PSY 110 Exam 3

Larger variance tends to lower the likelihood of rejecting the null hypothesis.

= SS+SS/(n-1)+(n-1)

somewhere between 20 and 30

They tend to decrease

n-2

fail to reject null hpyothesis

the two means must be equal

the value of the standard error

n1 = n2 = 100 and small sample variances

large mean difference and small sample variance

uses a different sample for each of the different treatment conditions being compared

how much difference there is between the two treatments

a small sample size and a large sample variance

?120/5 + 120/10

k = groups of participants. dfbetween = 3 = k - 1 therefore k = 4. dfwithin = 24 = N - k. therefore N = 28. total participants/groups of participants = participants in each treatment = 28/4 = 7

There is little or no effect on measures of effect size, but the likelihood of rejecting the null hypothesis increases.

at least one of the three population means is different from another mean

It will decrease (move toward 0 at the center of the distribution).

Increase the sample mean difference

Using several t tests increases the risk of a Type I error.

Much greater than 1.00

Order effects

large mean differences and small variances

Comparing pain tolerance with and without acupuncture needles

A significant effect does not necessarily mean that the effect size will be large.

useful when you have data about a continuous measure, and youwant to see twhether the sampleas a whole differs from one specific value, and when you are trtyin to see if a continuous set of data differs from chance. an approximate z. used to test hypothesses about an unkwon population mean when the standard deviation is also unknown. is significant if t is large enough and p is small enough.

describes how much difference is reasonable to expect between M and m, = SD/square root of n

uses sample mean to estimate and approximate population mean. problem with z scores is they requires knowledge of the population standard deviation, that sometimes researchers dont have. no measure of effect size is included and something with a small effect can be statistically significant, therefore results should be accompanied by a measure of effect size

n is greater than 30 or the original distribution is approximately normally distributed

n-1, influences shape of distribution for small samples but not large. lower df means higher value for critical region. one sample(paired sample) tests df is n-1, multiple groups (independent sample) df is n-1 for each group

a family of distributions, one for each value of degrees of freedom

what you are measureing

is flatter and more spread out than the normal zdistribution

measures effect size, computed using the sample standard deviation. 0.2 is small, 0.5 is medium, and 0.8 is large

determines the amount of variability in scores determiend by treatment effect. .01 is small, .09 is medium, .25 is large

alternative technique fordescribing effect size. absed on the reasonable assumption that M should be near m, it estimates m from sample M. a big confidence interval range means you are less likely to make an error. m = M+/- t(SEM). if the range does not include 0 Fthen it is significant and null can be rejected. more confidence desired increases interval width. larger sampleequals smaller interval

independent is always categorical, dependent is always continuous

to determine critical values, take t and df and look at table. to determine t, take critical value (a) and df and look at table

non directional most commonly used, but sometiems one direction is. in one direciton, critical region is defined in just one tail of the distribution, one tailed makes it easier to reject null

data from two completely different, independent participant groups, also called between subjects design. this is what a cross sectional study is

data from the same or related participant groups, also called within subjects. this is what longitudinal studies are

m1 - m2 = 0

m1 - m2 does not equal 0

square root of variance1 divided by n1 plus variance2 divided by n2. OR square root of pooled variance divided by n1 plus pooled varaince divided by n2 (better if sample sizes are different)

if p is less than .05 than null hypothesis is rejected and equal variances are not assumed

should be determined if null hypothesis is rejeccted. mean difference/square root of pooled variance. .2 is small, .5 is medium, and .8 is large

how much difference there is between two treatments

requires equal population variances for an independent measures test, sample variances jsut need to be similar

one tailed test only used when predicting a specific direction of the variance is justified

repeated measures. good for comparing scores (on a continuous DV) in one group of participants at two different time points, usually before and after treatment

use paired samples/dependent samples/pretest-posttest (one group, df=n-1)

use independent samples test (two groups, df=n-2)

similar in structure, but comparing difference scores instead of raw scroes

h0: mean difference = 0 h1: mean difference does not equal 0

larger sample mean difference increases t, as does larger sample size, larger variance and standard deviation deccrease t

variability is low

repeated pros: requires fewer subjects, able to study change over time, reduces influence of individual differences, and has substantially less variablity in scores. cons: factors besides treatment may cause change in score, order effects (participation in first treatment may influence score in second)

one sample: must know the test value independent measures: must be sure groups are equivalent using random sampling or random assignment repeated measures: must test the same group twice and control for learning and order effects

combines cross sectional and longitudinal, ex: study one group at age 8 and 10, and another at age 10 and 12

Progressive effects: participants are altered by the sequence of conditions they encounter carryover effects: participants responses in one condition are affected by the prior condition, can besolved by counterbalancing which uses all possible sequences at least once. in partial counterbalancing a subset of the total sequences is used. reverse counterbalancing presents conidtions in one order and then again in reverse. block randomization has every condition occur before any condition is repeated

similar to repeated measures, uses two seperate sampels but each individual in one sample is matched one to one with an individual in another sample. very similar tests, but matched has twice as many participants

the independent/quasi independent variable that designates the groups being compared

individual conditions or values that make up a factor

a study that combines two or more factors (ex: how gender influences movie preferences)

an analysis of varience, good for when you have more than two groups (in your categorical indpendent variable) that you're comparing on one continuous outcome or DV or when you have more than one factor that you are considering (whether theres an interaction between one factor like age and another like GPA). used to evaluate mean difference between two or more treatments, and uses sample data as basis for drawing general conclusions about populations

not possible to calculate, instead use f ratio (mean squares/variance between divided by mean squares/variance within). mean squares between is the numerator and determines how far the sample means are from the grand mean (SS between divided by df between). mean squares within measures difference between sample mean and individual scores (SS within divided by df within)

number of treatment conditions

number of scores in each treatment

total number of scores

n-k

k-1

h0: m1 = m2 = m3, h0 can be wrong if all means are different from each other or if only some means differ from each other while others are the same

the more t tests you run, the higher chance that the significance is due to chance. by evaluating them all simultaneously anova eliminates this issue

between measures differences caused by systematic treatment effects and random factors, within only measures random

t tests are just a special case of anova where only two conditions are being prepared. that is why t squared = F when there are two conditions

if between variablity is low and within varability is high, then difference is not significant

if h0 is true, size of treatment effect is small and f is near 1 (when variance between is similar to variance within), if h1 is truec size of treatment effect is large an f is noticeably bigger than 1

SSbetween

?² = SS between/SStotal, small = .01, medium = .06, large = .14

significant f ratio means at least one difference in means is statistically significant but does not indicate which means are different. post hoc tests help determine exactly which means are different. they compare two means at a time (pairwise comparison). each comparison includes a risk for type 1 error that accumulates and is called the experimentwise alpha level. these posttests use special methods to try to control alpha level (only used when anova is significant)

one of the safest possible posthoc tests uses f ratio to evaluate the significance of the difference between two treatment conditions. Favsb = MSbetween/MSwithin calculated with SS of two groups. another popular posttest is Tukey'shonestly signifcant difference, or HSD

large mean differences and small sample variances

t or f can be used

-2 > t > 2 and F > 4

observations within each sample must be independent, population from which sample is selected must be normal and have equal variance

measures and describes the realtionships between two variables, good for when you have one group of people and more than one continuous measure (DV) that may be related, and when you want to know whether you can predict one continous (not categorical, examples of continuous: height, age, GPA) variable from another. can vary in direction (positive or negative), form (linear is most common), and strength (varies from 0 to 1). may imply causation, but relationship can be due to third variable

r = covariability of x and y/variability of x and y separately AND r = SP/? (SSx)(SSy) AND sample: r = the sum of (zx)(zy)/n-1 OR population: r = the sum of (zx)(zy)/N. measures degree and direction of linear relationship between two variables. in a perfect linear relationship every change in x corresponds with a change in y, and will be +1.00 or -1.00. usually computed for sample data, but used to test hypotheses about the relationship in the population. developed for data having linear relationships, with data from interval or ratio measurement. alternative correlations are used for data having non linear relationships and with data from nominal or ordinal measurement scale

SP = sum of (x - meanx)(y - meany) similar to sum of squared deviations (SS), measures amount of covariability between two variables in a correlation

measures the degree of a relationship on a scale of 0 to 1. is not a proportion, but squared correlation may be interpreted asthe proportion of shared variability (called the coefficient of determination, represents percentage of y that can be predicted by x). value affected by range of scores in data, severely restricted range may provide a different correlation than a broader range of scores

outlier is an extremely deviant individual. produce disproportionately large impact on the correlation coefficient

correlations do not provide proof of causation, that requires an experiment in which one variable is manipulated and others carefully controlled

measures the relationship between two variables while mathematically controlling the influence of a third variable by holding it constant. rxy • z = rxy - (rxy • ryz)/ ?(1-r2xz)(1-r2yz)

used for ordinal scales, also used for interval or ratio that does not have a linear relationship (ex: curved or with an asymptote). ifscores are tied, they need to be ranked. to assign rank, list scores from lowest to highest, assign a rank to each position on list, compute mean of ranked position for 2 (or more) tied scores, and assign mean as rank to each tied score.

measures relationship between 2 variables, one varaible has only 2 values (called dichotomous or binomial). point biserial r2 has the same value as r2 computed from t statistic (measures effect size). useful when trying to figure out whether performance on a single question (right or wrong) correlates with the overall score. both x and y are recoded as 0 and 1. the regular pearson formulation is used to calculate r. r2 measures effect size (proportion of variablity in one score predicted by the other)

finds the equation describing the best fitting line for a set of data (a line is the best fit for the actual data that minimizes prediction errors). makes relationship indicated in pearson correlation obvious by putting a line through the scatterplot data. this makes the relationship easier to see, shows the central tendency of the relationship, and can be used for prediction. y(pointy) is the value of y predicted by the regression line for each value of x. y - y(pointy) is the distance each data point is from the line (error of prediction). when calculating predicted y (ypointy) for a provided x when you have a and b, use equation for line. regression procedure produces a line that minimizes total squared error of prediction (method is called least squared error solution)

y = bX + a (similar to y =mx + b). x and y are variables, while a and b are fixed constants. change in y/change in x in the slope. value of a is where line crosses the x axis (so when x equals 0).

similar to analysis of variance, uses f ratio of two mean square values. each MS is SS divided by its df. H0 = the slope of the regression line (b or beta) is zero (a flat line). h1: the line slopes to the left or the right. MSregression = SS regression/df regression. MSresidual = SS residual/df residual. F = MSregression/MSresidual

true, when r = .58, r2 = .336 (roughly 1/3)

hypothesis tests test hypotheses about population parameters. parametric tests share several assumptions (normal distribution in population, homogeneity of variance in population, and numerical score for each individual).

are needed when the research situation does not conform to the requirements of parametric tests (normal distribution in population, homogeneity of variance in population, and numerical score for each individual). chi square and other nonparametric tests do not state hypotheses in terms of a specific population parameter. participants are usually classified into categories, nominal or ordinal scales are used and the data from these tests are frequencies

appropriate when you have normal independent variables but only group membership (frequencies) as your raw data. test assumptions: each observed frequency is generated by a different individual (observed frequency) and test is not performed when expected frequency of any cell is less than 5 (expected frequencies).

uses sample data to test hypotheses about the shape of proportions of a population distribution. tests to fit the proportions in the observed sample with the hypothesized proportions of the population. specifies the proportion of the population in each category. h0 = no preference among categories and no difference in one population from the proportions in another known population. uses sample data to test hypotheses about the shape or proportions of a population distribution. test the fit of proportions obtained in the sample with the hypothesized proportions of the population

if the expected frequencies are based purely on chance (random model), then you can calculate them based on how many categories you have in your analysis

individuals in each actegory are counted, observed frequencies in each category are measured, and each individual is counted in only one category. compares the observed frequencies (fO) of data with the assumptions of the null hypothesis. fO is just frequency counts and cant be fractional.construct expected frequencies (fE = frequency value that is predicted from h0 and sample size) that are in perfect agreement with the null hypothesis. chi squared = x2

includes values (all vare greater than 0) for all possible random damples when h0 is true. null hypothesis should be rejected if the discrepancy between observed (fO) and expected (fE) values is large (aka if x2 is large). distribution is positively skewed, it is a family of distributions (determined by df determined by C-1, where C is number of categories). slightly different shape for each df value.

significance level is determined, critical value for chi square is located in a table of critical values according to df and signficance level chosen. if the chi square is higher than the critical value reject the null

chi square can test for the existence of a relationship between 2 variables. each individual is classified on each variable, counts are presented in the cells of a matrix, and research may be experimental or non experimental. frequency data from a sample is used to evaluate the relationship of two variable in the population. h0 = two variables are independent. single population = no relationship between two variables in this population. two separate populations = no difference between distribution of variable in the two populations (defined by a nominal variable). variables are independent when there is no consistent predictable relationship between them. frequencies in the sample = fO, and null hypothesis of same proportions in each category (population) = fE

fE = (fC)(fR)/n. fC is frequency total for column and fR is frequency total for row

same equation as chi square for goodness of fit, x2 = sum of (fO - fE)2/Fe. degrees of freedom = (R - 1)(C - 1), R is number of rows, C columns

chi square hypothesis test indicates difference did not occur by chance, but does not indicate effect size. for a 2x2 matrix, the phi coefficient ? measures the strength of a relationship. ? = ? x2/n. for a larger matrix, use cramer's v. V = ?x2/n(df). df is the smaller of (R-1) or (C-1)

chi square and pearson correlation both evaluate relationships between two variables. the type of data obtained determines which one is appropriate. chi square is used instead of t test or anova, when counts rather than means of categories are being compared. chi square can evaluate the significance, parametric tests measurer strength and effect with greater precision

the observations must be independent

typically used for ordinal data whererank orders might be different between groups, similar to spearmans correlation. paired t test -> wilcoxon, independent t test -> mann-whitney U, one way anova -> kruskal-wallis

Spearman correlation

a b > 0

chi square is always positive but can contain fractions or decimal values

just once

it uses one sample to test a hypothesis about one population

it will be positive

the sample data (observed values) do not match the hypothesis

Increases in X tend to be accompanied by increases in Y

When both X and Y are dichotomous variables

3

for expected frequency, multiply n (200) with provided percentage (20 % or .2). 200 x .2 = 40

chi square df = (r - 1)(c - 1) = (3 - 1)(2 - 1) = 2

The critical value depends on the number of categories, not the sample size.

whatever has biggest number, negative or positive

y = bx + a. y = 3(4) - 6 = 6