# Psych 2017 Chapter 7: Summarizing and interpreting data using statistics

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1 Psych 2017 Chapter 7: Summarizing and interpreting data using statistics Descriptive statistics - The gal f descriptive statistics is t describe sample data - Can be cntrasted with inferential statistics where the gal is t make inferences abut ppulatins frm sample data Frequency distributins - A listing f values in a data set alng with their frequency Graphic representatins f data - Bar graph f frequency distributin Used with categrical variables Height f bar represents frequency f categry Bars shuld nt tuch - Histgram Used with cntinuus quantitative variables N space between bars - Line graphs Als used with quantitative variables Particularly useful fr interpreting interactins - Scatterplts Depicts relatinship between tw quantitative variables Crrelatins Measures f central tendency - Prvides a single value that is typical f the distributin f scres Mde Mst frequently ccurring value Least useful measure f central tendency Median Middle scre when numbers are in ascending r descending rder Mean Arithmetic average Mst cmmnly used measure f central tendency Measures f variability - Prvides a numerical value indicating the amunt f variatin in a grup f scres Range Highest scre minus lwest scre Rarely used as a measure f variability Variance Average deviatin f the data values frm their mean in squared units Standard deviatin Square rt f variance Rughly the average amunt that individual scres deviate frm the mean Standard deviatin and the nrmal curve Z-scres Standardized values transfrmed frm raw scres Mean f z-distributin is always zer; standard deviatin always ne

2 Indicates hw far abve r belw a raw scre is frm its mean in standard deviatin units; e.g., a z-scre f indicates a raw scre that is ne standard deviatin unit abve the mean In a nrmal distributin, the prprtin f scres ccurring between any tw pints can be determined Examining relatinships amng variables - Unstandardized difference between mean A cmparisn f mean differences between levels f an independent variable - Standardized difference between means Inferential statistics - Hyptheses - Significance testing - Errrs Hyptheses - Null hypthesis Effect size Chen s d is a cmmn measure f effect size Mean difference is divided by standard deviatin Small, medium, and large effect sizes are indicated by values f at least.2,.5, and.8 respectively Predicts n effect r relatinship in the ppulatin - Scientific/ Alternative hypthesis Predicts an effect r relatinship in the ppulatin Significance testing - Determines the likelihd f btaining sample data when null hypthesis is true - A decisin making prcess- determining if yu are dealing with ne r tw ppulatins Hw d yu decide t reject the null hypthesis? - Must base this n analysis f data cllected - Cmparisn f grup means Tw ppulatins if yu reject the null hypthesis One ppulatin if yu fail t reject the null hypthesis Mean- arithmetic average Example: peple wh sleep lnger will scre higher n a cgnitive skills test Randm assignment t tw levels f the IV 4 hurs r 8 hurs SCAT (Sam s Cgnitive Ability Test) Errr- grups will differ by chance alne - Standard deviatin and variance Bth measure the variability f scres arund the mean Standard deviatin is the square rt f variance If there is verlap in the scres f the varius grups the mean difference in the scres may be due t chance - Inferential statistical technique These techniques enable yu t estimate the prbability f the grup mean differences ccurring by chance By judging the difference between their means relative t the spread r variability f their scres

3 Significance testing - Alpha level Chsen by researcher- highest prbably value taken as evidence against the null hypthesis (i.e., sample value is t extreme fr null hypthesis) - Critical regin Prtin f distributin f sample means cntaining extreme scres- size is equal t alpha level - p value prbability f btaining sample values when the null hypthesis is true- cmpared with alpha t determine if null hypthesis can be rejected (i.e., test is significant) Errrs - Type I errr: reject the null hypthesis when it is true - Type II errr: fail t reject the null hypthesis when it is false Type I and Type II errrs are threats t validity Fail t Reject the H Reject the H

4 Chapter 14: The nuts and blts f using statistics Selectin f a statistical test - The statistical test selected is based n the design f the study Is it a within r between participants design Hw many independent variables are there- ne r mre than ne Hw many levels f the IV are there

5 Inferential statistical test guides - Independent samples t-test Between participants design Tw levels f ne independent variable - One- way analysis f variance Between participants design Mre than tw levels f ne independent variable - Tw- way analysis f variance Between participants design Tw r mre independent variables - Paired samples t-test Within-participants design Tw levels f ne independent variable - Repeated measures analysis f variance Within- participants design

6 Mre than tw levels f the independent variable Independent samples t-test - Used with a between participants design with ne IV and tw levels f the IV T-value rati f the between grup mean difference t the average within grup variability Hw large must the rati be t reject the null? Significance level - Definitin- prbability that an bserved difference is due t chance Reject the null if there is less than a 5% (alpha=.05) r 1% (alpha=.01) chance f the between grup difference being due t chance variability - Hw t determine if the significance level is reached Cmpare the t-value btained with the critical value f t Critical value f t identified by degrees f freedm and alpha Degrees f freedm= N-2 fr independent samples t-test Making a decin based n the cmputed and critical values - Reject the null if Cmputed t-value critical t-value P-value <.05 - Fail t reject the null if Cmputed t-value < critical t-value P-value >.05 One- way analysis f variance - Invlves partitining ttal variance int tw independent surces f variance - Between- grups variatin: measure f tw surces f variability Any treatment effect that exists Chance variatin - Within- grups variatin: Chance variatin - Ttal variatin= between+ within grups variatin Mean square - Mean square (MS) is a variance estimate used in Anvas - Between and within-grups variatin is divided by their degrees f freedm MS = grups variatin/ degrees f freedm - Between degrees f freedm number f grups minus 1 - Within degrees f freedm- number f research participants minus the number f grups F-rati - F-rati= MS (between)/ms (within)=(treatment + chance)/chance

7 - N treatment effect, then F-rati=1 - Fr a treatment effect t exist F-rati must be greater than 1 Interpreting results f analysis f variance - First identify the critical value f F crrespnding t the selected significance level--.05 r.01 significance level Identified by lking in the table f critical values f F Enter tables using the between and within degrees f freedm - Reject null f F-value critical value f F - Fail t reject the null if F- value < critical value f F - If yu reject the null, then yu must interpret the results Calculate the mean f each grup t see which grup perfrmed best D pst hc tests t see which grups were significantly different Tw-way analysis f variance - Statistical test applied t data cllected frm factrial designs - Prvides a test f main and interactin effects - Lgic is the same as with ne-way ANOVA Partitin ttal variatin fr each independent variable Interactin variatin Measure f chance r errr variatin - Steps in calculating a tw-way ANOVA Cmpute each surce f variatin Cmpute the MS fr each surce f variatin- divide the variatin by its df Calculate an F-rati fr each main effect and interactin surce f variatin by dividing each by the MS (errr) Interpreting tw-way ANOVA - Cmpare each F-value with the critical value f F Reject null if F-value critical value f F Fail t reject the null if F-value < critical value f F - If yu reject the null then must interpret the results Main effects Interactins Rejecting r failing t reject the null hypthesis - Reject the null if the t r F-value yu calculated meets r exceeds the critical value btained frm the t r F tables - Fail t reject if it des nt meet the critical value Because it is lgically impssible t accept the null Smetimes may need t prvisinally accept it When n data refute a null cnclusin When the prbability f the null being false is large When the design is pwerful in cntrlling fr extraneus variable Ptential errrs in statistical decisin- making - Type I errr- falsely reject the null Cntrlled by the significance level - Type II errr- fail t reject a false null - Tends t be an inverse relatinship between Type I and II errrs - Assume Type I errrs are the wrst s fcus n cntrlling these

8 Chapter 8: Reprting Research Guidelines fr effective writing - Knw yur audience - Identify yur purpse Expsitry writing discurse designed t cnvey infrmatin r explain what is difficult t understand - Write clearly Ecnmy f expressin: using as few wrds as pssible t cnvey an idea Precisin Adherence t grammatical rules - Write an interesting reprt Structure f a research reprt - Title page - Abstract - Intrductin - Methds - Results - Discussin

9 - References - Appendixes - Ftntes The APA frmat - Page 1- title page Running head Title Authr(s) name(s) and institutinal affiliatins Authr nte Department affiliatins f each authr Identify grants r ther supprt and acknwledge assistance in the cmpletin f the prject Identify persn f cntact - Page 2- abstract On every page put a header and the page number in the upper right hand curner f the manuscript Abstract in nly ne paragraph 150 wrds State prblem under investigatin Describe experimental methd State the main findings State cnclusin and implicatins - Next series f cntinuus pages Intrductin Intrduce the general tpic/research questin Review backgrund studies in terms f relevance t research questin and hypthesis develpment Briefly describe current study State hyptheses and justificatin fr hyptheses Overall, argue that current study is imprtant and will add new knwledge t the field Methd Purpse f the methds sectin Allws reader t assess validity and reliability f the study Allws researchers t replicate yur study Cmpnents f the methd sectin Participants Design Materials/apparatus Prcedure Can cmbine sectins- Participants and prcedure are mst imprtant Participants Number Imprtant demgraphics Where btained Cmpensatin

10 Design Type f research design Variables (dependent, independent) Hw variables were measured/manipulated Materials/ apparatus Descriptin f stimuli r scales used in the study Where stimuli/scales were btained r hw they were develped Descriptin f any apparatus used in the study Prcedure Chrnlgical descriptin f what the participants/ subjects experienced in the study Descriptin f instructins given t participants Order f tasks Results The results sectin summarizes the data cllected and the statistical treatment f them. First, briefly state the main results f findings. Discussing the implicatins f the results is nt apprpriate here. Mentin all relevant results, including thse that run cunter t the hypthesis. D nt include raw scres r raw data with the exceptin, fr example, f single case designs r illustrative samples. Dependent measure analyzed Statistical tests used Alpha level used fr tests Descriptive statistics- figures/tables Statistical values frm tests p values frm tests Statements abut significant effects r relatinships Discussin Begin with a clear and cncise statement f the essential findings What have I cntributed here? Hw has my study helped t reslve the riginal prblem? Cmpare current results with thse frm past studies Prvide explanatins f unexpected results What cnclusins and theretical implicatins can I draw frm my study? Discuss pssible flaws in the study Discuss future research - References -- starts a new page The reference sectin prvides a cmplete listing f all the surces cited in the article The references are listed in alphabetical rder by the last name f the first authr - Ftntes- n a separate page - Tables - Figure captins APA 6 th - n same page as figures - Figures - Appendixes- used t prvide a verbatim cpy f questinnaires, respnse sheets, and/r instructins - Multiple study articles Intrductin sectin that prvides backgrund fr all yur studies

11 Methd and results fr each study General discussin sectin that describes cnclusins fr all the studies cmbined Other APA frmatting issues t keep in mind - Cite all surces Past studies (Smith & James, 2009) have shwn r Smith and James (2009) have shwn Include a title page with a title, running head (ges n every page), page number, authrs names, and authrs affiliatins - 1 inch margins fr all pages - Fllw heading structure: centered in bld, left justified in bld - New page fr abstract, intrductin, references, tables, figures nly - Qutatins- fewer than 40 wrds, insert int text - Numbers- use wrds fr numbers less than 10 - Physical measurements- use metric - Tables- use nly when they can cnvey and summarize the data mre ecnmically and clearly than can a discussin - Figures- use when they cnvey a cncept mre effectively than can a table - Figure captins- a brief descriptin f the cntent Presentatin f statistical results - Mean and standard deviatin The sample as a whle was relatively yung (M = 19.22, SD = 3.45) The average age f students was years (SD = 3.45) - Percentages Nearly half (49%) f the sample was married - Chi-square - T-tests - ANOVAs The percentage f participants that were married did nt differ by gender, X^2(1, N = 90) = 0.89, p >.05. There was a significant effect fr gender, t(54) = 5.43, p <.001, with men receiving higher scres than wmen. There was a significant main effect fr treatment, F(1, 145) = 5.43, p <.01, and a significant interactin between treatment and time f day, F(2, 145) = 3.13, p < Crrelatins The treatment and depressin scres were strngly crrelated, r(55) =.49, p <. 01. Specifically, as amunt f treatment increased, depressin scres increased (see Figure 2). Submissin f the research reprt fr publicatin - Chse a jurnal t submit yur article t - Jurnal impact factr Based n the average frequency f citatins fr articles in a jurnal The higher the impact factr, the mre selective the jurnal and the harder it is t get papers published in the jurnal Psychlgical sciences Send t the editr f the selected jurnal Include a cver letter stating yu are submitting the manuscript Editr will send the manuscript ut fr review

12 In several mnths yu will have the manuscript returned with the reviewers cmments and the editrs decisin Reject Accept revise - Jurnals fr undergraduate research Jurnal f Undergraduate Studies Mdern Psychlgical Studies: A Jurnal f Undergraduate Research The Jurnal f Psychlgy and the Behaviral Sciences The Psi Chi Jurnal f Student Research Presenting research results at prfessinal cnferences - Oral presentatin Fllw general APA fr rder f infrmatin Briefer frm than paper Designed fr visual and ral acquisitin Clarity f visual aids (e.g., PPTs) imprtant - Pster presentatin Fllw general APA fr rder f infrmatin Visual acquisitin imprtant Use pictures and bullet pints fr clarity and space issues Make sure infrmatin flws clearly dwn clumns and frm left t right n pster Prepare shrt ral explanatin f what is n the pster t guide viewer thrugh - Cnferences where undergraduates can present Suthern Sciety fr Philsphy and Psychlgy MPA (Midwestern Psychlgy Assciatin) Psi Chi APA (American Psychlgical Assciatin) and APS (American Psychlgical Sciety). Cmmn pitfalls - Prblem: misuse f citatins and qutes- students tend t veruse qutes in research reprts and incrrectly cite surces - Prblem: incrrect use f verb tense- students ften use the wrng verb tense t describe their studies - Prblem: prviding t many details f backgrund studies- writing a full summary f a past study in the intrductin f a research reprt - Prblem: describing backgrund literature frm secndary surces0 students ften use secndary surces fr literature reviews leading t prblems with misrepresentatin f the primary surce - Prblem: fcus n statistics in results sectin- making statements abut the statistics instead f the effect r relatinship tested

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