Psyc Stats Exam 3 (Ch 12-15)
least-squared-error solution
best-fitting rule with the smallest total squared error
A chi-square test for independence has df = 2. What is the total number of categories (cells in the matrix) that were used to classify individuals in the sample?
6
repeated-measures design
the same group is tested in all of the different treatment conditions
The chi-square test for goodness of fit evaluates ______.
the shape or proportions for a population distribution
Standard deviation
the square root of the variance
independent-measures designs
the study uses a separate sample for each of the different treatment conditions being compared
N
the total # of scores in the entire study
2 interpretations of Anova correspond to....
the two hypotheses (null and alternative)
Each person in a sample of 180 male college students is cross-classified in terms of his own political preference (Democrat, Republican, Other) and that of his father (Democrat, Republican, Other). The null hypothesis would state that
there is no relationship between the political preferences of fathers and sons
The *null* hypothesis for the chi-square test for independence states that ____.
there is no relationship between the two variables
The null hypothesis for the chi-square test for independence states that ____.
there is no relationship between the two variables
levels of the factor example; a study that examined performance under three different telephone conditions would have __________ levels of the factor.
three
slope
value which determines how much Y variable changes when X is increased by one point
Y-intercept
value which determines the value of Y when X = 0
factor
variable that designates the groups being compared -in the context of ANOVA, an independent variable or a quasi-independent variable -made up levels - ie. age group
quasi-independent variable
when a researcher uses a non-manipulated variable to designate groups -ex. the three groups in Figure 12.1 could represent six-year-old, eight-year-old, and ten-year-old children
Point biserial correlation: one variable is _____
dichotomous
Contingency table
displays data collected when there are two independent variables
linear relationship equation
equation expressed by the equation Y = bX + a
between degrees of freedom
number of groups minus 1
ratio
numerical, can be split or "broken" into multiple parts of sections, nominal and ordinal cannot
Goodness-of-Fit Equations variables
p ~ n ~ fo ~ fe ~ C ~
Goodness-of-Fit Test Equations
pn -> ∑(ƒ₀ − ƒe)²/ƒe -> C − 1
the X^2 distribution is
positively skewed
analysis of regression
process of testing the significance of a regression equation
dichotomous variable
quantity with only two values
Pearson correlation equations
r=SP/√SSxSSy SSx=∑X^2-(∑X)^2/n SSy= " same thing but substitute Y instead of X "
posttest
refers to measuring the dependent variable after changing the independent variable
The three F-ratios have the same basic structure
- Numerator measures treatment mean differences - Denominator measures treatment mean differences when there is no treatment effect
Find the estimated standard error for the sample mean for each of the following samples:a. n = 4 with SS = 48;b. n = 6 with SS = 270;
-First calculate sample variance (s2) which is SS/df, then calculate estimated standard error [sM = √(s2/n)]a) s2 = 16 with estimated SE = 2b) s2 = 54 with estimated SE = 3
HOW TO: Hypothesis Testing with a Two-Factor ANOVA
1. State the hypotheses and select an alpha level. 2. Locate critical region 3. compute f-ratios 4. make decision
Using a sample of 120 creative artists, you wish to test the null hypothesis that creative artists are equally likely to have been born under any of the twelve astrological signs. Assuming that the twelve astrological signs each contain an equal number of calendar days, the expected frequency for each category equals
10
Refer to the two-variable chi-square study shown below. The entries in the table represent observed frequencies. Men Women Prefer Coke 8 2 Prefer Pepsi 4 6 What is the expected frequency in the Women-Prefer Pepsi cell?
4
An analysis of variance produces SStotal = 80 and SSwithin = 30. For this analysis, what is SSbetween?
50, because SSbetween=SStotal-SSwithin
A soda manufacturer wishes to test the hypothesis that more people like his brand than Brand X. The manufacturer obtains a sample of 100 people and finds that 53 people prefer his brand and 47 prefer Brand X. In this study, chi square is equal to:
9/50 + 9/50
Under what circumstance is a t statistic used instead of a z-score for a hypothesis test?
A t statistic is used instead of a z-score when the population standard deviation and variance are not know.
advantage of ANOVA over t-tests
Advantage #1: t tests are limited to situations w/ only 2 treatments to compare ANOVA major advantage #2: useful for comparing 2 or more treatments -provides researchers w/ much greater flexibility in designing experiments & interpreting results
What does ANOVA stand for?
Analysis of variance
Which of the following statements is true for X^2?
As the number of categories increases the critical value of X^2 increases
When conducting a chi-square test it is appropriate to
Compare actual probabilities that could have been developed by chance When conducting a chi-square test it is appropriate to
Which of the following assumptions must be satisfied in order for chi square to give accurate results? A. None of the expected frequencies should be less than 2 B. none of the above C. No response should be related to or dependent on any other response D. A participant must fall in only one category E. All of the above
E. All of the above
F
F-ratio
How does sample size influence the outcome of a hypothesis test and measures of effect size? How does the standard deviation influence the outcome of a hypothesis test and measures of effect size?
Increase sample size increases the likelihood of rejecting the null hypothesis but has little or no effect on measures of effect size. Increasing the sample variance reduces the likelihood of rejecting the null hypothesis and reduces measures of effect size.
A researcher suspects that vegetarians prefer Pepsi and meat-eaters prefer Coke. The researcher obtains a sample of 80 people, and the results are: 30 vegetarians prefer Pepsi, 10 vegetarians prefer Coke; 5 meat-eaters prefer Pepsi, and 35 meat-eaters prefer Coke. If chi square is statistically significant using the .05 criterion, what should the researcher decide?
Meat-eaters prefer Coke, whereas vegetarians prefer Pepsi.
What does it mean to obtain a negative value for the chi-square statistic?
The chi-square statistic can never be negative
two sample t-test (aka independent measures) variance Pooled variance equation
Pooled variance= SS1+SS2/df1+df2
variance equations/symbols
Population (N) Sample variance (N-1)
to convert SD to SS
SD=√(SS/n)
nondirectional
Since all discrepancies between observed and expected frequencies are squared, the chi-square test is...
chi square test for independence
The Chi-Square Test of Independence determines whether there is an association between categorical variables (i.e., whether the variables are independent or related). It is a nonparametric test
The data that you collect suggest that the between-treatments variance is small, relative to the within-treatment variance, so the F-ratio for your study is likely to be (close to 1.00/ substantially larger than 1.00), suggesting that (the null hypothesis will be rejected/will not be rejected)
The data that you collect suggest that the between-treatments variance is small, relative to the within-treatment variance, so the F-ratio for your study is likely to be close to 1.00, suggesting that will not be rejected
T/F ANOVA allows researchers to compare several treatment conditions without conducting several hypothesis tests.
True
T/F All ANOVAs are non-directional
True
T/F MSbetween is variance that includes both treatment effects and random chance
True
If there is no systematic treatment effect, then what value is expected, on average, for the F-ratio is an ANOVA?
When Ho is true, the expected value for the F-ratio is 1.00 because the top and bottom of the ratio are both measuring the same variance.
The observed frequencies are different than the expected frequencies
When X^2 (observed) exceeds X^2 (critical) one can conclude
independent variable
When a researcher manipulates a variable to create the treatment conditions in an experiment
levels
aka "*levels* of the factor" the individual groups or treatment conditions that are used to make up a factor
Stages of repeated-measures analysis (stage 1)
analysis of the SS and df into within-treatments and between-treatments components
as sample size (n) increases what happens to normal distribution?
as sample size (n) increases, distribution becomes more normal and standard deviation becomes smaller
chi square test
assesses whether the observed frequencies differ significantly from expected frequencies
Slope of a line, b, can be calculated...
b = SP/SSx OR b = r sy/sx the line goes through (Mx,My) therefore a=My-bMx - this regression line equation results in the least squared error between the data points and the line
A large discrepancy between 𝒇e and 𝒇o for a chi-square test means...(select all that apply) a. The value for the chi-square statistic will be smaller -IT WILL BE LARGER b. The probability of rejecting the null hypothesis increases c. The probability that the data do not fit the null hypothesis increases d. All of the above
b. The probability of rejecting the null hypothesis increases c. The probability that the data do not fit the null hypothesis increases
The following scores were measured on an interval scale. If the scores are converted to an ordinal scale (ranks), what values should be assigned to the two individuals who started with scores of X = 5? Scores: 2, 3, 5, 5, 7, 10, 18
both should receive a rank of 3.5
cell
box within the table showing different combinations of the variables
The expected frequencies in a chi-square test ________.
can contain decimal values (or fractions)
expected frequencies ___.
can contain fractions or decimals
nominal
categorical or variables grouped by names
The chi-square test is designed for use when observations are classified according to...
categories
between-treatments variance
caused by either systematic age group variance or random unsystematic variance due to individual differences and sampling error
within-treatments variance
caused by random unsystematic variance caused by individual differences or sampling error
Stages of repeated-measures analysis (stage 3)
computation of variances and the F-ratio
monotonic relationship
consistently one-directional relationship between two variables
Phi correlation: both variables are _____
dichotomous
residual variance
denominator of the F-ratio -variance (differences) expected with no treatment effect
covariability
describes how much scores are spread out or differ from one another, but takes into account how similar these differences or changes are for each subject from one variable to the other
independence
descriptor for the three hypothesis tests, meaning results from each test are totally unrelated
goal of ANOVA in this experiment
determine whether the mean differences observed among the samples provide enough evidence to conclude that there are mean differences among the three populations
Percentage of variance accounted for
determining amount of variability in scores explained by treatment effect is an alternative method for measuring effect size r^2=t^2/t^2+df
correlation matrix
diagram of results from multiple relationships -shows the correlation coefficients between several variables
When will only half of a correlation matrix be displayed?
if correlation matrix is perfectly symmetrical
calculating estimated standard error equation (type B)
if sample sizes are different, calculate pooled variance sp^2=SS1+SS2/df1+df2
Which Chi-Square tests hypotheses about the relationship between two variables in a population?
independence
single factor, independent-measures design (ANOVA)
limited to one independent variable (IV) or one quasi-independent variable -the study uses a separate sample for each of the different treatment conditions being compared
regression equation for Y
linear equation
main effect
mean difference among the levels of one factor
descriptive statistic
mean, standard deviation, and number of scores for each treatment
Cohen's w
measure of effect size that can be used for both chi-square tests
Stages of repeated-measures analysis (stage 2)
measure of individual differences and removal of individual differences from the denominator of the F-ratio
Can chi square be a negative number?
no
dichotomous definition
nominal variables which have only two categories or levels -ex. if we were looking at gender, we would most probably categorize somebody as either "male" or "female"
Spearman Correlation
relationship between two variables when both are measured in ordinal scales
phi-coefficient
relationship between two variables when both measured for each individual are dichotomous
point-biseral correlation
relationship between two variables, one consisting of regular scores and the second having *two* values -"bi-" = 2
positive correlation
relationship in which two variables tend to change in the same direction
perfect correlation
relationship of 1.00, indicating an exactly consistent relationship
factorial design
research study involving more than one factor
testwise alpha level
risk of a Type I error for an individual hypothesis test
single sample t-test variance equation
s^2=SS/df
Pearson chi-square
set of data including calculated chi-square value, degrees of freedom, and level of significance
Alternatives to pearson correlation
spearman correlation, point-biseral correlation, and phi-coefficient
3 Stages of repeated-measures analysis
stage 1: analysis of the SS and df into within-treatments and between-treatments components stage 2: measure of individual differences and removal of individual differences from the denominator of the F-ratio stage 3: computation of variances and the F-ratio
Variance
standard deviation squared
T-statistic and equations
t= and estimated standard error (SM) ALSO, Standard deviation equation: s^2
matrix
table showing different combinations of the variables, producing different conditions
parametric test
test that concerns parameters and requires assumptions about parameters
as the number of categories (C) increases,
the Critical value of the chi-square statistic for a one-way test increases
The critical value of the chi-square statistic for a one-way test increases as:
the number of categories (C) increases
Within degrees of freedom
∑(n-1)=∑df in each treatment The sum of # of scores in each treatment minus one equals the sum of the degrees of freedom within each treatment
interaction
"extra" mean difference
A x B interaction
"extra" mean difference not accounted for by the main effects of the two factors
n
# of scores in each treatment
k
# of treatment conditions
Analysis of Variance
(ANOVA) statistical hypothesis-testing procedure used to evaluate mean differences between two or more sample means or populations - determines whether three or more means are statistically different from one another
Cohen's d (equation)
(effect size)
F ratio
***
how is f-ratio related to the t-statistic?
***
inferential statistic
***
typical research situation in which ANOVA would be used
***
t-test uses ___ standard error
*estimated* standard error
Overview of Two-Factor, Independent-measures ANOVA
- We can examine three types of mean differences within one analysis Complex analysis of variance - Evaluates differences among two or more sample means - Two independent variables are manipulated(factorial ANOVA; only two-factor in textbook) - Both independent variables and quasi-independent variables may be employed as factors in a two-factor ANOVA - An independent variable (factor) is manipulated in an experiment - A quasi-independent variable (factor) is not manipulated but defines the groups of scores in a nonexperimental study - *factorial designs* -*three hypotheses tested by three F-ratios*
how to identify hypotheses for ANOVAs (instead of t-tests), and what does this do?
...... *** -it evaluates mean differences
What is the implication when an ANOVA produces a very large value for the F-ratio?
A large F-ratio indicates there is a treatment effect because the differences between the numerator are much bigger than the differences expected if there was no treatment effect (denominator) - between groups differences are significantly different.
Q3. Explain why t distributions tend to be flatter and more spread out than the normal distribution (z-score distribution).
A z-score is used when the population standard deviation (or variance) is known. The t statistic is used when the population variance or standard deviation is unknown. The t statistic uses the sample variance or sample standard deviation in place of the unknown population values.
To evaluate the effect of a treatment, a sample (n = 16) is obtained from a population with a mean of µ = 30 and a treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 31.3 with a standard deviation of s = 3.Are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α = .05?
CR = 2.131 SM = 0.75 t = 1.733 Fail to reject the null; t(15) = 1.733; p > .05The data are not sufficient, there is no treatment effect.
Two-factor, Independent-measures ANOVA
Complex analysis of variance - Evaluates differences among two or more sample means - Two independent variables are manipulated(factorial ANOVA; only two-factor in textbook) - Both independent variables and quasi-independent variables may be employed as factors in a two-factor ANOVA - An independent variable (factor) is manipulated in an experiment - A quasi-independent variable (factor) is not manipulated but defines the groups of scores in a nonexperimental study - *factorial designs* -*three hypotheses tested by three F-ratios*
Factorial designs
Consider more than one factor - We will study two-factor designs only - Also limited to situations with equal n's in each group Combined impact of factors is considered
T/F A positive value for the chi-square statistic indicates a positive relationship between the two variables, and a negative value for the chi-square statistic indicates a negative relationship between the two variables.
False, Chi-square cannot be a negative number, so it cannot accurately show the direction of the relationship between the two variables
T/F If the null hypothesis is true, the F-ratio for ANOVA is expected (on average) to have a value of 0.
False, If the null hypothesis is true, the F-ratio will have a value near 1.00
T/F A large value for chi-square will tend to the statistical decision to retain (i.e., fail to reject) the null hypothesis.
False, Large values of chi-square indicate that observed frequencies differ a lot from null hypothesis predictions
T/F Posttests are needed if the decision from an analysis of variance is "fail to reject the null hypothesis."
False, Post hoc tests are needed only if you reject H0 (indicating that at least one mean difference is significant)
True or False: If the null hypothesis is true, the F-ratio for ANOVA is expected (on average) to have a value of 0.
False: If the null hypothesis is true, the F-ratio will have a value near 1.00.
True or False: Sample size has a great influence on measures of effect size.
False: Measures of effect size are not influenced to any great extent by sample size.
True of False: Post tests are needed if the decision from an analysis of variance is to fail to reject the null hypothesis.
False: Post hoc tests are only needed when at least one mean difference is significant
True or False: If the Y variable decreases when the X variable decreases, their correlation is negative
False: The variables change in the same direction, a positive correlation
True or False: When the value of the t statistic is near 0, the null hypothesis should be rejected.
False: When the value of t is near 0, the difference between M and μ is also near 0.
When n is small (less than 30), the t distribution ____.
Is flatter and more spread out than the normal z distribution
Three hypotheses tested by three F-ratios
Large F-ratio 🡪 greater treatment differences than would be expected with no treatment effects
Which combination of factors is most likely to produce a large value for the F-ratio?
Large mean differences and small sample variances
a. H0: The racial/ethnic distribution of police-involved shooting deaths will match the racial/ethnic distribution of the US population. b. H1: The racial/ethnic distribution of police-involved shooting deaths will not match the racial/ethnic distribution of the US population. c. df = 3 d. Critical chi-squared value = 7.81
Let's say we're interested in whether police-involved shootings are disproportionately distributed compared to national data on race/ethnicity. We know that the 2019 population distribution is as follows: Number of Individuals in Various Racial/Ethnic Groups of the US Population: White 198 million Black 44 million Hispanic/Latinx 60 million Other 26 million Shooting Deaths by Police in 2019, based on Victim's Race/Ethnicity: White 404 Black 250 Hispanic/Latinx 163 Other/Unknown 184 Total 1001 Data come from the US Census Bureau and The Washington Post's Fatal Force project. Population groups are rounded to the nearest 1 million. Using a standard alpha of 0.05, select the attributes that best/most appropriately describe this study's: -null hypothesis -alternative hypothesis -degrees of freedom -critical chi-squared value
A sample of n = 25 scores has a mean of M = 83 and a standard deviation of s = 15. Compute the estimated standard error for the sample mean and explain what is measured by the estimated standard error.
The estimated standard error is 3 points [sM = √(s2/n) or s/√n]. The estimated standard error provides an estimate of the average distance between a sample mean and the population mean, or how well our sample mean represents our population mean (It does what standard error does for z-score tests but now we don't know pop SD which is needed to calculate SE).
Goodness-of-fit
The extent to which observed frequencies in a chi-square test match the expected frequencies
Which of the following is not an assumption of the chi-square test?
The observations are measured on a continuous measurement scale
*Alternative* hypothesis for non-directional; chi-square tests
The observed distribution of frequencies does not equal the expected distribution of frequencies for each category
3 hypotheses of two-factor anova
The two-factor ANOVA is composed of three distinct hypothesis tests: 1. The main effect of factor A (often called the A-effect). Assuming that factor A is used to define the rows of the matrix, the main effect of factor A evaluates the mean differences between rows. 2. The main effect of factor B (called the B-effect). Assuming that factor B is used to define the columns of the matrix, the main effect of factor B evaluates the mean differences between columns. 3. The interaction (called the AxB interaction). The interaction evaluates mean differences between treatment conditions that are not predicted from the overall main effects from factor A or factor B.
T/F For a fixed alpha level of significance used for a hypothesis test, the critical value for a chi-square statistic increases as the degrees of freedom increase.
True
T/F In a chi-square test, the observed frequencies are always whole numbers.
True, Observed frequencies are just frequency counts, so there can be no fractional values
True or False: By chance, two samples selected from the same population have the same size (n = 36) and the same mean (M = 83). They will also have the same t statistic.
True: All elements of the t statistic will be the same for each sample
True or False: A report shows ANOVA results: F(2, 27) = 5.36, p < .05. You can conclude that the study used a total of 30 participants.
True: Because dfwithin = N - k
True or False: ANOVA allows researchers to compare several treatment conditions without conducting several hypothesis tests.
True: Several conditions can be compared in one test.
True or False: It is possible for the regression equation to have none of the actual data points on the regression line.
True: The line is an estimator.
True or False: Compared to a z-score, a hypothesis test with a t statistic requires less information about the population
True: The t statistic does not require the population standard deviation; the z-test does.
True or False: If r = 0.58, the linear regression equation predicts about one third of the variance in the Y scores.
True: When r = .58, r^2 = .336
T/F A report shows ANOVA results: F(2, 27) = 5.36, p < .05. You can conclude that the study used a total of 30 participants.
True; Remember that dftotal = N - 1 and dftotal = dfbetween + dfwithin So: dftotal = dfbetween + dfwithin = 2 + 27 = 29 And since dftotal = N - 1, then 29 = N - 1 So N = 30
Let's say that we are interested in the most effective way of soothing anxious dogs (like Rocky, our course TA). We design a study where 18 dogs have their blood pressure tested 4 times, under 4 different conditions. (Blood pressure increases under stressful conditions and decreases during relaxation). Condition 1 = Control condition (experimenters sit quietly, not interacting with the dog as he rests for 5 minutes before measurement). Condition 2 = Head pats (the experimenter pats the dog's head for 5 minutes). Condition 3 = Belly rubs (experimenter rubs the dog's belly for 5 minutes). Condition 4 = Verbal positive reinforcement (experimenter spends 5 minutes telling the dog nice things, such as "Who's a good boy? You're a good boy!"). •Does this experiment call for a one-factor ANOVA or a two-factor ANOVA? •Is this a repeated-measures ANOVA, or independent-samples? •How many levels of the factor are there? One-factor ("one way") ANOVA Two-factor ("two-way") ANOVA repeated measures ANOVA independent samples ANOVA k = 2 k = 3 k = 4
Two-factor ("two-way") ANOVA ........... repeated measures ANOVA ........... k = 4
How tho check calculations for the Mann-Whitney U
UA + UB = (nA)(nB)
If there is no systematic treatment effect, then what value is expected, on average, for the F-ratio in an ANOVA?
When Ho is true the expected value for F = 1.00 because the numerator and denominator are both measuring only non-sys differences (expected error) - thus NO treatment or conditional effects are present
Under what conditions can the phi-coefficient be used to measure effect size for a chi-square test for independence?
When both variables consist of exactly two categories
Compare actual probabilities that could have been developed by chance
When conducting a chi-square test it is appropriate to
regression equations
Y=bX+a - this regression line equation results in the least squared error between the data points and the line
ordinal
[think "ordered"] happens in a specific, sometimes repeated way (can be qualitative or quantitative)
Statistical procedures that deal with ordinal statistics are generally not valid when:
a large proportion of the cases are tied
independent-measures design
a separate group of participants (sample) for each of the different treatment conditions being compared
The Pearson correlation coefficient is not applicable in all situations(i.e. when we have outliers or a restriction of range), so statisticians have created alternatives to Pearson. Match the Pearson alternative to the situation in which it would be used. Write the letter a, b, or c next to the corresponding situation a. Spearman Correlation __ 2 dichotomous variables b. Point-biserial Correlation __ 1 dichotomous variable & 1 variable is interval or ratio c. Phi-Coefficient __ ordinal variable(s) and curvilinear relationship
a. Spearman Correlation _c_ 2 dichotomous variables b. Point-biserial Correlation _b_ 1 dichotomous variable & 1 variable is interval or ratio c. Phi-Coefficient _a_ ordinal variable(s) and curvilinear relationship
Which of the following are true of post-hoc tests? (Select all that apply) a. They are done after a significant difference is found in an ANOVA b. They only apply to one-way ANOVAs c. Tukey's and Scheffe are the most common examples d. They help you locate where the significant difference is e. They measure effect size
a. They are done after a significant difference is found in an ANOVA b. They only apply to one-way ANOVAs c. Tukey's and Scheffe are the most common examples d. They help you locate where the significant difference is e. They measure effect size
negative correlation
correlation in which two variables tend to go in opposite directions
linear equations/regression
correlations give rise to a line of best fit -regressions analyze the relationship this line reflects (IDs the equation of that line)
Partial correlation
evaluating relationship b/w X and Y while controlling variance caused by Z
pn
expected frequencies for the goodness-of-fit test
outlier
extreme datum point
In analysis of variance, the variable (independent or quasi-independent) that designates the groups being compared is called a __________.
factor
two-factor design is also known as....
factorial design***???
how to compute SP (sum of products) and formulas
find the products of X times Y
SStotal-SSwithin
formula for between treatments sum of squares
k-1
formula for between-treatments degrees of freedom
N-1
formula for total degrees of freedom
∑X² − G²/N
formula for total sum of squares
∑(n-1) = ∑df in each treatment
formula for within-treatments degrees of freedom
∑SS inside each treatment
formula for within-treatments sum of squares
Which Chi-Square test uses frequency data from a sample to test hypotheses about a population?
goodness of fit
linear relationship
indicator of how well the data points fit a straight rule
single-factor study
indicator that the research study involves only one independent variable
level(s) of the factor (in ANOVAs)
individual condition or value that makes up a variable/factor -ie. if age group is the factor, 16- to 20-year-olds, 21- to 25-year-olds, and ≥ 26-year-olds are the levels of the factor.
The value of chi square can never be...
less than zero
coefficient of determination
measure of proportion of variability in one variable determined from the relationship with another variable
standard error of estimate
measure of standard distance between predicted Y values on regression line and actual Y values
sum of products of deviations
measure of the amount of covariability between two variables
Pearson correlation
measure of the degree and the direction of the linear relationship between two variables - has a value between -1 and 1 where: • -1 indicates perfectly negative linear correlation b/w two variables • 0 indicates no linear correlation between two variables • 1 indicates perfectly positive linear correlation between two variables
between-subjects variance
measure of the size of the individual differences
Spearman correlation
measures relationship b/w two variables that are both measured on an ordinal scale (Both X and Y values are ranks) -it measures the degree of consistency of direction for the relationship but does *not* require that the points cluster around a straight line -to compute: Pearson formula is applied to ordinal data
Cramér's V
modification of the phi-coefficient that can be used to measure effect size
restricted range
set of scores that do not represent the full range of possible values
variance equals
standard deviation squared
regression
statistical technique for finding the best-fitting straight rule for a set of data
correlation
statistical technique used to measure and describe the relationship between two variables
repeated-measures ANOVA
strategy in which the same group of individuals participates in every treatment
two-factor ANOVA
strategy where multiple variables (or mean differences) are manipulated while a third variable is observed -test for mean differences in research studies -the two-factor ANOVA allows us to examine three types of mean differences within one analysis. In particular, we conduct three separate hypothesis tests for the same data, with a separate F-ratio for each test
two-factor design
study that combines two variables -the sample size is the same for all treatment conditions
single-factor design
study that has only one independent variable
two-factor, independent-measures, equal n design
study with exactly two factors that uses a separate sample for each treatment condition
G
sum of all of the scores in the research study
T
sum of the scores for each treatment conditino
f-ratio equation and definition
the numerator of the F-ratio measures the actual mean differences in the data, and the denominator measures the differences that would be expected if there is no treatment effect -large value for the F-ratio indicates that the sample mean differences are greater than would be expected by chance alone, and therefore provides evidence of a treatment effect -To determine whether the obtained F-ratios are significant, we need to compare each F-ratio with the critical values found in the F-distribution table in Appendix B.
For the MANN-WHITNEY U test, when n is greater than 20, U is converted to a z score
true
