Descriptive Statistics, Inferential Statistics - Notes | PSY 3213C, Study notes of Psychology

Download Descriptive Statistics, Inferential Statistics - Notes | PSY 3213C and more Study notes Psychology in PDF only on Docsity! 10.18.2010 ***Ch. 9- Using Statistics to Answer Questions *Using Statistics to Answer Questions -Statistics: Branch of mathematics that involves the collection, analysis, and interpretation of data. ~Two main branches of statistics assist your decision in different ways. >Descriptive Statistics --Procedures used to summarize --Measure of central tendency: typical of representative score --Variability: what spread exists in the scores >Inferential Statistics --Inferential statistics are used to analyze data after you have conducted an experiment to determine whether your independent variable had a significant effect *Scales of Measurement -Measurement: The assignment of symbols to events according to a set of rules -Scale of measurement: A set of measurement rules -Nominal Scale ~Events are assigned to categories; classify your research participants as men or women, as right-handed or left-handed, as Catholic or Protestant ~Differences between categories are qualitative (kind) and not quantitative (degree) ~Do number of individuals in one category differs as a function of some treatment? ~EX. Jersey #’s, telephones, zip codes -Ordinal Scale ~Permits events to be rank ordered; usually single continuum that underlies a classification system ~EX. College football standings, pop music charts, class standings, might divide participants up on basis of creativity and end up with three categories (noncreative, creative, highly creative) ~Degree of quantitative difference that nominal scale does not have ~Differences between consecutive values are not necessarily equal, top 20 football teams (differences between 1 and 4, not necessarily same as 6 and 9) – don’t know how much distance exists between ranks -Interval Scale ~Rank ordering and assumption of equal distance between ranks; household thermometer, ACT, SAT; often chosen b/c no true zero -Ratio Scale ~Rank ordering of events, assumption of equal distance between ranks and a true zero point; weight, length, calorie content of food *Measures of Central Tendency -Mode ~The score in a distribution that occurs most often; can be more than one mode >12, 15, 20, 20, 20 >mode= 20 -Median ~The number that divides a distribution into equal halves, to calculate first rank them >56, 15, 12, 20, 17 >12, 15, 17, 20, 56 >Median = 17 -Mean ~The arithmetic average of a set of numbers. It is found by adding all the scores in a set and then dividing by the number of scores *Graphing Your Results -Pie Chart ~Graphical representation of the percentage allocated to each alternative as a slice of a circular pie. -Histogram ~a single number that represents how much each scores varies from the mean; the larger the number, the greater the total spread of scores -standard deviation ~the standard deviation is the square root of the variance *Correlation -Evaluate the direction and degree of relationship between the scores in two distributions -Use a measure of association -Pearson Product-Moment Correlation Coefficient or Pearson ~use when your dependent measures are interval or ratio scale ~pearson r or correlation coefficient >the value of a correlation coefficient can range from -1 through 0 to +1. >sign of coefficient tells you the direction of the relationship >pos. corr.= direct relationship, one distribution scores increase, do the scores in second distribution >negative correlation= inverse relationship, as scores increase, second distribution scores decrease >0= no relationship, gets closer to +1 or -1 the strength of relationship increase *inferential statistics -what is significant? ~an inferential statistical test can tekk us whether the results of an experiment can occur frequently or rarely by chance ~if something occurs often by chance, then it is not significant and the IV is not responsible for affecting the DV ~rule of thumb >frequently by chance, not significant >rarely by chance, significant -null hypothesis ~a hypothesis that says all differences between groups are due to chance (i.e., not the operation of the IV) ~if the result occurs rarely by chance (it is significant), then we conclude that some factor other than chance is the reason and if we did our experiment correctly, exercised control, etc. then we can assume the IV we manipulated did affect the DV scores ~When do we consider and event to occur rarely chance? >occurs by chance alone when it occurs 5 times of fewer in 100 occasions >.05 significance level 10.25.2010 A. Random samples are drawn from a population. B. The administration of the IV causes the samples to differ significantly C. The experimenter generalizes the results of the experiment to the population. -Null says populations are the same; the treatment didn’t have an effect. [Ho] -Alternate [H1]: populations are different, because the IV effected it and shifted over *When statistics go astray: Type I and Type II Errors HANDOUT Type I: saying that there is a a difference between populations when there isn’t FIX: lower significance level Type II: you decide the null is false, the iV had an effect but reject even when there is FIX: harder to control, make IV stronger, more participants *decrease both errors *One-Tail Versus Two-Tail Tests of Significance *The t Test -Clothes Study (pg 193 text) ~IV: Type of Clothing, DV: Time takes clerk to wait on customer ~n=16 clerks (8 randomly assigned to Group A or dressy shoppers; 8 randomly assigned to group B or sloppy shoppers) ~Higher scores reflect longer wait times for clerk before offered service t test will evaluate difference between means of 2 groups Group N M SD Dressy 8 48.38 9.46 Sloppy 8 63.25 11.73 T=2.61 Df=14 P=.021 -Interpretation of t value ~Determine the degrees of freedom (df) involved. Df=(n-1) ~Use the degrees of freedom to enter a t table (pg. 389) >This table contains t values >Compare your t value >TO be significant, the calculated t must be equal to or larger than the one on the table ***CH. 10: Designing, Conducting, Analyzing, and Interpreting Experiments with Two Groups *Experimental Design -Experimental Design ~The general plan for selecting participants, assigning participants to experimental conditions, controlling extraneous variables, and gathering data. ~If can show when comparing across levels of IV that performance differed and those differences are reliable, conclude that change in level of IV causes change in value of DV. -2 ways to manipulate the IV ~What is an IV? ~What is the minimum number of values an IV must have? ~What are other words that mean value? Group/ treatment/ level/ value ~Quantitatively: change amount of IV that Ss are exposed to >vary amount of Prozac that they are exposed to 10mg, 15mg, 20mg ~Qualitatively: type of IV >Use different antidepressants (Prozac, lexapro, Zoloft) ~presence/ absence manipulation most common way to create two groups from one IV >presence of the IV is contrasted with the absence of the IV >what is the experimental group? >what is the difference between random assignment and random selection >allow us to look a whether IV has an effect, but not specific effects --next step is to look at more or less of IV, will different IVs produce stronger (weaker) effect, what optimum amount (or type) of the IV? >can’t always do presence/absence (book example stereotyping) ~a multiple-group design >compare 3 or more levels of amounts of an IV >can have a control group and two more -experimental groups or no control group ~non random assignment to groups >if we are faced with a situation in which we have few potential research participants and we are worried that random assignment may not create equal groups, what can we do? >might suspect that some Ss characteristic correlates significantly with DV --Ss often differ considerably in reaction time to simple stimuli and this creates large amounts of error variance -Matched Pairs/ Sets: Assess on one or more characteristic that believe exert influence on dependent measure and then group Ss and characteristic match (correlated assignment) ~group based on reaction time and then one from every pair randomly assigned to one of treatments EX. Clerks, female/female then randomly assign sloppy/dressy ~participants are matched on a variable that will affect their performance on the DV (matching variable) For each level of 3 or more ???-->PROBLEM: make mistake/ sub. Var & DV don’t correlate sub. Var. has no relationship --you added problem to design -natural pairs/ sets ~pairs of participants are created from naturally occurring pairs (e.g. biologically or socially related >EX. Psychologists who study intelligence often use twins as their research participants ~use littermates, siblings, won’t be able to use husband/wives or twins *Within Ss Design/ Repeated Measure Design -each Ss is exposed to ALL levels of your IV rather than being randomly assigned to one level ~each Ss is measured under Treatment A and then again under Treatment B -closely related to matched pair/set, it is the ultimate in matching -advantages ~matched with exact clone, because same Ss ~more powerful because of the reduced error variance, ,means more likely to detect the effect of IV ~can use fewer Ss >4 levels BtwSs (n=40-10 for esch level) >4 levels W/inSs (n=10) -disadvantages ~more demanding on Ss because each Ss must be exposed to every level of experiment treatment >A treatment that is a great deal of time who is likely to commit to this experiment, could become bored, fatigued, higher mortality ~carryover effect >previous treatment alters the behavior in subsequent treatment -when to use ~subject differences contribute highly to variation in DV ~Economizing on Ss >Ss are limited and carryover effects are absent or minimize ~interested in effects of increased exposure and how changes performance (DV) ~IF you believe that relationship between subject variable and DV is weak better to use a randomized design 11.1.2010 *Statistical Analysis: What Do Your Data Show? -Analyzing two-group designs ~Need to decide which t-test to use >This depends on how you assigned Ss to groups --Independent groups design= t test for independent samples --Correlated group design= t test for correlated samples ~Interpreting computer statistical output >Examine descriptive statistics *Table 10-1 >Need to double check everything you entered and check printout to see if it seems accurate --If only n=7 and you know n=8 then computer didn’t read something and now you are interpreting junk data -Analyzing two-group designs ~Interpreting computer statistical output >The t test for independent samples --Check for Homogeneity of variance: assumption that variances are similar --TO use a t test we assume the variances are similar ^Look at Fmax test see says F=1.634 p=.222 ^Rule: if p is greater than .05 then variances are similar, if less then variances are different --Heterogeneity of variance: assumption that variances are different or not comparable