * 2a.** This study meets the assumptions of the Independent-Groups //t// Test with a one-tailed test.
 * 2b.** H 0 : μ NM ≥ μ Mus ; Ha: μ NM < μ Mus
 * 2c.** //t// cv 1.86; //t//(8)* obt 2.193; //p// < .05, one-tailed test **[this should be //t//(16)** obt **= 2.578** ,** //p// < .01] **
 * 2d.** __Reject the null hypothesis__, and conclude that studying without music leads to better test scores.
 * 2e.** r 2 = t 2 / t 2 + //df =// 2.193 2 / 2.193 2 + 8 = 4.809 / (4.809 + 8) = 4.809 / 12.809 = __r__ 2 __= 0.375__ for a large effect size.*
 * 2f.** [image in Word file]
 * 2g.** CI = M1 – M2 ± t cv (s M1 – M2 ) = 7.556 – 6.000 ± 1.86* (0.503 – 0.333) = 1.556 ± 1.86*0.170 = 1.556 ± .316 = __CI = 1.240 to 1.872__
 * 4a.** This study meets the assumptions of the //t// Test for Correlated Groups with a one-tailed test.
 * 4b.** H 0 : μ NM ≥ μ Mus ; H a : μ NM < μ Mus
 * 4c.** //t// cv
 * t-Test: Paired Two Sample for Means ||  ||   ||
 * || //No Music // || //Music // ||
 * Mean || 6.666666667 || 7.666666667 ||
 * Variance || 1.466666667 || 0.666666667 ||
 * Observations || 6 || 6 ||
 * Pearson Correlation ||  || 0.674199862 ||
 * <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">Hypothesized Mean Difference ||  || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">0 ||
 * <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">df ||  || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">5 ||
 * <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">t Stat ||  || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">2.738612788 ||
 * <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">P(T<=t) one-tail ||  || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">0.020429702 ||
 * <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">t Critical one-tail ||  || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">2.015048372 ||
 * <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">P(T<=t) two-tail ||  || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">0.040859404 ||
 * <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">t Critical two-tail ||  || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">2.570581835 ||
 * 4d.** __Reject the null hypothesis__, and conclude that studying without music leads to better test scores.
 * 4e.** r 2
 * 4e.** r 2
 * 4f.** [image in Word file]
 * 4g.** CI = M1 – M2 ± t cv (s M1 – M2 ) = 7.667 – 6.667 ± 2.015 * (0.494 – 0.333) = 1 ± 2.015 * 0.161 = 1 ± 0.324 = __CI = 0.676 to 1.324__
 * 6a.** This study meets the assumptions of the Wilcoxon Rank-Sum Test one-tailed test.
 * 6b.** H 0 : μ gs ≥ μ r s ; H a : μ gs < μ rs
 * 6c.** W(n1=7, n2=7) cv
 * <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: center;">Red Sauce ||  |||| <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: center;">Green Sauce ||
 * <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">7 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">8 ||  || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">4 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">1 ||
 * <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">6 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">4.5 ||  || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">5 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">2 ||
 * <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">9 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">12.5 ||  || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">6 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">4.5 ||
 * <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">14 ||  || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">8 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">10.5 ||
 * <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">6 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">4.5 ||  || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">7 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">8 ||
 * <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">7 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">8 ||  || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">6 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">4.5 ||
 * <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">8 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">10.5 ||  || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">9 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">12.5 ||
 * || **<span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">62 ** ||  ||   || **<span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">43 ** ||
 * 6d.** Fail to reject null hypothesis. Taste scores for the two sauces did not differ significantly.
 * 8a.** χ 2 (1, N = 105) = 6.732, //p// < 0.05
 * <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">Men || <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">Women ||  ||   ||   ||
 * <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">15 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">27 || <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">Front || **<span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">42 ** ||  ||
 * <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">32 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">19 || <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">Back || **<span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">51 ** ||  ||
 * **<span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">47 ** || **<span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">46 ** ||  || **<span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">93 ** ||   ||
 * <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">Expectation ||  ||   ||   ||
 * <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">21.2 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">20.8 ||  ||   ||   ||
 * <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">25.8 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">25.2 ||  ||   ||   ||
 * || <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">cv || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">3.841 ||  ||   ||
 * <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">Chi-Squared || **<span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">6.732 ** || <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">df= || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">1 ||
 * <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">1.826 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">1.866 ||  ||   ||   ||
 * <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">1.504 || <span style="color: #000000; display: block; font-family: 'Calibri','sans-serif'; font-size: 14.6667px; text-align: right;">1.537 ||  ||   ||   ||
 * 8b.** //df// = (2-1)*(2-1) = 1
 * 8c.** χ 2 cv = 3.841
 * 8d.** Reject the null hypothesis. There is a significant difference in seating preferences between women and men. More men sit in the back rows and more women sit in the front row.
 * 8c.** χ 2 cv = 3.841
 * 8d.** Reject the null hypothesis. There is a significant difference in seating preferences between women and men. More men sit in the back rows and more women sit in the front row.

Part I Assignment Question Answers
<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**What are degrees of freedom? How are they calculated?** The degrees of freedom are the number of scores in any sample that can freely change. For any given mean, all of the values can freely change to maintain the mean except the last one. Thus, the degrees of freedom can be calculated with the formula df = N – 1.* <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**What do inferential statistics allow you to infer?** The inference in inferential statistics is what you can say about a population based on the conclusions found in a research study <span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">on a sample of the population <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">following specific <span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">sampling and <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"> statistical procedures. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**What is the General Linear Model (GLM)? Why does it matter?** The general linear model (GLM) unifies various statistical models into a flexible generalization of linear regression such that response variables can be other than normally distributed. Since the goal of data analysis “ <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">is to summarize or describe accurately what is happening in the data <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">” ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Trochim & Donnelly, 2012, p. 297 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">) the GLM enhances this ability. The GLM has brought together disparate statistical tools into one model, while also allowing for the discovery of advanced models, such as SEM and HLM, for testing complex models. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**Compare and contrast parametric and nonparametric statistics.** **Why and in what types of cases would you use one over the other?** Parametric statistics are used when analyzing interval or ratio data. To use parametric statistics, the data must be bell-shaped and will have known or calculable population means and standard deviations. Parametric statistics allow for more accurate and precise estimates than nonparametric measures as long as the assumptions upon which they are based are true. Parametric statistics allow for predictability of scores based on probabilities. Nonparametric statistics are used when analyzing nominal or ordinal data. With nonparametric statistics the distribution of data does not have to be bell-shaped and population parameters are not needed. Nonparametric statistics are used in situations where (a) an assumption of distribution probability is not warranted, (b) ranking is involved, and (c) assessing preferences. The design of a study may affect which particular statistical test is used, but does not differentiate between parametric and nonparametric statistics. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**Why is it important to pay attention to the assumptions of the statistical test? What are your options if your dependent variable scores are not normally distributed?** Parametric statistics are only accurate, or have statistical power, when the assumptions upon which the test is based are true. If the test assumptions are not met, the results can be inaccurate, misleading, or wrong. When dependent variable scores are not normally distributed, but are bell-shaped, a t-test parametric analysis can be performed. If, however, the dependent variable scores are not bell-shaped the only option for analysis is the use of nonparametric statistical tests.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Part II Assignment Question Answers
<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**What does p = .05 mean? What are some misconceptions about the meaning of p =.05? Why are they wrong? Should all research adhere to the p = .05 standard for significance? Why or why not?** Also known as the significance level, or alpha, of a study; p represents the probability of committing a Type I error, of rejecting the null hypothesis when it is true. Schmidt (2010) identified six misconceptions regarding significance, including: (a) reliable replication, (b) identifies the size of a relationship, (c) when not significant it indicates no relationship, (d) are essential to research, (e) guarantee impartiality, and (f) contribute to the field. Significance bears no relationship <span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">on <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"> replication, and indicates that in situations where there is no actual relationship between variables there is a 1:20 chance that a significant finding will be found. Correlation or effect size identifies the strength of a relationship; the significance does not. Type II and Type I errors are predicted because there is always a chance that a significant result will be found even if no relationship occurs, or that a nonsignificant result will be found even if there should be <span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">a significant <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"> one. Significance identifies* the probability of the first possibility. Significance can be manipulated though sample size, is not the best measure for summarizing research data, and is not essential to research, does not guarantee impartiality of observations, and may distort and “ <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">retard the development of cumulative knowledge <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">” ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Schmidt, 2010, p. 239 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">). <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Cohen (1992) identifies that when multiple null hypotheses are being tested the significance level be lowered so that “ <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">experimentwise [sic] risk not become too large <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">” ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">p. 156 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">) and conclusion validity decreased with a “ <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">fishing and the error rate problem <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">” ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Trochim & Donnelly, 2012, p. 255 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">). While a significance level of 0.05 is traditional, there is nothing sacrosanct regarding that level of Type I probability, and Faul, Erdfelder, Land, and Buchner (2007) concluded that there is no reason why the exact significance level of results should not be reported in reports and articles. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**Compare and contrast the concepts of effect size and statistical significance.** There are four important components of statistical power; significance, sample size, effect size, and power ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Cohen, 1992; Faul, Erdfelder, Land, & Buchner, 2007; Trochim & Donnelly, 2012 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">). Many researchers focus on significance almost to the exclusion of the other components ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Cohen, 1992 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">). The idea behind statistical analysis of research is to determine whether a treatment creates two separate populations whose differences can be measured. The effect size is a measure showing the degree the experimental mean is expected to deviate from the control mean or the variance accounted for in a study. Statistical significance is the maximum allowable risk of erroneously rejecting the null hypothesis and committing a Type I error. Both are similar because as each decreases the minimum sample size must increase in order to maintain sufficient power to find a significant result. As each increases in value the minimum sample size decreases to maintain consistent power. Other than their relationship to statistical power, significance and effect size are not similar at all. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**What is the difference between a statistically significant result and a clinically or “real world” significant result? Give examples of both.** A statistically significant result traditionally can occur by chance 1 in 20 times even if the null hypothesis is false. Clinical, or real-world, significance occurs when research results are useful to expanding the knowledge of the field. Statistical significance indicates results obtained are different from the population mean and probably are not due to chance. Schmidt (2010) identified the results of a meta-analysis in which eight studies were found to be statistically nonsignificant, while another eight studies were found to be statistically significant, even though all 16 studies used the same “ <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">test of decision making to supervisory rating of job performance in various midlevel jobs <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">” ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">p. 234 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">). A study can return statistical significance even if the null hypothesis is true or not be statistically significant even though the null hypothesis is false; clinical significance is never achieved unless the underlying data represent an important difference ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Carver, 1978 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">). Schmidt’s meta-analysis is an example of practical significance because eliminating the sampling and measurement error from the 16 studies resulted in “ <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">basically a single value (.32) because there is nearly no variation <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">” ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">p. 236 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">). <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**What is NHST? Describe the assumptions of the model.** Null hypothesis significance testing (NHST) assumes that differences in means from the H0 are due principally because of sampling variance or by chance ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Kirk, 2003 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">). If a statistically significant result is found, the null hypothesis is rejected on the assumption that the result is probably not due to those factors. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**Describe and explain three criticisms of NHST.** Three criticisms of null hypothesis significance testing are, (a) the wrong question is being answered, (b) it is a trivial exercise, and (c) it makes an ordinal value out of a ratio value, losing much in the conversion.* Researchers want to ascertain truth when conducting research; what is the probability that this treatment will consistently result in the outcomes predicted (reliability) and that the research hypothesis is true (validity)? Significance testing contributes to answering neither of these questions, but instead answers a different question; what is the probability that the results obtained were not a chance occurrence? The assumptions of significance testing identify that there is sampling variance in all research measures. Based on this assumption, the probability that two means on any measure will be exactly the same to an infinite number of decimal places is zero. Therefore, the null hypothesis will be false in every case, making it a trivial exercise to compare anything with it. The third criticism of NHST is that significance testing creates an arbitrary “ <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">go-no-go decision straddled over p = .05 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">” ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Cohen, 1992, p. 156 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">) or a “ <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">cliff effect <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">” ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Kirk, 2003, p. 87 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">) that tends to mark significant findings as important and nonsignificant finds as unimportant; a “ <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">hurdle, with the statistical significance test coming before further consideration of the results <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">” ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">Carver, 1978, p. 388 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">). This hurdle, in essence, places chance and sample size before real-world significance. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**Describe and explain two alternatives to NHST. What do their proponents consider to be their advantages?** An alternative to NHST proposed by Schmidt (2010) is to follow the example of physical scientists and utilize confidence intervals. He suggests that confidence intervals provide more information than do significance tests and are just as objective. He further cites the 1999 APA Task Force Report on significance testing that confidence intervals should be reported in research results.* Kirk (2003) identified that confidence intervals provide all of the information associated with significance, but also contains “ <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">a range of values within which the population parameter is likely to lie,. . . the same unit of measurement as the data,. . . [and] are especially useful in assessing the practical significance of results <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">” ( <span style="font-family: 'Times New Roman',Times,serif; font-size: 90%;">p. 88 <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">). <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">Both Schmidt (2010) and Kirk (2003) also propose the reporting of effect sizes in research results. Effect sizes summarize data by identifying the strength of an association. Through reporting this strength estimation can be made regarding the practical usefulness of the results. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">**Which type of analysis would best answer the research question you stated in Activity 1? Justify your answer.** I did not propose or state a research question in Activity 1, nor was one asked of me.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;"> [TT1] <span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">This isn’t quite correct. It should be about -1.59. Here you first need to find out the standard error of the mean before you can calculate your obtained z value. This, of course, impacts other parts of your answer. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">[TT2] <span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">This should be 16. Your obtained t is a bit low. I’m don’t mind at all if you want to use a data analysis program, but I’m not sure what might have happened in SPSS, maybe all the data was not included in the calculation? This, of course, means other parts of your answers are not correct, 2e, etc.. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">[TT3] <span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">This is not quite right because your df is not right! Please see comment 2. <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">[TT4] This should be about 1.12. [Interesting, but an effect size cannot be more than 1 since it is something divided by the same something plus the degrees of freedom.] <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">[TT5] This might change, depending on your statistical test. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">[TT6] <span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">Watch out for personification in your writing. See the Writing Center for details! <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">[TT7] <span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 120%;">Add citation. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">[TT8] This is a great idea. I’m very supportive of reporting confidence intervals and effect sizes. <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%;">[TT9] You are right! This is an error in the syllabus. I have asked our instructional design team to update it in the next version of the syllabus.


 * = References ||
 * * Carver, R. P. (1978). The case against statistical significance testing. //Harvard Educational Review, 48//(3), 378-399. Retrieved from http://scholasticadministrator.typepad.com/thisweekineducation/files/the_case_against_statistical_significance_testing.pdf
 * Cohen, J. (1992). A power primer. //Psychological Bulletin, 112//(1), 155-159. doi:10.1037/0033-2909.112.1.155
 * Faul, F., Erdfelder, E., Lang, A.-G., & Buchneer, A. (2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, biomedical sciences. //Behavior Research Methods, 39//(2), 175-191. Retrieved from http://www.psycho.uni-duesseldorf.de/abteilungen/aap/gpower3/download-and-register/Dokumente/GPower3-BRM-Paper.pdf
 * Jackson, S. L. (2012). //Research methods and statistics: A critical thinking approach// (4th ed.). Belmont, CA: Wadsworth Cengage Learning.
 * Kirk, R. E. (2003). The importance of effect magnitude. In S. F. Davis (Ed.), //Handbook of Research Methods in Experimental Psychology// (pp. 83-105). doi:10.1002/9780470756973.ch5
 * Schmidt, F. (2010). Detecting and correcting the lies that data tell. //Perspectives on Psychological Science, 5//(3), 233-242. doi:10.1177/1745691610369339
 * Trochim, W. M. K., & Donnelly, J. P. (2008). //The research methods knowledge base// (3rd ed.). Mason, OH: Cengage Learning. ||