Psy 202 Final
Strong correlation
Data that is very close to being a line
Quantify the relationship between the number of Scoville units (the measurement of the spicy chemical, capsaicin, in chili peppers) a pepper has and the number of seconds a person who eats the pepper can wait to drink some milk.
Pearson Correlation
range of correlation coefficients
-1.00 to +1.00; closer to -1 or 1 = strong relationship; closer to 0 = weak relationship; 0 = no relationship
Nonparametric tests
-doesn't assume normal distribution (distribution free) -nominal/ordinal data -doesn't test specific population parameters (tests whole distributions) -less specific assumptions -LESS POWER -EX:Chi-square goodness-of-fit test Chi-square test of independence Spearman rank-order correlation coefficient Mann-Whitney U Test
Parametric tests
-normal distribution -interval/ratio data -tests specific population parameters -very specific assumptions -robust in terms of assumption violation -MORE POWER -EX: z, t, F, r
Descriptive Statistics
-numerical data used to measure and describe characteristics of groups; Includes measures of central tendency (mean, median, mode) and measures of variation; -refers to procedures for organizing, summarizing, and describing data
Pearson r Assumptions
1. random sample 2. independent observations 3. normal distribution 4. linear relationship
goodness-to-fit assumptions
1.) Random Sample 2.) Independence of Observations 3.) Sufficiently large sample size (fe at least 5 for each cell)
Test of independence Assumptions
1.) Random Samples 2.) Independence of Observations 3.) Sufficiently large sample size (fe at least 5 for each cell)
A developmental psychologist is interested whether children of 3 different age ranges differ in their liking for a certain kind music. The psychologist studies 200 children at a local school district. The results are shown in the contingency table below. IS there a significant relationship between these 2 variables
Chi-Square Test of Independence
A coffee manufacturer advertises that in a recent experiment in which their brand (A) was compared with four other leading brands of coffee, more people preferred their brand to other food. That data are A=60, B=45, C=52, D= 43, E= 50
Chi-Square goodness-to-fit
coefficient of determination (r^2)
Effect size that reveals the percentage of variability in one (criterion) variable that is accounted for by the other (predictor) variable; r^2 = literally r squared; approximately _% of the variability in the criterion (ind) variable can be accounted for by the predictor (dep) variable - Small effect ≈ 1% - Medium effect ≈ 9% - Large effect ≈ 25%
A homeopathic nutritionist believes that eating local honey will help to decrease seasonal allergies. She gathers enough local honey for 60 local people to have a tablespoon of honey each day for a month before the spring allergy season. These participants then report their daily allergy symptoms for two weeks. She compares the results to another sample of 60 local people (who were not given honey) who report their daily allergy symptoms for the same two week period (control group).
Independent-Samples T Test
A professional golf coach has developed a new kind of golf club that she thinks can improve the game of any player, regardless of the player's skill level. She wants to compare her club to three other top-selling golf clubs. She goes to a local golf course and randomly offers one of the four clubs to golfers who come to play the first hole. She does this until she has over 80 different scores on the first hole using each of the four clubs.
One-Way ANOVA
A sporting goods store wants to assess whether wooden kayaks are faster in the ocean than plastic kayaks are. The store's researchers have access to only a few kayakers who are skilled enough to paddle in that kind of setting and in both kinds of kayaks. In order to increase the power of the study, the researchers have each kayaker paddle each kind of kayak over a distance of 500 yards and measure time it takes to cross the finish line.
Paired-Samples T test
Dr. Stevens compared the effects of a new therapy on three groups of cardiovascular patients (treatment, control, and care as usual), and the groups were matched on age, gender, and disease severity.
Repeated Measures ANOVA
A sixth-grade Spanish teacher has implemented a new curriculum in her classroom that she thinks will increase her students' vocabulary to exceed the national average (SD unknown) for native English speakers who are learning Spanish.
Single-Simples T test
Linear Regression
Statistics procedure in which 1 or more predictor variables are used to make predictions based on outcomes of relationships
What effect does violating the random sample assumption have on a researcher's interpretation of the results of a chi-square goodness-of-fit test?
Violating the random sample assumption reduces the generalizability of the results.
Simple Linear Regression Equation
Y'= bX+a Y' = predicted value of Y b = slope of the regression value b= r(Sy/Sx) X = value of X for which one wants to find Y' a = y-intercept of the regression line a = My-bMx
Correlation Coefficient
a number that summarizes the strength of the linear relationship between two variables.
Postive Correlation
a relationship between two variables in which both variables either increase or decrease together; positive = up and to the right;
One-Way ANOVA
aka between subjects ANOVA; use when comparing independent samples across 1 independent variable.
Test of Independence Decision Rules
alpha = .05 df = (# of rows -1)(# of column-1) Reject null if x^2 greater than or equal to critical value
goodness-to-fit decision rules
alpha level = .05 df = N-1 reject null if x^2 is greater than equal to critical value
Pearson r Decision Rules
alpha level = .05 to find r critical value, look up df = N-2 and whether it is two-tailed/non-directional; Reject the null hypothesis - if r is less than or equal to (-) critical value or if r is greater than or equal to (+) critical value; fail to reject null hypothesis (-) is less than or qual to r which is less than or equal to (+) critical value
Chi-Square Test of Independence
answers the statistical question of whether the groups of individuals have the same distribution of representation across several categories; 1 variable is dependent on another/ related to or associated with one another
Chi-Square test of independence
answers the statistical question of whether the groups of individuals have the same distribution of representations across several categories; variables dependent of the other; related/associated; 2 variables
Chi-Square Goodness-of-Fit Test
answers the statistical question of whether the observed distribution of cases conforms to or fits the expected distribution
Chi-square goodness-to-fit
answers the the statistical question of whether the observed distribution of cases confirms to or fits the expected distribution; 1 variable
How large should expected cell frequencies be in order to obtain a valid result?
at least 5
Weak correlation
data that is further apart
What factors contribute to the size of the x^2 observed ?
frequency observed and frequency efficient
Pearson r Interpretations
if null is rejected then evidence suggests either a statistically positive (linear) relationship or negative (inverse) relationship between the 2 variables. If fail to reject the null hypothesis then r is not significantly different from 0 -APA Phrase example - APA format, r(6) = .76, p < .05
expected frequency
in a chi-square test, number of people in a category or cell expected if the null hypothesis were true; -goodness-to-fit = N/fo -test of independence = use contingency square to calculate
How do null hypotheses differ between parametric and nonparametric tests?
in parametric tests there are symbols and only words in nonparametric tests - there is not a significant difference
Inferential Statistics
includes methods for making inferences about a group of individuals (population) on the basis of data actually collected on a much smaller group (sample)
Goal of Regression
is to be able to predict Y values from X values
Spearman Rank correlation Coefficient
measures the association between ordinal variables
Pearson Correlation
measures the degree and the direction of the linear relationship between two variables
Pearson Correlation
measures the degree and the direction of the linear relationship between two variables (interval/ratio)
Variables are said to be independent of each other when:
no relationship exists between the two variables.
In what circumstances should the chi-square statistics be utilized?
nominal data
Pearson r Hypotheses
non-directoral; null hypothesis - p(rho) = 0 alternative hypothesis - p(rho) doesn't equal 0 directional- null hypothesis - p(rho) is opposite of what question says alternative hypothesis - p(rho) is what question is
goodness-to-fit hypotheses
null: There is not a significant difference.. alternative: There is a significant difference..
Test of Independence Hypotheses
null: there is no relationship between variables alternative: there is a relationship between 2 variables
Conditions that affect Pearson r
outliers linearity restriction of range
Nonparametric Alternatives
paired-samples T test = Wilcoxon test Independent-samples T test = Mann-Whitney U One-Way ANOVA = Kruskai - Wallis Test Repeated- Measures ANOVA = Freeman Pearson r = Spearman r
Least Squares Criterion
the best prediction is the one that yields the smallest errors between predicted outcomes and actual outcomes
observed frequency
the frequency with which participants fall into a category
When calculating chi-square, a researcher will compare:
the observed versus expected frequencies.
Negative Correlation
the relationship between two variables in which one variable increases as the other variable decreases; down and to the left; on a scatterplot the dots will be further apart
Paired-Samples T test
use for a repeated-measures design and matched cases design
Repeated-Measures ANOVA
use for a repeated-measures design or matched cases design when comparing populations across 1 independent variable
Independent-Samples T test
use when comparing 2 independent samples.
Single Sample T Test
use when comparing a single sample to a known population with an unknown population standard deviation
Single Sample Z Test
used to compare a sample mean to a population mean when the standard deviation of the population is known
straight line equation
y = mX +b
The spot where the regression line passes through the Y-axis is called the:
y-intercept
