PSY 110 exam 3

critical significance guidelines

-2 > t > 2 and F > 4

An independent-measures experiment with three treatment conditions has a sample of n = 10 scores in each treatment. If all three treatments have the same total, T1 = T2 = T3, what is SSbetween?

0

If the null hypothesis is true, what value is expected on average for the repeated-measures t statistic?

0

A chi-square test for goodness of fit has df = 2. How many categories were used to classify the individuals in the sample?

3

pooled variance

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

If a repeated-measures study shows a significant difference between two treatments with a = .01, then what can you conclude about measures of effect size?

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

For which of the following situations would a repeated-measures research design be appropriate?

Comparing pain tolerance with and without acupuncture needles

Under what circumstances is the phi-coefficient used?

When both X and Y are dichotomous variables

Assuming that other factors are held constant, which of the following would tend to increase the likelihood of rejecting the null hypothesis?

Increase the sample mean difference

What is indicated by a positive value for a correlation?

Increases in X tend to be accompanied by increases in Y

In general, if the variance of the difference scores increases, what will happen to the value of the t statistic?

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

In a hypothesis test using a t statistic, what is the influence of a large sample variance?

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

on average, what value is expected for the F-ratio if the null hypothesis is false?

Much greater than 1.00

In a repeated-measures experiment, each individual participates in one treatment condition and then moves on to a second treatment condition. One of the major concerns in this type of study is that participation in the first treatment may influence the participant's score in the second treatment. What is this problem is called?

Order effects

within studies order effects

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

sum of products (SP)

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

SStotal - SSwithin =

SSbetween

For a group of graduating college seniors, a researcher records each student's rank in his/her high school graduating class and the student's rank in the college graduating class. Which correlation should be used to measure the relationship between these two variables?

Spearman correlation

What happens to the critical value for a chi-square test if the size of the sample is increased?

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

Which of the following describes the effect of increasing sample size?

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

As sample variance increases, what happens to measures of effect size such as r2 and Cohen's d?

They tend to decrease

When comparing more than two treatment means, why should you use an analysis of variance instead of using several t tests?

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

If there is a positive correlation between X and Y, then the regression equation Y = bX + a will have

a b > 0

t distribution

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

Which set of sample characteristics is most likely to produce a large value for the estimated standard error?

a small sample size and a large sample variance

factorial design

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

confidence intervals

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

ANOVA

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

chi square test

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).

nonparametric tests

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

For an ANOVA comparing three treatment conditions, what is stated by the alternative hypothesis (H1)?

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

between treatments variance vs within treatments variance

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

special applications of chi square

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

for an independent-measures research study, the value of Cohen's d or r2 helps to describe

how much difference there is between the two treatments

for an independent measures test, the value of cohens d or r squared helps describe

how much difference there is between two treatments

chi square test for independence

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

A researcher is using a chi-square test for independence to evaluate the relationship between birth-order position and self esteem. Each individual is classified as being 1st born, 2nd born, or 3rd born, and self-esteem is categorized as either high or low. For this study, what is the df value for the chi-square statistic?

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

measuring effect size of chi square

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

Which of the following best describes the possible values for a chi-square statistic?

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

cohort sequential design

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

correlations and causation

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

repeated measures

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

independent measures design

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

standard error

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

percentage of variance

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

computing expected frequencies

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

if p is greater than .05

fail to reject null hpyothesis

regression

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)

Ten years ago, only 20% of the U.S. population consisted of people more than 65 years old. A researcher plans to use a sample of n = 200 people to determine whether the population distribution has changed during the past ten years. If a chi-square test is used to evaluate the data, what is the expected frequency for the older-than-65 category?

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

statistical hypotheses for anova

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

hypotheses for repeated measures

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

parametric tests

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).

determining significance with variability

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

f ratio

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

equal variances

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

calculation of expected

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

chi squared distribution

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.

independent vs dependent variables

independent is always categorical, dependent is always continuous

levels

individual conditions or values that make up a factor

data for goodness of fit

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

when the n is small, the t distribution

is flatter and more spread out than the normal zdistribution

Which of the following accurately describes the chi-square test for goodness of fit?

it uses one sample to test a hypothesis about one population

The Pearson and the Spearman correlations are both computed for the same set of data. If the Spearman correlation is rS = +1.00, what can you conclude about the Pearson correlation?

it will be positive

In the observed frequencies for a chi-square test for independence, how often is each participant counted?

just once

An analysis of variances produces dfbetween = 3 and dfwithin = 24. If each treatment has the same number of participants, then how many participants are in each treatment?

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

between treatments degrees of freedom

k-1

what combo of mean and variance leads to a decision that there is a significant treatment effect?

large mean difference and small sample variance

which combination of factors is most likely to produce a large value for f ratio?

large mean differences and small sample variances

in general, what factors are most likely to reject the null hypothesis for an ANOVA?

large mean differences and small variances

factors that influence hypothesis test outcome

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

null hypothesis for independent measures

m1 - m2 = 0

alternative hypothesis for independent measures

m1 - m2 does not equal 0

correlations

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

estimated cohens d

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

point based correlation

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)

correlation coefficient

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

partial correlation

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)

z scores form a normal distribution if

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

degrees of freedom

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

independent samples t-tests involve two groups so the df is

n-2

within-treatments degrees of freedom

n-k

Assuming that there is a 5-point difference between the two sample means, which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic?

n1 = n2 = 100 and small sample variances

non directional vs one direcitonal test

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

sample mean difference for more than two samples

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)

n1

number of scores in each treatment

k

number of treatment conditions

ANOVA assumptions

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

scheffe test

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

what is needed for each test

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

directional hypotheses and one tailed test

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

correlations and outliers

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

pearson correlation

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

paired samples t test

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

repeated measures vs independent measures

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)

homogeneity assumption

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

chi square statistic for test independence

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

effect size

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

critical region for chi square test

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

post hoc tests

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)

t test for repeated measures

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

testing regression significance

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

matched subjects design

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

One sample has a variance of s2 = 20 and a second sample has a variance of s2 = 30. The pooled variance for these two samples will be

somewhere between 20 and 30

standard error of the difference

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)

for two independent samples, either

t or f can be used

t tests and anova

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

factor

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

advantage of anova

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

a basic assumption for a chi square hypothesis test is

the observations must be independent

What is indicated by a large value for the chi-square statistic?

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

In an independent-measures hypothesis test, if t = 0, then

the two means must be equal

A sample of n = 10 scores has M = 58, s2 = 160, and an estimated standard error of 4 points. Which of these values will probably decrease if the sample size is increased to n = 100?

the value of the standard error

critical values

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

N

total number of scores

if r = 0.58, the linear regression equation predicts about 1/3 of the variance in y scores

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

nonparametric equivalents of popular parametric tests

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

for independent measures = between subjects

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

for repeated measures = within subjects

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

spearman correlation

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.

one sample t test

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.

An independent-measures study uses

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

chi square for goodness of fit

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

hypothesis testing with z scores

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

when a treatment has a consistent effect

variability is low

dependent variable

what you are measureing

Which of the following Pearson correlations shows the greatest strength or consistency of relationship?

whatever has biggest number, negative or positive

linear equations

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).

A linear regression equation has b = 3 and a = - 6. What is the predicted value of Y for X = 4?

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

effect size for anova

η² = SS between/SStotal, small = .01, medium = .06, large = .14

A researcher computes the pooled variance for two samples and obtains a value of 120. If one of the samples has n = 5 scores and the second has n = 10 scores, then what is the value of the estimated standard error for the sample mean difference?

√120/5 + 120/10