PSYCH 140-STATS FINAL STUDY GUIDE
A researcher obtains an F-ratio with df=(2, 12) from one-way within subjects ANOVA. How many subjects participated in the research study
(2=bT/k-1, 12=(n-1)(k-1)) 12=(n-1)(2) 12/2=6=n-1 n=7
Degrees of freedom for 2 factor ANOVA: dfb
(number of columns) c-1
Degrees of freedom for 2 factor ANOVA: dfA
(number of rows) r-1
Formula for r2
(r)2x100 - r2 percentage of variability in one variable that is accounted for by the other variable EX: r=.76 (.76)^2x100 .5776x100 =57.76%
The validity of the ANOVA presented in the chapter depends on three assumptions common to other hypothesis tests
- Observations w/in each sample must be independent of each other - Populations from which samples are selected must be normally distributed - Populations from which samples are selected must have equal variances
Interaction
- When one factor modifies the effects of a second factor - When the effects of one factor depend on the different levels of a second factor - If the two factors are independent, there is no interaction
Mean differences among levels of one factor
- differences are tested for statistical significance - each factor is evaluated independently of the factors in the study H0A: MA1=MA2, H1:.... H0B: UB1=UB2, H1....
How to tell reading SPSS results if relationship is positive or negative
- in front of = means it's negative
Within treatments variance measures differences caused by
1) Random, unsystematic factors
Between treatments variance measures differences caused by
1) Systematic treatment effects 2) Random, unsystematic factors
H1 ANOVA
At least one population mean is different from the others
In repeated measures ANOVA, the SS within treatments is divided into two components
Between subjects and error
A researcher reports an F-ratio with df-3, 36 for a one way between subjects design. How many treatment conditions were compared in this experiment.
DFBetween subjects=k-1 k-1=3 k=4
SStotal
EX2-G2/N
Definitional formula for SP
EXY-(EXEY)/n
Degrees of freedom for 2 factor ANOVA: dfwithin treatments
Edf inside each treatment (A + b + AXB)
In between subjects, two way ANOVA, MSinteraction=124.22 and MSwithin=103.13, what is Finteraction
F(Interaction) = MSinteraction/MSwithin aka error 124.22/103.13=1.20
How to write results SPSS APA format
F(dfbetween, dfwithin)=f(2 decimals rounded), p><.05, .01 or .001
The appropriate denominator for the F-ratio for a repeated measures ANOVA
F=MSbt/MSe The variance that remains after the variance between subjects is subtracted from the variance within treatments.
F Ratio in the Repeated Measures ANOVA
F=variance between treatments/variance expected w/ no treatment effect
Mean squares and F-ratios for two factor anova: FA,Bor FAXB
Fa, Fb, or Faxb/MSwithin
One tailed Hypothesis tests w/ Pearson correlation
H0: p<=0 (not a positive correlation) H1: p>0 (positive correlation)
Two tailed Hypothesis tests w/ Pearson correlation
H0: p=0 H1: p does not = 0
ANOVA
Hypothesis testing procedure to evaluate mean differences between two or more treatments (or populations)
First stage of two factor anova
Identical to independent samples anova, compute SS total, SSbetween and SSwithin treatments
Factorial designs
Involve two or more independent variables, at least one of which is manipulated by the researcher. Factors - independent variables levels - categories (male and female) Two Factor design: two independent variable
Which of the following scenarios could be analyzed using a two-way ANOVA? - Samantha examines the effects of anxiety on music students' performances during a recital - Bill tests whether males and females differ on a measure of emotional expressiveness - Kamal measures the impact of noise and task difficulty on a memory task - Kai assesses whether experiencing life events correlates with distress
Kamal measures the impact of noise and task difficulty on a memory task
For one way between subject design comparing three treatment conditions with a sample of n=10 in each treatment, the F ratio would have df equal to
Look for BT and W/IN dfBT=k-1 (3-1)=2 dftotal=N-1, N=nk 10x3=30-1=29 dfWT=29-2=27. 2 & 27
H0 ANOVA
M1=M2=M3
F ratio formula
MS between/MS within
F ratio
MSbetween/MSwithin
Interactions between factors
Mean differences between individuals treatment conditions, or cells, are different from what would be predicted from the overall main effects of the factors. H0: No interaction between factors A & B H1: There is an interaction between factors A & B
ANOVA total degrees of freedom (dfTOTAL)
N-1
Degrees of freedom for 2 factor ANOVA: dftotal
N-1
ANOVAwithin treatment df (dfWITHIN)
N-k
point-biserial correlation
One variable has 2 values: dichotomous variable - male female - college grad vs not a college grad - first born child vs later born child assign value or 0 & 1 and use Pearson correlation formula
A statistical procedure used to test hypotheses for one factor with two or more levels concerning the variance among treatment means, where the same participants are observed at each level of a factor is called for the
One-way within subjects anova (bc it uses repeated measures)
What quantifies the degree of linear relationship between two interval and/or two ratio variables.
Pearson correlation coefficient
If the interaction effect is found to be significant in a two-way ANOVA, which of the following statements is true? - All group means differ and a post-hoc test is neccessary - Post-hoc tests should be done to determine differences in row effects - Post-hoc tests should be done to determine differences in column effects - Post-hoc tests should be done to determine differences in cell means
Post-hoc tests should be done to determine differences in cell means
r formula
SP/sqrtSSxSSy
Total sum of squares
SS total
Between treatments sum of squares
SS total-SSwithin treatment
MS (w/in, between)
SS/DF
Mean squares and F-ratios for two factor anova: MS
SS/df
In Analysis of Variance, large mean differences from one sample to another produce will a large value for
SSbetween treatments
Within treatments sum of squares
SSwithin each treatment=ESS inside each treatment
a repeated measures ANOVA has SSwithin treatments=20 and SS between subjects=12, for this analysis, what is the value for SSerror
SSwithin=SSbetween + SSerror 20=12 + SSerror SSerror=8
what measures the association between ordinal variables
Spearman rank-order correlation coefficient
Correlation
Statistical technique used to measure and describe a relationship between two variables Direction of relationship: positive correlation vs negative correlation Form of the relationship: measure straight line (linear relationships) Degree of the relationship
One-way repeated measures ANOVA
TBD
one-way independent-measures ANOV A
TBD
A researcher studies the effect of cognitive psychotherapy on positive self-regard. The number of positive statements made about oneself is recorded for each participant during the first meeting. After 8 weekly therapy sessions, the measures are repeated for each person. Which of the following is a correct statement based on the SPSS output?
The number of participants is 4.
Structure of two factor ANOVA
Three distinct tests Main effect of Factor A Main effect of Factor B Interaction of A & B A separate F test is conducted for each
Dr. Orbach compared a group of suicidal mental hospital patients (individuals who had made serious suicide attempts), non-suicidal mental hospital patients with similar diagnoses, and a control group of volunteers from the community. The purpose of the study was to test the theory that suicidal individuals have a higher tolerance for physical pain. The idea is that their higher pain threshold makes it easier for them to do the painful acts usually involved in suicide. A higher score indicates a higher level of pain tolerance. What is the total number of participants in the study?
Total number of participants x=39-1 40
ANOVA Logic Between Treatments Variance
Variability results from general differences between the treatment conditions Variance between treatments measures differences among sample means
ANOVA Logic Within Treatments Variance
Variability within each sample Individual scores are not the same within each sample.
Dr. Orbach compared a group of suicidal mental hospital patients (individuals who had made serious suicide attempts), non-suicidal mental hospital patients with similar diagnoses, and a control group of volunteers from the community. The purpose of the study was to test the theory that suicidal individuals have a higher tolerance for physical pain. The idea is that their higher pain threshold makes it easier for them to do the painful acts usually involved in suicide. A higher score indicates a higher level of pain tolerance. Using the results, r (128) =-.64, p < .05, what is the MOST appropriate conclusion?
X and Y have a negative relationship.
Two-way ANOVA
a hypothesis test that includes two nominal independent variables, regardless of their numbers of levels, and a scale dependent variable
Paired t-test
a t-test performed on a repeated measures two-group design
Independent t-test
a test using the t-statistic that establishes whether two means collected from independent samples differ significantly.
post hoc tests
additional significance tests conducted to determine which means are significantly different for a main effect
r
degree to which X and Y vary together (covariability of X and Y)/degree to which X and Y vary separately
error term
denominator of the F-ratio (uncontrolled and unexplained variability)
Purpose of post hoc test
determine which treatments are different
Degrees of freedom for 2 factor ANOVA: dfaxb
dfAxdfB
In a positive relationship, cases:
follow the same pattern, when x goes up y goes up and when x goes down, y goes down
Scatterplot
graph clustered of dots allowing you to see relationship between x and why
Effect size
how big is the effect?
How to tell reading SPSS results if relationship is significant
if it's <.05 then it's significant, if it's >.05 then it's not significant.
Factor
independent variable
ANOVAbetween treatment df (dfbetween)
k-1
Degrees of freedom for 2 factor ANOVA: dfbetween treatments
k-1
In two-factor ANOVA, an independent variable is ________ in an experiment
manipulated
Pearson correlation
measures the degree and direction of the linear relationship between two variables
Spearman correlation
measures the relationship between variables measured on an ordinal scale of measurement
degrees of freedom for correlation test
n-2 (B.6 table)
Interpreting correlations
not a cause and effect relationship between the two variables Affected by the range of scores represented in the data Affected by outliers
In two-factor ANOVA, a quasi-independent variable is
not manipulated but defines the groups of scores in a non experimental study
n
number of scores on each treatment
K
number of treatment conditions (number of groups/levels of factor)
In F ratio, when treatment has an effect, the ____________ should be larger than ___________
numerator; denominator
Dr. Orbach compared a group of suicidal mental hospital patients (individuals who had made serious suicide attempts), non-suicidal mental hospital patients with similar diagnoses, and a control group of volunteers from the community. The purpose of the study was to test the theory that suicidal individuals have a higher tolerance for physical pain. The idea is that their higher pain threshold makes it easier for them to do the painful acts usually involved in suicide. A higher score indicates a higher level of pain tolerance. Which statistical test was applied to test the hypothesis?
one-way independent measures ANOVA
A researcher studies the effect of cognitive psychotherapy on positive self-regard. The number of positive statements made about oneself is recorded for each participant during the first meeting. After 8 weekly therapy sessions, the measures are repeated for each person. Which statistical test should be applied to test the hypothesis?
paired t test
Second stage of two Factor ANOVA
partition the SS between Treatments into 3 separate components, attributable to factor A; factor B and to the AxB interaction
Tukey's HSD
q=sqrtMSwin treatment/N
Coefficient of determination
r2 - effect size reveals the percentage of variability in one variable that is accounted for by the other
what tells the percentage of variability in one variable that is accounted for by the other variable
r^2
Conditions that affect a Pearson r
restriction of range nonlinearity Outliers
Interpretation of r2
small effect around 1% Medium effect around 9% Large effect around 25%
Mean squares and F-ratios for two factor anova: MSwithin treatments
sswithin/dfwithin
David conducts a study to look at the effects of stress and social support on physical symptoms. If stress is categorized into low medium and high and social support is categorized into low and high, what correctly describes two way ANOVA design?
stress: k=3 social support: k=2 3x2
G
sum of all the scores in the study (grand total)
Two way ANOVA should be used when
the effects of two independent variables are being tested
Levels
the individual conditions or values that make up a factor
In a two factor analysis of variance, a main effect is defined as
the mean differences among the levels of one factor
Main effects
the mean differences among the levels of one factor
The phrase, "Correlation does not equal causation" means:
there is no guarantee that a cause-and-effect relationship exists between two variables
T
total for each treatment condition
N
total number of scores in entire study
Repeated measures ANOVA
two or more treatments with a single sample sample
F ratio is based on
variance instead of sample mean differences