AEC 874 (2007) Field Data Collection & Analysis in Developing Countries. VII. Data Analysis & Project Documentation

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1 AEC 874 (2007) Field Data Cllectin & Analysis in Develping Cuntries VII. Data Analysis & Prject Dcumentatin Richard H. Bernsten Agricultural Ecnmics Michigan State University 1 A. Things t Cnsider in Planning Data Analysis 1. Yur Research Prpsal What were yur riginal research bjectives? Are these bjectives still apprpriate, r d yu need t mdify them? 2. Yur Target Audience a) Wh is the audience fr yur analysis? Academic faculty? Plicy makers? Anther client? Multiple audiences? b) What are the expectatins f yur target audience, regarding the type f analysis? 2 1

2 3. Yur Data a) What type f analysis is pssible, with the data yu have cllected? Sample size Few vs. many cases? Measurement level (see Andrews et. Al.) Nminal categrical? Ordinal Likert scales? Scale-cntinuus numeric data? Data level Husehld vs. variety level? 4. Yur Statistical Expertise a) Nvice? b) Expert? 3 B. Statistics, Data & Analysis 1. Rle f Statistics Summarize data (descriptive statistics) Reveal relatinships (measures f assciatin) 2. Classes f Statistics Univariate - ne variable (e.g,, mean, median, mde) Bivariate - tw variables (e.g, Chi square, crrelatin analysis) Multivariate - several variables (requires gd data) (e.g., regressin, lgit/prbit analysis) 4 2

3 3. Types f Data (measurement level, SPSS) Nminal data--data values represent categries with n intrinsic rder (e.g., gender, types f incme surces) Ordinal data data values represent categries with sme intrinsic rder (e.g., Likert, rank-rder scales) Scale data data values are cntinuus numeric values n an interval r rati data scale (e.g., age, incme, yield) Nte Yu can transfrm scale data t categrical data, but categrical data can t be transfrmed t cntinuus data implicatins fr data cllectin? 5 4.Types f Analysis (by data type) a) Descriptive Analysis (Fig. 10.3) 1) Nminal/categrical data Frequencies tables--describe data distributins with numbers r percents SPSS utput reprts data categries, numbers f bservatins, & percent (ttals, adjusted, cumulative) May als ask SPSS t reprt data as histgrams, hrizn bar charts, pie charts Limit the number f data categries t <10 If yu have >9, cmbine categries with few cases int ther 6 3

4 2) Scale/cntinuus numeric data Measures f central tendency Mean is the average case (arithmetic average) Nt valid fr nminal/categrical data Nt usually used fr rdinal data (i.e., can t assume equal distance between items) Very sensitive t distributin f scale data Median is the middle case Use if scale data are asymmetric Use fr rdinal data Mde is the mst cmmn data value Only is an indicatr f central tendency fr nminal/categrical data Nte--Fr nrmally distributed data, mean=median=mde 7 Measures f Dispersin/Spread Minimum is lwest value Maximum is highest value Range is high/lw interval Standard deviatin (SD) indicates percent f cases in a certain ranges (if the data are nrmally distributed) Shape f the Distributin (fr scale data) (Fig. 10.5, 10.9) Skewness shws degree & directin f asymmetry If symmetrical, cefficient = 0 If skewed left, cefficient = psitive (left) If skewed right, cefficient = negative (right) 8 4

5 Kurtsis measures peakedness f distributin (Figs. 10.6, 10.10) If same as nrmal distributin, cefficient = 0 If very peaked, cefficient = psitive If very flat, cefficient = negative Nte--If skewness r kurtsis value is nt clse t 0 Mean isn t an apprpriate measure f central tendency Standard deviatin isn t an accurate measure f dispersin Prblem n clear definitin f meaning f nt clse t 0 9 b) Analysis f the Relatinship/Assciatin Between Variables Questin--D pairs f variables mve tgether r are they independent? Bivariate analysis des nt require yu t assume/identify a dependant/independent variable Multivariate analysis assesses the relatinship between a dependant & independent variables Dependant variable --variable being affected Independent variable --variable(s) affecting the dependent variable Crrelatin des nt imply nt causatin Statistics that measure assciatin d nt indicate causatin Only thery implies causatin 10 5

6 Chice f apprpriate statistic t assess relatinships depends n Type f variables nminal, rdinal r scale (cntinuus) Which variable is independent/dependent Cnsideratins in Chsing a Statistical Methd Dependant Variable Nminal r Ordinal Data Interval r Rati Data Nminal r Ordinal Data (Discrete Categrical) Crss-Tabulatin Paired t test ANOVA Independent Variable Interval r Rati Data (Cntinuus, numeric Discriminant, Prbit, Lgit Crrelatin Regressin See Andrews, A Guide fr Selecting Statistical Techniques fr Scial Science Analysis fr details. Overheads 11 C. Strategies fr Analyzing Survey Data 1. Review yur research bjectives, hyptheses, and questinnaire 2. Develp a tentative reprt utline (analytical plan) 3. Use descriptive statistics t explre yur data (e.g., frequencies, mean, median, mde, SD, skewness, kirtsis) Use these results t decide What sub-grup cmparisns are pssible/lk interesting explre (e.g., Is there enugh variability t justify further analysis?) What assciatin can yu assess with the data? 4. Revise yu analytical plan, based n yur new knwledge, regarding the characteristics f the data 5. Finally, use bivariate/multivariate statistics t assess relatinships/assciatins 12 6

7 D. Strategies & Cnsideratins in Using Statistics Begin yur analysis using descriptive analysis, then lk fr assciatins t explain relatinships 1. Describe the Variables Basic analysis a) Nminal/categrical variables 1) Strategies t cnsider First run frequencies/percents (Example 10.1) if there are very few cases in a categry, cmbine/recde sme categries t ther Be sure t save the riginal variables (with riginal cdes) in an archive file r rename t a new variable befre recding 13 If there are many cases in the categry ther, recde sme f these cases t specific categries (if pssible) Cnsider recding cntinuus data int a few grups (e.g., recde cntinuus variable educatin t: 1=0-11, 2=12, 3=13-15, 4=> 16; r likert scale data (1-5) t 1-2, 3, 4-5) Review the frequency distributin t decide what break pints t use fr regruping cntinuus data t categrical data (e.g., first ½=lw, secnd ½=high; first 1/3=lw, secnd 1/3, medium, third 1/3=high) After recding data, g t the variable view and update variable values/infrmatin fr the new/recded variables 2) Statistics fr nminal/categrical data Mde it the apprpriate statistic fr assessing central tendency 14 7

8 b) Scale (interval/rati, cntinuus data) variables 1) Strategies t cnsider Run means, mde, median, range, skewness, kurtsis, and standard deviatin Then, lk fr utlyers; assess the nrmal distributin assumptin 2) Statistics If data ARE apprximately nrmally distributed Present mean (mde, median) If data are NOT apprximately nrmally distributed: Recde t categrical data and present the distributin spread in a frequency table Lking fr Relatinships--Statistical Inference Def. Making inferences abut the ppulatin parameters frm estimates f sample statistics (requires randm sampling) a) Sme Cncepts 1) Standard Errr f the Estimate Backgrund We sample frm a ppulatin t generate sample statistics t estimate unknwn ppulatin parameters. Different samples will give different estimates. The theretical distributin f all pssible values f a statistic btained frm a ppulatin is the sampling distributin f the statistic. The mean f the sampling distributin is the expected value f the statistic. The standard deviatin is the standard errr. When we estimate the SE frm a single sample SD SE x = \/ N 16 8

9 SE f mean (a SPSS descriptive statistics ptin) indicates hw clse/far the sample mean is t ppulatin mean Fr means f interval/rati data & percentages, reprt the SE and/r the margin f errr, which is a multiple f the SE At 99% CI, ME=2.57 SE At 95% CI, ME=2.00 SE At 90% CI, ME=1.65 SE Sample Size and Data Distributin A Cautin If the sample is large, the sampling distributin f the sample mean is apprximately nrmal, even if ppulatin was nt nrmally distributed. If the ppulatin is small and nt nrmal, the sampling distributin f mean wn t be nrmal, limiting statistical inference In such cases, yu shuld use nn-parametric statistics t analyze the data This is why survey researchers ften use the chi square 17 statistic t analyze survey data 2) Cnfidence Interval (CI) Def. A range arund sample mean, based n the SE (i.e., 95% CI is range +/- 2 SEs) SE and CI indicate reliability f a statistic b) Statistical Significance These statistics all shw the degree f assciatin & statistical significance (nn-significance) Significance indicates the prbability that a relatinship exists in sample, if it desn t exist in ppulatin (e.g., 1% prbability that yu accept a false H as true) Alpha/critical level f prbability fr acceptance is researchers/spnsr determined 18 9

10 Traditinal alpha levels f 99%/95% are cnventins, nt abslutes (Fisher, agricultural research). Must cnsider the cnsequence f accepting a false result as true Example A traditinal variety yields 500 kg/ah & a mdern variety yields 800 kg/ha, but the difference is nly significant at the 80% level. Each variety cst the same price. Wuld yu plant the MV r the TV? It s ften mre infrmative t reprt the level at which yur results are significant, rather than simply saying they are nn-significant (e.g., The means are significantly different at the 88% level) Lack f statistical significance may be due t the fact that N relatinship exists Nn-sampling errr was large, s data are nt accurate The sample size is small, s the SE is large 19 Statistical significance des NOT indicate the imprtance f yur result!!! The imprtance f a result is a functin f the size f the cefficient & the meaning that the variables/relatinships imply. Statistical results are either significant r nn-significance (NOT insignificant) A result may be statistically significant, but still insignificant (i.e., very small, and thus nt imprtant) Even if the differences in the numerical values are large (e.g. mean yields f 500 kg/ha vs. 1,000 kg/ha), if the relatinship is nn-significant, this implies that the values are essentially the same. S, dn t emphasize the magnitude f the nn-significant difference when reprting yur results

11 c) Measures f Assciatin Used t Analyze Survey Data 1) Crsstabulatin (Chi square analysis, X 2 ) Objective T test if the distributin f ne variable differs significantly fr values f ther variable Data Requirements: Bth variables must be categrical (I.e., nminal, rdinal) But yu can cnvert scale data variables t categrical variables and then use Chi square analysis Dn t need t assume the data are nrmally distributed Dn t need t identify a dependent/independent variable Mst cmmn measure f assciatin fr survey variables (Why?) 21 A Wrd f Cautin The X 2 statistic is invalid if the expected value is <5. Hwever SPSS will still reprt a X 2 value even if it is meaningless!!! In a crss-tab table, the cell with the smallest expected frequency (nt the actual frequency) is the ne n the rw with the smallest rw ttal & in the clumn with the smallest clumn ttal (Table 10.3) T estimate the expected cell frequency, divide the smallest rw ttal in the crss-tab table by N & multiply this number by the smallest clumn ttal. Evaluate: < 5?) Suggestins (Table example) (Example 11.4) The variable yu chse as the rw/clumn variable nt critical It s cnfusing t interpret the results if yu request bth clumn & rw percents, s request nly clumn percents 22 11

12 If N is small (< 200?), cnstruct crss-tab tables with 3 r fewer categries/variable Why? If the N is very small (< 100?), use the results in the crss-tab table t estimate the expected frequency Why? If the expected value < 5, recde the data int fewer equal size grups t increase the expected value Statistics SPSS reprts the X 2 statistic (larger is better) & the prbability level (smaller is better) (Example 11.3) In the text f an article, reprt the directin f the bserved relatinship & prbability level (in parentheses) [e.g., X 2 analysis indicates a significant (95% level) negative relatinship between age & educatin] In the table, reprt crss-tab results, X 2 statistic & the prbability level 23 2) Analysis f Variance (ne-way) Objective Determine if the mean values f the dependant variable are fr each categry f the independent variable, significantly different (t-test is a special case) Data Requirements Must identify an independent & dependant variables Independent variable--categrical data with 2 r mre categries (e.g., 2 r varieties) (Fig. 11.5) Dependent variable--scale (cntinuus) data (e.g., yield f several varieties) Each case f the dependant variable must be independent f the ther Cautin Spread f data pints (I.e., variance) in independent variable must be similar fr each data categry & nrmally distributed 24 12

13 Suggestins Test fr hmgeneity f variances Dn t use ANOVA, if variances are very different r sample sizes f grups differ greatly Statistics (Example 11.5) F-test evaluates significance (i.e., HO that all means are equal) Multiple cmparisns test (Shaffe) indicates if individual means are different (pairwise cmparisns) In the text f an article, reprt directin f the relatinship, significantly different means & F-test statistic [e.g., ANOVA indicates the mean yield f variety A (845 kg/ha) & B (933 kg/ha) are significantly (95% level) higher than the yield f variety C (534 kg/ha), with a F-value f 6.75] In tables, reprt grup means, F-test (prbability level fr the ANOVA) & the multiple cmparisn test (Scheffe) results 25 3) Crrelatin Analysis Objective Measures the degree that 2 cntinuus variables mve tgether frm ne case t anther Data Requirements Bth variables must be scale (cntinuus) r rdinal data Dn t need t identify a dependant/independent variable Suggestins Run crrelatins t explre ptential relatinships Statistics Different types f data require different statistics Fr interval/rati scale data, use Pearsn s prductmment crrelatin Fr rdinal data, use Spearman rank crrelatin 26 13

14 Crrelatin cefficient (r) indicates strength f relatinship & ranges frm 0 t +/-1 (Example 11.6) Sign indicates directin f relatinship (Fig. 11.7) Sign psitive (+), direct Sign negative (-), inverse Cefficient f determinatin (r 2 ) indicates the percent f shared variance In text f an article, reprt the directin f the relatinship (psitive/negative), crrelatin cefficients (r) & r 2 [e.g., Crrelatin analysis indicated that yield & N-fertilizer rates are psitively crrelated (r =0.79), with a R 2 f 0.62] In the table, reprt the crrelatin cefficient (r), signs, and the prbability level (r 2 ) May present several variables/crrelatins in matrix frmat, which is ften included as an appendix 27 4) Regressin Analysis Objective Measures the relatinship between cntinuus independent & dependent variables (Fig. 11.9) Data Requirements Must identify 1 dependant variable, 1 r mre independent variables Independent & dependant variables are usually scale data But can use dummy independent variables (0,1) in multiple regressin Linear mdels are mst cmmn, but can use ther functinal frms, depending n yur assessment f the theretical relatinship (e.g., lg, quadratic mdels) 28 14

15 Suggestins The scatter f plts indicates the data distributin, which must be well-distributed ver the range f data values (Fig ) Print ut scatter plts f dependent/independent variables (e.g., yield, fertilizer) & assess the scatter plts t find utlyers Check fr utlyers befre running a regressin & cnsider drpping cases with extreme/impssible values (i.e., small plts > measurement errr) Use thery (and pssibly scatter plts) t specify mdel & functinal frm, but avid stepwise prcedure (data mining) Thery suggests that yield increases with higher N applicatin & then declines suggesting a quadratic mdel But farm-level data seldm includes extremely high N rates justifying a linear mdel 29 Review the crrelatin matrix t identify highly crrelated (>90%) variables (mulicllinearity) in the mdel. If any variables are highly crrelated, drp ne r mre f these variables (Example 11.6) Missing data fr any variable will eliminate that case frm the mdel, which is especially a prblem in multiple regressin The criteria fr deciding if the mdel is a gd fit (R 2 ) fr the data is a functin f the type f relatinship scial analysis ften reprts data with a lw R 2 Avid including dminant independent variables in yur mdel (e.g., Prductin = harvested area, fertilizer, labr, etc.). Can use standardized cefficient mdel t estimate the percent cntributin f each independent variables 30 15

16 Statistics (Example 11.7) The cnstant shws the value f the dependant variable when the independent variable(s) equal(s) zer The regressin cefficient indicates the change in the dependant variable that is assciated with a 1 unit change in the independent variable Significance f a cefficient is estimated by dividing the cefficient by its SE, and then cmparing this value t the t-distributin value R 2 indicates strength f f the influence f the independent variables n the dependant variables--ranges frm 0-1 (i.e., nne/cmplete); Evaluate R 2 bar, which adjusts fr degrees f freedm Why? F-value indicates the prbability that all betas are equal 31 In the text f an article, reprt the directin f the relatinship, beta cefficient, its significance, R 2 & the F-value [e.g., Regressin analysis indicated that the nitrgen applicatin rate (0.44) & weeding days (0.22) are significantly assciated (95% level) with yield. The mdel had a R 2 value f 0.65 & a significant (99%) F-value. Als, list & discuss nn-significant cefficients Why are they nn-significant? In tables, reprt all variables, cefficients, SE (in parentheses belw cefficient), significance levels (***=.01,** =.05,** =.10*), F-value & R 2 bar Nte: Many relatinships that are significant in bivariate relatinships, will be nn-significant in a multivariate mdel Why? 32 16

17 5. Lgit & Prbit Analysis Objective Measures the degree & directin f the relatinship between a cntinuus independent variables & a categry f a dependant variable Data Requirements Dependant variable is categrical (e.g., adpter/nn-adpter) Independent variable is scale (cntinuus) data Statistics Number f cases crrectly classified, cntributin f each independent variable t predictin (cefficients), significance f each independent variable 33 E. Respnsibility fr Analysis Primary respnsibility fr analysis lies with the researcher(s) wh Designed the prject Identified the research issues Develped the questinnaires Supervised data cllectin & therefre Knw the analytical needs & limitatins f the data 34 17

18 F. Dcumenting the Prject Purpse Prvide a permanent recrd f the prject Prvide a reference fr yur analysis Prvide a reference fr ther users 1. Archive Prject Materials & Leave at the Research Lcatin Assemble questinnaires (fr future reference), pst-cding sheets, etc. Make a cpy f the data n CDs Make a cpy f the Prject Dcumentatin Categrize, label & stre all material in a safe place that is prtected frm heat (sun), magnetic interference, mld, etc Prject Dcumentatin (bund vlume) Prject Dcumentatin (summary) (e.g., prject title, spnsrs, gegraphical cverage, dates, prject verview, publicatins) Descriptin f Survey Methdlgy (e.g., verview f research issues, survey lcatins, sampling methd/limitatins, enumeratr selectin/training, mdule design prcess, survey instruments, data entry) Survey Dcumentatin (fr each mdule) (e.g., purpse, tpics cvered, sample size, data level, unit f bservatin, number f runds, survey areas & dates, time reference fr data (seasn, mnths), base fine name, cpies f mdules (all languages), names f enumeratrs & respndents by survey lcatin) 36 18

19 SPSS Systems/Data File Summaries (all SPSS files) (e.g., name f all base files (mdule name), descriptin f data, data limitatins, file infrmatin printuts, histry f base file mdificatins/transfrmatins including names f new files created) 3. Suggestins fr Dcumenting Mdified Systems Files Failure t updated files/variable descriptins is a majr prblem a) Suggestins fr Recded/Cmputed Variables Dn t recde the riginal variable. First create a new variable frm the data and recde these data Name recded/cmputed variable with a name that begins with R/C t indicate it was recded/cmputed Immediately create value labels /etc. fr all new variable Describe variable transfrmatins in the variable label [i.e., Yield (yield=prd/area)] 37 b) Keep a Permanent Recrd (file) f Data Transfrmatins Paste SPSS cmmands int the Syntax Editr, then run them frm the editr. Save this file! At the end f the first SPSS sessin, cpy the syntax that yu want t save/archive int a wrd prcessing file and at the end f each subsequent SPSS sessin, add the new syntax cmmands t a wrd prcessing file c) Peridically Print ut the File Infrmatin After making transfrmatins, print ut the new file infrmatin d) Cleaning Up Yur Current Wrk File After transfrming a variable, drp ld variable frm the current versin f the file Be sure t save the riginal variable in an earlier versin f the file 38 19

20 Return t p Return t p

21 Return t p Return t p

22 Return t p Return t p

23 Return t p Return t p

24 Return t p Return t p

25 Return t p Return t p

26 Return t p Return t p

CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came.

MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the