ChiSquare P216; 269


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1 ChiSquare P16; 69
2 Confidence intervals CI: % confident that interval contains population mean (µ) % is determined by researcher (e.g. 85, 90, 95%) Formula for ztest and ttest: CI = M +/ z*(σ M ) CI = M +/ t*(s M ) Where z* or t* is the critical value Example: CI = 86 +/ 1.96(1.7) = 8.67 to % confident pop mean in this range
3 Inference by eye: Interpreting CI s Why use CI instead of null hypothesis? Move beyond dichotomous decision Writeup suggestions We are 90% confident that the true improvement on the test ranges from to Values outside of this range are relatively implausible. The lower limit of is a likely lower bound estimate of improvement. Rules of eye What do bars on a graph represent (i.e. sd, se, CI)? Focus on the means, but take variability into account Interpret CI any value outside CI is unlikely Double SE bars to get approximate 95% CI
4 Chisquare Kristen is interested in evaluating whether the method of cooking potato chips affects the taste of the chips. She tests 48 individuals. Each tastes 3 types of chips, then select which chip they prefer to eat. Method of cooking potato chi ps Fried in animal f at Fried in Canola oil Baked Total Observ ed N Expected N Residual ChiSquare a df Asy mptotic Signif icance Test Statistics Number who Method of pref erred cooking each type of pot ato chips chip a. 0 Cells.0% low f reqs 16.0 expected low...
5 Nonparametric tests Parametric tests: assumptions about population distribution ttest, ANOVA Compare means & standard deviations Nonparametric tests Chisquare Compare frequency counts Evaluate hypotheses about population frequencies No assumptions regarding population distribution (M, s)
6 ChiSquare (X ) Goodness of fit test Uses proportions from sample to examine hypothesis about population proportions One sample, one variable (but, as many levels as needed) Test of independence Examines if there is a relationship between two variables One sample, two variables Similar to correlation with discrete variables
7 Chisquare (X ) Frequency table of data Observed frequencies (f o ) Compare to null hypothesis Expected frequencies (f e ) Null hypothesis No preference No difference vs. comparison population Expected frequency f e = pn ( f o f x Chisquare equation e ) df = C 1, where C = # of categories Chisquare distribution: Table A.4 p410 f e
8 Chisquare test Compare observed (O) and expected counts (E) Measure distance If distance = 0 then no difference between O & E = null hypothesis If distance > 0 then difference between O & E = evidence against null hypothesis Chisquare distributions df based on #cells not n
9 Goodness of fit: 1 sample Art appreciation: Painting shown to 50 participants. Asked to hang picture in correct orientation. 4 possible ways can hang painting H 0 : no preference (5% chance/orientation) Expected frequencies:.5(50) = 1.5 Top up (correct) Bottom up Left up Right up Observed frequencies Top up (correct) Bottom up Left up Right up
10 Chisquare table What is critical value? X cv α =.05 df = 4 1 =
11 Calculate Chisquare Observed Frequencies Expected Frequencies X ( f o f e ) f e X (18 1.5) 1.5 (17 1.5) 1.5 (7 1.5) 1.5 (8 1.5) Exceeds critical value (7.815), so reject H o
12 Chisquare writeup A chisquare statistic was calculated to examine if there is a preference among four orientations to hang an abstract painting. The test was found to be statistically significant, X (3, n = 50) = 8.08, p<.05. The results suggest that participants did not just randomly hang the art on any orientation. Instead it appears the correct topup orientation (p = 18/50) and bottomup orientation (p = 17/50) were used more often than the left sideup (p = 7/50) or right sideup (p = 8/50) orientation.
13 Goodness of fit: Chisquare Assess whether women become less depressed, remain unchanged, or become more depressed after giving birth Tested 60 women pre and postbirth Null hypothesis: no difference Postpartum Depression less depress ed same more depressed Total Observ ed N Expected N Residual
14 SPSS: Chisquare less depressed same more depressed Postpartum Depression
15 SPSS: Chisquare Postpartum Depression Test Statistics less depressed same more depressed Total Observ ed N Expected N Residual Postpartum Depression ChiSquare a df Asy mptotic Signif icance.00 a. 0 Cells.0% low freqs 0.0 expected low... Postpartum Depression Test Statistics less depress ed more depressed Total Observ ed N Expected N Residual Postpartum Depression ChiSquare a.037 df 1 Asy mptotic Signif icance.847 a. 0 Cells.0% low freqs 13.5 expected low...
16 Writeup A onesample chisquare test was conducted to assess whether women become less depressed, remain unchanged, or become more depressed after giving birth. The results were found to be significant, X (, n = 60) = 1.70, p <.01. The proportion of women who were unchanged (55%) was greater than the hypothesized proportion (33%). While women who became less depressed (3%) and more depressed (%) were approximately the same to the hypothesized proportion. A followup test indicated that the proportion of women who became less depressed did not significantly differ from women who became more depressed, X (1, n = 7) = 0.04, p = ns. Overall, these results suggest that women in general do not become more or less depressed after childbirth.
17 Goodness of fit hypotheses Compare proportions of cases with hypothesized values Are there more smokers in study than nonsmokers? No difference in categories H 0 : 50% smokers; 50% nonsmokers Or specific proportions obtained from prior studies H 0 : 0% smokers; 80% nonsmokers
18 Writeup A chisquare goodness of fit test indicates there was no significant difference in the proportion of smokers identified in the current sample (19.5%) as compared with the value in the nationwide study (0%), X (1, n = 436) =.07, p =.79.
19 Assumptions for Chisquare Independence of observations Each subject gives 1 response Each observation is a different subject Size of expected frequencies Should not be less than 5 per cell Avoid by using larger samples Distorted when f e is very small
20 Chisquare (X ) Goodness of fit test Null hypothesis No preference hypothesis Test for independence variables! Null hypothesis Same proportions for variables i.e. no relationship between variables
21 Treating Cocaine Addiction Desipramine Lithium Placebo Success Relapse
22 Independence Chisquare test: variables Examine relationship between variables Treating cocaine addiction Relapse No Yes Total Desipramine Lithium 6 18 Placebo 4 0 Total 4 48 Compare study findings to expected findings f e f c n f r No relapse: 4*4/7 = 8 (successes expected/drug) Yes relapse: 48*4/7 = 16 (failures expected/drug)
23 Independence Chisquare test X Null hypothesis: no relationship between type of drug and relapse df = (R 1)(C 1) = 1(31) = Critical value = 5.99 X (14 8) 8 Significant! ( f o f e ) (6 8) 8 f e (4 8) 8 (10 16) 16 Examine proportions (#/total) of no relapse 10.5 Drug1: 14/4 =.58, Drug: 6/4 =.5, Drug3: 4/4 =.17 (vs. expected: 8/4 =.33) (18 16) 16 Relapse No Yes Desipramine 14 / 8 10 / 16 Lithium 6 / 8 18 / 16 Placebo 4 / 8 0 / 16 (0 16) 16
24 Writeup A chisquare test was conducted to assess whether cocaine addicts would relapse when treating addiction with Desipramine, Lithium, or a placebo drug. The results were found to be significant, X (, n = 7) = 10.5, p <.05. The proportion of addicts who did not relapse when treated with Desipramine (58%) was greater than the hypothesized proportion (33%). While the number of addicts who did not relapse when treated with Lithium (5%) and the placebo (17%) were approximately the same than the hypothesized proportion. The results suggest that there is a relationship between probability of a relapse and drug used to treat the addiction. It appears that Desipramine assists cocaine addicts to prevent relapse of drug abuse.
25 Gender and smoking example Is there an association between gender and smoking behavior? Is the proportion of males that smoke the same as the proportion of females?
26 Writeup A chisquare test for independence indicated no significant difference in the proportion of males or females that smoke, X (1, n = 436) = 0.494, p =.48.
27 Other nonparametric statistics MannWhitney U test Equivalent to independentsamples ttest DV (scores) converted to ranks; examine median Ex. IV: gender; DV: selfesteem rank Wilcoxon signed rank test Equivalent to pairedsamples ttest Converts scores to ranks; compares T1 & T KruskalWallis test Equivalent to oneway ANOVA Scores converted to ranks; 1 betss IV w/ 3+ levels Friedman test Equivalent to repeatedmeasures ANOVA Scores converted to ranks; 1 w/in Ss IV w/ 3+ levels
28 Chapter 13 Quasiexperimental research Nonmanipulated IV: Ss not randomly assigned to condition Lacks internal validity (confounding variable?) Quasiexperimental designs One sample Singlegroup posttest only design Singlegroup pre/posttest design Singlegroup timeseries design Two samples Nonequivalent control group posttest only design Nonequivalent control group pre/posttest design Multiplegroup timeseries design
29 Chapter 13 Crosssectional design Ss at different ages at one testing time Pro: fast and cheap Con: possible cohort effect Longitudinal design Ss repeatedly tested over time Pro: examine change (age effect) Con: attrition Sequential design Mix of crosssectional and longitudinal Pro: benefits of both cross/longitudinal designs Con: statistics are difficult/unknown
30 Schaie, K. W. (1994). The course of adult intellectual development. American Psychologist, 49,
31 Figure. CrossSectional Mean T Scores for Single Markers of the Primary Mental Abilities
32 Figure 3. Longitudinal Estimates of Mean T Scores for Single Markers of the Primary Mental Abilities
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