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 Zscres Standardized values transfrmed frm raw scres Mean f zdistributin 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 zscre 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 ttest 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 ttest Withinparticipants 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 ttest  Used with a between participants design with ne IV and tw levels f the IV Tvalue 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 tvalue btained with the critical value f t Critical value f t identified by degrees f freedm and alpha Degrees f freedm= N2 fr independent samples ttest Making a decin based n the cmputed and critical values  Reject the null if Cmputed tvalue critical tvalue Pvalue <.05  Fail t reject the null if Cmputed tvalue < critical tvalue Pvalue >.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 withingrups 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 Frati  Frati= MS (between)/ms (within)=(treatment + chance)/chance
7  N treatment effect, then Frati=1  Fr a treatment effect t exist Frati 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 Fvalue 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 Twway 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 neway ANOVA Partitin ttal variatin fr each independent variable Interactin variatin Measure f chance r errr variatin  Steps in calculating a twway ANOVA Cmpute each surce f variatin Cmpute the MS fr each surce f variatin divide the variatin by its df Calculate an Frati fr each main effect and interactin surce f variatin by dividing each by the MS (errr) Interpreting twway ANOVA  Cmpare each Fvalue with the critical value f F Reject null if Fvalue critical value f F Fail t reject the null if Fvalue < 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 Fvalue 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  Chisquare  Ttests  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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