Assignment Paper

PSYC2012 – PSYCHOLOGY: AN EVIDENCE-BASED APPROACH 2

APA Statistical Write-Up Guide

Writing Statistical Copy in APA Style

Prepared by Professor John Reece

Presented below are some examples of correct presentation of statistical results in APA style. Clearly, there are other correct ways of presenting this material in terms of descriptions of the experimental design and basic style of expression. Some general points to note are:

1. Exact p levels should be reported where possible. When your SPSS output provides you with a significance level that consists of a string of zeroes (e.g., p = .000), the rule is: Drop the last zero and change it to a 1, and write p < [whatever]. For example, if your significance level on a correlation is sig=.000, you would write p < .001. It is quite common for SPSS output to provide you with significance levels that consist of strings of zeroes. You should never write p = .000, because this is statistically impossible. 2. With regard to decimal places, some general rules are: Report correlations to two decimal places (e.g. r(N = 120) = .89). Report F ratios and t scores to two decimal places. With significance levels, report to two decimal places if the first digit is not a zero (e.g. p = .34); if the first digit is a zero (e.g. p = .037), you can report to either two or three decimal places (e.g., p = .037 or p = .04 are both correct and acceptable); if the first and second digits are zeroes (e.g. p = .003), report to three decimal places; never report to more than three decimal places. The smallest p level you should report is p < .001, as described above. 3. Only include leading zeroes (e.g. 0.56) if the statistic can take on a value greater than 1. Correlations and significance levels never take leading zeroes. t and F values do. 4. With many assumption tests the norm is to present significance levels only, although there is nothing wrong with providing complete information, and many SPSS procedures provide you with complete information for assumption tests. The Levene test, for example, is an F ratio, and can be reported in full, but it’s not essential. Similarly, for post-hoc procedures, there is no need to provide detailed statistical information, and most SPSS procedures will not provide you will detailed results anyway; depending on which version of SPSS you are using, all you might get are significance levels. 5. Provide correct Greek letters where possible (e.g., ); it looks more professional. Greek letters are found under the Symbol font in MS Word (any version), or you can use Insert Symbol. Never italicize Greek letters. 6. Different types of correlation coefficient are represented by the use of sub-scripts. For example, Pearson’s Product-Moment correlation is represented simply as r, but a point-biserial correlation is presented as rpb; a Spearman’s rho is r. In all other respects, correlations are presented identically. The one exception to this is Kendall’s tau, which is presented as the Greek letter . 7. For students at Honours level and above: You should always provide some measure of effect size where possible. Many journals are now requiring the reporting of effect sizes each time a test of significance is reported. Undergraduate students don’t need to worry about this. 8. Sections 2.07 and 4.41 – 4.46 (pages 116 – 123) of the APA Publication Manual (6th edition) provide clear information on correct presentation of statistical copy. Other information relevant to the reporting of statistical material is scattered throughout the APA Publication Manual in related sections; use the index to locate relevant material. There is lots of very useful information in the APA manual related to this. As students majoring in psychology, you should have your own copy of the APA Publication Manual; you should not relying on second-hand APA style guides or online resources. 9. At the end of each chapter of Field’s text, Discovering Statistics Using IBM SPSS Statistics (4th ed.), examples of APA style write-up are included. These are detailed and very useful. The APA symbol for a mean is M, and for a standard deviation, SD. If you want to be really smart, you can present these as small capitals, which is the preferred method of printing capital letters when they are acronyms or initials; for example, M, and, SD. Also, means and standard deviations are two of the few statistical results that are presented in parentheses: Scores for males (M = 11.45, SD = 4.56) were higher than those for females (M = 9.88, SD = 2.78). Finally, please note that this guide is provided for students and at many levels of data analysis expertise, ranging from undergraduate to higher degree by research. It’s important to understand that not all of the material provided here is going to be necessary for you to provide in the context of any assignment that you might be doing. For example, in the analysis of covariance, the test of the assumption of homogeneity of slopes is quite an advanced topic that is only taught at higher levels, as is testing for simple main effects in factorial ANOVA, and the various measures of effect size. When using this guide in the context of an assignment, you should only feel obliged to provide the results that you have been taught to use. If something looks unfamiliar to you, that’s because it hasn’t been discussed in class, and you can ignore it. A Chi-Square Contingency Table A contingency table analysis of sex with voting preference revealed a significant relationship between these two variables,  (3, N = 101) = 35.15, p = .019, V = .25. Examination of standardised residuals indicated that the high proportion of women voting labour (standardised residual = 2.4) contributed to the significant result. Notes: The “V” is a measure of strength of association/effect size (Cramer’s V), and is relevant only for students at Honours level and above. An Independent Samples t-Test With Associated Assumption Test A Levene test found that the assumption of homogeneity of variance was met, p = .71; therefore, a two-tailed independent samples t-test based on equal variances was carried out. No significant sex difference in sequential processing ability was found, t(99) = 1.53, p = .13, d = 0.12, 95% CI [0.06, 0.18]. Notes: This result includes the effect size measure, Cohen’s d, and a 95% confidence interval around that effect size measure. This is relevant only for students at Honours level and above. The confidence interval that is provided by the t-test command is NOT the same as this and should not be reported. Also note, that the SPSS t-test procedure doesn’t provide much info on the Levene test, so all you are able to report is the p level. The EXPLORE procedure provides full ANOVA output for the Levene test. A Matched Samples t-Test A two-tailed paired samples t-test found no significant difference between left- and right-hand reaction time, t(100) = 1.47, p = .14, d = 0.18, 95% CI [0.08, 0.28]. Notes: This result includes the effect size measure, Cohen’s d, and a 95% confidence interval around that effect size measure. This is relevant only for students at Honours level and above. A Correlation Coefficient There was a significant positive correlation between State and Trait Anxiety, r(N = 125) = .68, p <.001, r2 = .46, 95% CI [.23, .91]. Notes: APA style does not require an indicator of sample size to be included with the result, but I prefer it. It is acceptable to leave the “N =” out of the parentheses (e.g., r(125)) Note that the symbol for sample size for a complete sample is N. Different types of correlation coefficient are identified by subscripts, which are not presented in italics; for example, a point biserial correlation is rpb; an intra-class correlation is ric, and so on. I have also included r2 with this result. This is not common, but it is informative, because it shows the proportion of shared variability associated with the correlation. This is followed by a 95% confidence interval around the r2. This is relevant only for students at Honours level and above. A One-Way Independent Groups (or Single-Factor Between-Subjects) ANOVA With Post-Hoc Tests A single-factor between-subjects ANOVA was used to analyse the relationship between the four memory enhancement methods and memory test performance; a significant overall treatment effect was found, F(3, 36) = 63.12, p < .001, p2 = .65, 95% CI [.23, .88]. Subsequent post-hoc tests using Tukey’s HSD procedure  = .05) revealed significant differences at p < .001 between all possible pairwise comparisons among the treatment groups. Notes: In the above example, all of the post-hoc tests were significant at p < .001, and I was able to report the results of the post-hoc tests with a single summary statement. However, this will often not be the case, and I would be obliged to report individual post-hoc test results. This result incorporates a measure of the effect size, partial eta-squared, 2 and its associated confidence interval. This is relevant only for students at Honours level and above. Planned Comparisons With Associated Assumption Test Results were analysed using three a priori between-subjects planned comparisons. Because a Levene Test found that the homogeneity of variance assumption had been violated, p = .001, hypothesis tests were based on unequal variances. A significant effect was found for the first comparison, which contrasted the control group with the combined effect of the three treatment groups, t(10.3) = 8.40, p < .001, d = 1.46, 95% CI [0.86, 2.06]. The second test compared the two cognitive-based methods, imagery and mnemonics; this comparison was also significant, t(12.4) = 4.75, p < .001, d = 0.88, 95% CI [0.68, 1.08]. Finally, the drug-based method was compared against the average effect of the two cognitive-based methods; again, a significant effect was found, t(21.4) = 9.79, p < .001, d = 1.30, 95 %CI [0.95, 1.65]. Notes: This result includes the effect size measure, Cohen’s d, and a 95% confidence interval around that effect size measure. This is relevant only for students at Honours level and above. Note the fractional degrees of freedom for the main tests; this is common when reporting the results based on unequal variances. A Between-Subjects Factorial ANOVA Data were analysed using a 4 x 2 between-subjects factorial ANOVA. The first factor consisted of the four memory enhancement methods (control, drug, imagery, mnemonics). The second factor was sex (male, female). A significant interaction was found between the two factors, F(3, 32) = 4.88, p = .007, p2 = .24, 95% CI [.04, .88]. Because the interaction term was found to be significant, main effects were not considered. Follow-up testing of the interaction effect using simple main effects found a significant difference among the four treatments for both males, F(3, 33) = 41.25, p < .001, p2 = .88, 95% CI [.23, .98], and females, F(3, 33) = 27.88, p < .001, p2 = .72, 95% CI [.35, .80]. There were no significant sex differences at any of the four levels of memory program, although the strongest effects were seen within the control subjects, p2 = .08, 95% CI [< .01, .33], and the mnemonic subjects, p2 = .03, 95% CI [< .01, .23]. Notes: For these results, the effect size statistic, partial 2, has been provided. Partial 2 is easily obtained from SPSS. There is a difference between partial 2 and 2, but for functional purposes, they mean the same thing. Partial 2 is differentiated from 2 by the sub-scripted p, p2, although p2 is commonly used when reporting both. This is relevant only for students at Honours level and above. Also, note that full statistical information has not been provided for the non-significant simple main effects. It is acceptable to do this, although were I writing this for a report, I would probably provide full statistical information. Finally, note the practice of considering the interaction test first and, if that is significant, ignoring the main effects and focusing exclusively on follow-up procedures related to the interaction. Although this approach is statistically “pure”, it is not incorrect to consider the overall main effects as well as the interaction. However, if the interaction is significant, it should be the focus of any follow-up analyses. A Single-Factor Between-Subjects Analysis of Covariance (ANCOVA) Data from the four memory enhancement conditions were analysed using a single-factor between-subjects analysis of covariance (ANCOVA), with IQ test scores serving as a covariate. A test of the assumption of homogeneity of slopes revealed no significant interaction between IQ and the four treatment groups, F(1,35) = 1.32, p = .68, p2 = .05, 95% CI [< .01, .31]. Results showed that IQ test scores covaried significantly with the dependent variable, F(1,35) = 295.85, p < .001, p2 = .75, 95% CI [.45, .90]. After partialling out the variance associated with IQ test scores, there was a significant difference among the four treatment groups, F(3, 35) = 4.28, p = .011, p2 = .28, 95% CI [.18, .56] Post-hoc testing using pairwise comparisons of the estimated marginal means with Bonferroni adjusted  levels revealed a significant difference between Group 1 and Groups 3 and 4 (both p < .001), Group 1 and Group 2, p = .041, and Group 2 and Group 4, p = .005. The comparisons between Group 3 and Group 4, p = .08, and Group 2 and Group 3, p = .14, were non-significant. Notes: The effect size partial 2 has been provided. Also, note the assumption test for the important assumption of homogeneity of slopes. This is relevant only for students at Honours level and above. Finally, note the complete detail on all relevant significance levels provided for the post-hoc tests. A Single-Factor Within-Subjects (aka One-Way Repeated Measures) ANOVA With Assumption Test and Post-Hoc Tests In order to test for any differences among the four essay-production methods, a single-factor within-subjects analysis of variance was performed on the essay quality scores. The multivariate approach to the analysis of within-subjects data was used. A significant difference was found among the four essay production conditions,  = .01, F(3, 37) = 3573.05, p < .001, p2 = .88, 95% CI [.46, .91]. Post-hoc testing was carried out using pairwise comparisons of estimated marginal means with Bonferroni adjusted  levels. Significant differences at p < .001 were found for all but one of the six possible pairwise comparisons. There was no significant difference between written essays and those produced using speech-recognition, p = .73. A Single-Factor Between-Subjects Multivariate Analysis of Variance (MANOVA) To investigate differences among the four memory enhancement conditions, the following four dependent variables were entered into a single-factor between-subjects multivariate analysis of variance (MANOVA): scores on the memory test, Stanford-Binet IQ scores, scores on the experimental IQ test, and scores on the test of learning anxiety. A significant multivariate effect was found,  = .05, F(12, 87.6) = 15.01, p < .001, p2 = .35, 95% CI [.10, .33]. Follow-up univariate analyses of each dependent variable found a significant difference among the four memory enhancement methods for only one of the dependent variables—Stanford-Binet IQ test scores, F(3, 96) = 14.07, p < .001, 2 = .28, 95% CI [.15, .41]. Post-hoc testing amongst the four groups on this dependent variable using Tukey’s HSD procedure revealed significant differences at p < .001 for all six post-hoc comparisons. Notes: For the follow-up univariate tests, significance levels only have been provided for the significant result, although were I writing this up for a thesis or a paper I would certainly provide complete statistical information for the non-significant results as well. Finally, note the steps that have taken place in this analysis: 1. The multivariate analysis is carried out. 2. If this is significant, you then move onto the analysis of each of the dependent variables separately. 3. If any of these are significant, you report the appropriate post-hoc tests. The following books also provide excellent examples of writing up the results of analyses in APA style: Green, S. B., & Salkind, N. J. (2016). Using SPSS for Windows and Macintosh: Analyzing and understanding data (8th ed.). Upper Saddle River, NJ: Prentice Hall. Amazon page: https://www.amazon.com/Using-Windows-Macintosh-Books-Carte/dp/0134319885/ref=mt_looseleaf?_encoding=UTF8&me= Tabachnick, B.G., & Fidell, L.S. (2001). Computer assisted research design and analysis.. Boston: Allyn & Bacon. Amazon page: https://www.amazon.com/Computer-Assisted-Research-Analysis-Barbara-Tabachnick/dp/020532178X/ref=sr_1_1?s=books&ie=UTF8&qid=1509412643&sr=1-1&keywords=computer+assisted+research+design+and+analysis Tabachnick, B.G., & Fidell, L.S. (2013). Using multivariate statistics (6th ed.). Boston: Allyn & Bacon. Amazon page: https://www.amazon.com/Using-Multivariate-Statistics-International-Sixth/dp/B00SW92ZWW/ref=sr_1_4?s=books&ie=UTF8&qid=1509412695&sr=1-4&keywords=using+multivariate+statistics&dpID=51Hw1mI17RL&preST=_SX218_BO1,204,203,200_QL40_&dpSrc=srch PSYC2012 - PSYCHOLOGY: AN EVIDENCE-BASED APPROACH 2 ASSESSMENT 2: Data Analysis Assignment You have been provided with the data for this assignment as an SPSS file. The data file has been provided with generic variable names (V1, V2, etc.), which you should change. You will need to provide more detailed VARIABLE LABELS and VALUE LABELS in the data file. The hypothetical study examines the relationship between body mass index (BMI), sex, and different measures of response inhibition, delay of gratification, and positive/negative affect. The researchers recruited 120 adults and recorded their sex (V1: 1 = female; 2 = male) and BMI (V2: 1 = underweight; 2 = normal; 3 = overweight). Participants reported their level of hunger (V3) – at the start of the study – on a Likert scale ranging from 1 = “not hungry at all” to 9 = “extremely hungry”. Participants then completed a range of self-report measures: • Kirby Monetary Choice Questionnaire: 27 items, each presenting two choices: either an immediate reward (e.g., “$55 today”) or a larger delayed reward (e.g., “$75 in 61 days”). The higher the overall score (V4), the more likely is the person to choose the smaller, immediate rewards. • Brief Sensation Seeking Scale: 8 items, scored on a Likert scale from 1 = “strongly disagree” to 5 = “strongly agree”. Example item: “I like wild parties”. The higher the overall score (V5), the more likely is the person to seek novel and stimulating experiences. • The Tightwad-Spendthrift Scale: 4 items, scored using either a 1-11 (item no.1) or 1-5 (items 2-4) ratings. The higher the score (V8), the more difficultly people have in controlling their spending. Tightwads (i.e., those with low scores), on the other hand, tend to become anxious and experience pain when they have to spend money. • The Positive and Negative Affect Schedule – Expanded form (PANAS-X): Participants are presented with a list of 60 adjectives (e.g., confident, joyful, upset, angry), and are asked to indicate the degree to which they feel each of these positive and negative emotional states in general. Items are scored on a Likert scale ranging from 1 = “very slightly or not at all” to 5 = “extremely”. V9 includes positive and V10 negative affect scores. High scores on V9 and V10 represent high levels of positive and negative affect, respectively. Finally, participants completed a Go/No-Go task, which measures inhibitory control. A Go/No-Go task presents two stimuli; one is a “go” target to which participants are instructed to respond as fast as they can (e.g., by pressing spacebar on a keyboard), and the other is a “no-go” target to which one must withhold responses. Failure to withhold responses to no-go targets is known as a commission error. The lower the commission error, the better is the inhibitory control. The current study used happy and sad faces as the stimuli. In the first half of the task, happy faces were the go and sad faces were the no-go targets. In the second half, the sad faces became the go while the happy faces were the no-go targets. Previous literature suggests those with reduced inhibitory control find it more difficult to resist responding to happy than sad faces. V6 represents commission errors to happy no-go targets, and V7 commission errors to sad no-go targets. Your first task is to provide appropriate variable labels for all the variables and value labels for V1 (sex) and V2 (BMI). After this, answer the following questions. You must provide the relevant SPSS output along with any write-up that is requested. Any figures or tables must be in APA style. You are not required to interpret any of the results in “common sense” terms. The exercise is solely related to the data analysis, and the variables and their scores are somewhat arbitrary, so don’t worry if the results don’t make “real world” sense. This is not real data, so don’t worry if the results seem odd. There are two parts to this report. The most important part consists of the write up of the analyses, including graphs and tables (if required) in correct APA style; in other words, in the style that you would use if you were presenting this material in a research report. The second part consists of the raw SPSS output of the analysis that you have carried out. Both sections need to be combined into a single Word file for submission to the online class space. Remember that SPSS provides a lot of output. Not all of this output needs to be submitted with your assignment. You should copy and paste only output that directly relates to the question that you are answering. Please note that you are required to answer ALL questions. 1. Examine all the variables from V3 to V10 for any violations of the normality assumption. Pick a variable that you feel violates the assumption. Run at least three transformations on that variable, and then make a decision as to which transformed version leads to the best improvement. If none of the transformed versions leads to any improvement, then continue to use the original variable. Write up the procedure you followed for that one variable (ignore the others that you tested) in the form that you would write it up were it part of a research report. For all of the remaining questions, use the transformed variable (assuming that you decide that the transformed variable is an improvement on the original; otherwise, stick with the original). 2. Test the homogeneity of variance assumption on variables V3 to V10, with variable V2 as the grouping variable/factor. Pick one variable that you feel violates the assumption and run the appropriate power transformation on that variable. Write up the procedure you followed for that one variable (ignore the others that you tested) in the form that you would write it up were it part of a research report. For all of the remaining questions, use the transformed variable (assuming that you decide that the transformed variable is an improvement on the original; otherwise, stick with the original) 3. Carry out a contingency table analysis using 2 to answer the question of whether there is a significant relationship between sex and BMI. In other words, are males and females equally represented across the three BMI groups? Show a bar chart of this relationship and present the descriptive statistics in a properly formatted APA table. Make sure that after running the 2 analysis you use the standardised residuals to help interpret the result. 4. Is there a sex difference for (a) the scores on the Kirby Monetary Choice Questionnaire (V4), and (b) the Brief Sensation Seeking Scale (V5)? Write up the results in APA style, including properly formatted APA-style graphs of the means and an APA style table of the descriptive results (you can provide the results for both variables in the one table or in separate tables). Two separate analyses and two graphs are required for this question, and at least one table. 5. Show a correlation matrix of the eight dependent variables, with significance levels. Present the matrix as a properly formatted APA-style table, then pick two significant correlations from the matrix and write up these results in APA style. 6. Is there a significant difference between commission errors to the happy (V6) and sad faces (V7)? Pick an appropriate significance test to answer this question, and write the results up in APA style, along with a properly formatted APA bar chart and a table of the descriptive results. Due Date The assignment is to be submitted Week 11 Tuesday 14/04/2020 at 11:55pm via Turnitin. Upload your completed report as a single Word document ONLY to the online class space. Loading The report is worth 30% of your grade for this unit. Marking Guide Each question will be marked out of five, giving a total grade out of 30. • A grade of 4 – 5 will be given for an answer that is of High Distinction standard • A grade of 3.5 will be given to an answer that is of Distinction standard • A grade of 3 will be given to an answer that is of Credit standard • A grade of 2.5 will be given to an answer that is of Pass standard • Answers that fail will be given a grade < 2.5 Each question will be assessed holistically, taking into account the following aspects: • Accuracy of data analysis; that is, have the correct procedures been used to answer each question. • Correct reporting of each analysis; that is, have the correct conclusions been reached, and accurately reported. • Adherence to APA style in all respects. • Where tables and/or figures have been reported, are they in correct APA style? The following overall guidelines will sit atop these criteria when assigning a final grade: HD Outstanding work in terms of originality, understanding, interpretation and presentation. DI A very high standard of work which demonstrates originality and insight. CR Demonstrates a higher level of understanding and presentation. PA Satisfies the minimum requirements for content and presentation. NN Fails to satisfy the minimum requirements of content and pres