Exam 2 Guide_631
If a researcher suspects the assumption of homogeneity of variances has been violated for an independent measures ANOVA, it can
be tested by Hartley's F-max test for homogeneity of variance (p. 415)
The F distribution is skewed
because groups vary or they do not vary; can't have negative variance
Why does the t distribution have greater variability in the tails of the distribution compared to a normal distribution?
because the sample variance is substituted for the population variance to estimate the standard error in this distribution
As n increases, the probability of outcomes in the tails
becomes less likely and the tails approach the x-axis faster
Why is Hedge's g statistic generally preferred to Cohen's d statistic?
better small sample properties when the sample sizes are significantly different (https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/hedgeg.htm)
When we conduct a related samples t test we remove the
between persons source of error because the same individual is participating in both groups
Two main common designs for comparing groups include
between-subjects design and repeated measures design
Difference between eta-squred formula and omega-squared formula
the first one does not subtract one in the numerator, while the second one does subtract one in the numerator
ANOVA uses one test with one alpha level to evaluate
the mean differences and thereby avoids the problem of an experimentwise alpha level (p. 396)
F statistic is to what extent
the means vary across groups
Estimated Cohen's d: Measure of effect size in terms of
the number of SDs that mean scores shift above or below the population mean stated by the null hypothesis
The type of ANOVA used to analyze data depends on:
the number of factors being tested, how the participants are observed across each level of a factor
The one-sample t test can be computed only when ______.
the population being sampled from is normally distributed
For the null hypothesis of a between subjects ANOVA, it indicates
the population means for the various conditions are all the same
Reducing the estimate of standard error increases
the power; the ability to detect an effect if an effect actually exists
level of confidence
the probability or likelihood that an interval estimate will contain an unknown population parameter.
The One-Way Within-Subjects ANOVA hypotheses
the same as those for between-subjects ANOVA
Repeated measures design means that
the same group of participants is measured at two points in time and there differences across time points are compared
Independent samples refers to
the selection of participants where the different participants are observed one time in each sample or group
The shape of the t distribution changes; ______________ as the _________
the tails approach the x-axis faster; sample size is increased (p.231)
In general, H1 for a between subjects one way ANOVA states
the treatment conditions are not all the same; there is a real treatment effect
Between subjects design means that
there are two groups of different participants where differences across groups are compared
When equal variances are not assumed for an independent samples t test
there is a slight correction applied to the sample sizes
Estimation allows us
to estimate an interval in which a mean can fall. A better way to think about the range of possibilities. - mean and standard error - alpha - critical values
pre-post design is limited
to observing participants at two times
Overlap is very tied
to the variances of the distributions
Sheffe and Bonferroni regarding 1 way between anova
too conservative
The experimentwise alpha level is the
total probability of a type I error accumulated from all of the separate tests in the experiment (p. 395)
Related samples t test is when we have
two measurements but we have the same group of people
Sample variance is an
unbiased estimator of the population variance
how the participants are observed across each level of a factor relates to
Within-subjects design: Same subjects observed across each level of the factor
The term "one-way" means
You are testing one factor
The within treatments variance for an ANOVA provides
a measure of the variability inside the differences between sample means
Using the estimated standard error in the denominator of the test statistic led to
a new sampling distribution known as the t distribution
Using the substitution of sample variance for population variance,
a new test statistic was introduced
t distribution
a normal-like distribution with greater variability in the tails than a normal distribution because the sample variance is substituted for the population variance to estimate the standard error in this distribution.
The t statistic is an inferential statistic used to determine the number of standard deviations in a t distribution that a sample mean deviates from ______.
a population mean or mean difference stated in the null hypothesis
The one sample t test is used to test hypotheses concerning
a single group mean selected from a population with unknown variance (p.233)
interval estimate
a statistical procedure in which a sample of data is used to find the interval or range of possible values within which a population parameter is likely to be contained.
estimation
a statistical procedure in which a sample statistic is used to estimate the value of an unknown population parameter. Two types of estimation are point estimation and interval estimation
point estimate
a statistical procedure that involves the use of a sample statistic to estimate a population parameter.
A pooled standard deviation concisely is
a weighted average of standard deviations for two or more groups
Measuring Effect Size: Between-subjects design for ANOVA
Eta-squared, R^2, or Omega-Squared
Two way ANOVAs
Examines mean differences between two groups that have split on two factors
In a two-way ANOVA, each factor if identified:
Factor A, Factor B) ◦ Levels of each factor are identified numerically
One way ANOVA: What if we have more than two groups? Examples
How 3 different systems affect user acceptance
To summarize the results of a post hoc test:
Identify which post hoc test you computed and the p value for significant results
A Shift to Analyzing Variance
In hypothesis testing, we are often interested in more than two groups
Chapter 9 covers
Independent samples t test
The _________ conditions or __________ that make up a factor are called the __________ of the factor
individual; values; levels (p. 394)
Between-Subjects Design: We use a test statistic to determine
the extent to which the scores between the two groups overlap
The t distribution overview
A bell shaped distribution symmetrical about its median used to make confidence intervals with small samples (<30) and unknown population variance; Degrees of freedom = # of Observations - 1
The F Distribution is derived from
A sampling distribution of F ratios
Post hoc test means
"after the event" in latin
Formula for t-statistic
(Sample Mean - Reference Value) / Standard Error of the Sample Mean
Trial, small, medium, and large effect sizes for eta squared and omega squared are these corresponding values
,.01, between .01 and .09., between .10 and .25, and greater than .25
Lecture: 11/2/22
- Next week is exam 2 --> EMAIL TEDONE TODAY to set up for Exam 2 - Mainly focusing on 1 way ANOVA, but for 2 way Anova: when used for, what it is will be, components, how to run in SPSS - Recommends rerunning analyses, running datasets through Sakai. Ran through x, y, z dataset, can you share your results? -- Correlations and regressions next -- one more hw: Correlation and regressions hw will be due date of excel workshop -- Exam review will be posted prior to exam -- Couple of bonus opportunities: Extra credit for research engagement, another bonus assignment will be discussed next week -> Nice activity to convert stats to research methods for next semester course
Related samples t test
A statistical procedure used to test hypotheses concerning two related samples selected from populations in which the variance in one or both populations is unknown
ZOOM class: October 19, 2022
- wants us to feel comfortable and catering to the widest net of people - will post to PANOPTO which will become available tomorrow - lecture -> breakout rooms -> class activity for today - Check out exam 1 grades -> Happy to review things that I missed -> schedule office hours to go over what I missed - Hopes quiz gave look and feel of the exam - Exam 2 will be very similar
A researcher computes the following test statistic for a one-sample t test: t(28) = 2.97, p < .05. What is the proportion of variance for this test using the formula for eta-squared?
0.24
Chapter 8 covers
1 sample t test
Chapter 8 learning objectives
1. Explain why a t distribution is associated with n-1 degrees of freedom and describe the information conveyed by the t statistic 2. Calculate the degrees of freedom for a one samples t test and locate critical values in the t table 3. Identify the assumptions for a one-sample t-test 4. Compute a one-sample t test and interpret the results 5. Compute and interpret effect size and proportion of variance for a one-sample t test 6. Describe the process of estimation and identify two types of estimation 7. Compute and interpret confidence intervals for the one-sample t test 8. Summarize the results of a one-sample t test in APA format 9. Compute a one-sample t test and identify confidence intervals using SPSS
The comparison of ____________ is common in behavioral research
2 samples or groups
A researcher conducts a one-sample t test. What are the critical values for a two-tailed hypothesis test at a .05 level of significance when df = 14?
2.145
A researcher conducts a one-sample t test with a sample of 24 participants. What are the degrees of freedom for this hypothesis test?
23
Using F (2,15): Of all the values in the F distribution, only ____ are larger than _____ and only ____ are larger than _____
5%; F = 3.68; 1%; F =6.36
A sample of 20 scores is normally distributed with M = 10 and SM = 2.7. What are the upper and lower 80% confidence limits for a one-sample t test?
7.3, 12.7
Running ANOVAs through SPSS
A. Stress levels effect on turnover - need to rearrange as one participant per row -> analyze compare means, group as 'factor' (3 levels coded 1, 2, 3), Post hoc dialogue box and tell it to run post hoc if results are signif- can check off a bunch o see their relationships --> TUKEY, 'options' Means and standard deviations of all groups by checking 'descriptive' -> can report eta squared and post hoc tests -- Compares all possible combination -> Analysis shows significant difference between high and low stress groups --> The 1 way ANOVA suggests that there are significant differences among the groups. Then specify the results of the post hoc test.
SPSS steps for one sample t test: After entering the data, click
Analyze -> Compare means -> One sample t test -> Move variable into "Test variable(s)) section -> Enter number in "Test Value" box -> click OK
Between-subjects design:
Different subjects observed across each level of the factor
Why is the sample variance okay as a substitute for the population variance, with the formula for the estimated standard error?
Because the sample variance is an UNBIASED ESTIMATOR of the population variance (p. 230)
There are two sources of variation in a 1 way ANOVA
Between groups variation
Three measures of effect size relevant to the one-sample t test
Estimated Cohen's d, Eta-Squared, Omega Squared
Why is it beneficial to use the same group of participants
Can be a better way to test your hypotheses and the sample size could be much smaller, minimizes standard error because differences are examined at the individual level rather than the group level
Between subjects design example:
Coffee with sugar, coffee without sugar. Average energy levels across the groups
Related samples t test concisely
Comparing mean difference between pairs of scores in population to those observed in a sample
The Process of Estimation: 3 steps
Compute the sample mean and standard error, choose the level of confidence and find the critical values at that level of confidence, complete the estimation formula to find the confidence limits
The two sources of variance in a 1 way between subjects ANOVA
Means across the different groups (within), variance attributed to error because attributed to external factors and not tied to what we are measuring in our study
Effect size for the one-sample t test- proportion of variance:
Measure of effect size in terms of the proportion or percent of variability in a dependent variable that can be explained or accounted for by a treatment
Tukey's HSD versus Fisher's LSD
More conservative than later
Degrees of freedom in denominator for 1 way ANOVA
N-k
Acronym for Two-Independent-Sample t Test assumptions: NRIE
N: Normality R: Random sampling procedure I: Independent outcomes E: Equal population variances
t-test assumptions: Key words
Normality, random sampling, Independence (p.233, 234)
Assumptions for the one-way within-subjects ANOVA
Normality: Data in population(s) are normally distributed, Independence Within Groups: Participants are independently observed within groups, not between groups, Homogeneity of Variance: Variance in each population is equal, Homogeneity of Covariance: Participant scores in each group are related because the same participants are observed across or between groups
You must split the total df (N - 1) into two parts:
One for each source of variation
Chapter 11 covers
One-Way ANOVA
The most basic type of ANOVA
One-way between-subjects ANOVA
Chapter 10 covers
Paired samples t test
Measuring effect size: Within subjects design for ANOVA
Partial eta-squared, partial omega-squared
Estimation formula for one-sample t test
Point estimate +/- t (Interval estimate)
The distribution of possible outcomes for the F statistic is
Positively skewed
The within-subjects design is associated with more
Power to detect and effect than the between subjects design
Interpret d = -0.74
Relatives caring for OCD patients reduces mean social functioning scores by 0.74 SD below the population mean
two independent sample t test class example interpretation in APA format
Results of an independent samples t-test show that the rate of eating, either slowly (M=600; SD=154.92) or fast (M=650; SD=130.38), failed to produce significant differences in food intake between groups, t(10) = -.605, p>.05.
The main difference between the one-sample t test and the z test is that
SPSS uses a distribution of t scores to evaluate the results (Salkind & Frey, 2020, p. 192)
Example of APA format for one-sample t test
Social functioning scores among relatives who care for patients with OCD (M=62.00; SD=20.94) were significantly lower than scores in the general healthy population t(17) = -3.13, p<.05
Prelecture 10/26
Test statistic, df formula might change. Overall the 4 steps of hypothesis testing will remain the same Next week, break apart the problem and focus on analyzing the results and interpreting the results and writing a summary in APA style -> Know what kind of test, how to do it, how to interpret it One sample and take sample find numbers and compare to a known population Generally speaking, what are the differences between groups rather than population parameters. Not comparing to population. Comparing two groups to one another to see if there's a difference
Equal variances for independent t test
The population variances are the same relatively
APA format for in class 10/19 one sample t test exercise
The results of a one-sample t-test suggest the reading scores at ABC Middle School significantly differs from the national average reading score for public middle school students (M=74.13, SD=14.28), t(199) = -5.76, p<.05. The 95% confidence interval in this population is a score between -7.81 and -3.82. 95% CI [-7.81, -3.82], d = 14.28.
Effect size in a nutshell according to (Salkind & Frey, 2020, p. 194)
The strength of a relationship between variables; measure of the magnitude of a treatment
Alternative hypothesis for a between-subjects design
There is a difference between groups
Page 401 (supplementary textbook): What is suggested by a value of 1 for the F-ratio in an ANOVA?
There is no treatment effect and you should fail to reject the null hypothesis
Chapter 12 covers
Two-Way ANOVA
Between groups variation in a 1 way ANOVA refers to
Variance of group means
Within groups (error) variation in a 1 way ANOVA refers to
Variation attributed to error
For the ANOVA, you also adjust the df, so subtracting the between persons variation will
Will not always increase the power of a one-way within-subjects ANOVA
4 sources of variation can be measured
Within groups variation, main effect for factor A, main effect for factor B, A x B interaction
F ratio equals to 0 means
all the group means are the same; no variance across the groups
A t distribution functions as
an estimate of the normal distribution (p. 232)
t statistic
an inferential statistic used to determine the number of standard deviations in a t distribution that a sample mean deviates from the mean value or mean difference stated in the null hypothesis. Also referred to as t observed or t obtained.
Similar to t test, source of variance is
any variance that can be measured in a study
1 way within subjects ANOVA: same participants
are being observed in each group with 1 factor
Between persons error and within persons error: Differences
are not due to having different groups
When we have two independent groups: We mean that there
are two groups of individuals
Alternative hypothesis for a between subjects one way ANOVA: There is
at least one mean difference among the populations (p. 395)
Between persons error
can be differences between how individuals respond to different treatments
Advantages for Selecting Related Samples
can be more practical, minimizes standard error, increases power
Two-Way ANOVA examines two
categorical independent variables on one continuous dependent variable, along with the interaction effect
Within subjects design have two conditions: Example
coffee with sugar one time and coffee without sugar another time
We are interested in the between groups effect when
conducting related samples t test. Have two different groups
Effect sizes can be
correlational values or values that estimate difference
What are the assumptions for a 1 way between subjects ANOVA?
data in the population normally distributed, random sampling, independence, homogeneity of variance
The substitution (estimated standard error) is the _______ of the ___; for the _____
denominator; test statistic; t test
In analysis of variance, the variable (independent or quasi-independent) that _____________ being compared is called a ________
designates the groups; factor (p. 394)
Between groups effect for related samples t test: We will use the test statistic to
determine whether this difference is significant
If the confidence interval does not cross 0, it means
difference between groups
The Hedge's g statistic expresses the
difference of the means in units of the pooled standard deviation (https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/hedgeg.htm)
The notation to identify the sample size for an ANOVA is
different from the notation used to describe sample size with the t test
Two ways of comparing groups
different groups or same participants at two time points
What is the most basic ANOVA
different participants are being observed at Each level of One factor -> 1 way between subjects ANOVA
One-way between-subjects ANOVA means
different participants are observed at each level of one factor
Between subjects design entails
different participants observed one time in each group or at each level of a factor
for one way within anova: SPSS
don't need to arrange the original data because the same individuals are utilized --> Just change the scale --> generalized linear models and repeated measures --> cues and define --> Post hoc under 'EM Means' -> move over factor to display means for, compare main effects -> Options descriptive stats -> ENTER --> *Sphericity is out of scope but we can assume sphericity* (2,12), <.001 -> Pairwise comparisions section for POST HOC There is a significant difference between smoking related cues and no cues (post hoc display) *Walk through 2 way ANOVA
The estimated standard error is an
estimate of the standard deviation of a sampling distribution of sample means selected from a population with an unknown variance (p. 230)
Point estimate: The use of a sample stat to
estimate the value of a population parameter
Estimation: A statistical procedure in which a sample statistic is used to
estimate the value of an unknown population parameter
The larger the sample size, the more closely a t distribution
estimates a normal distribution (p.232)
What do post hoc tests control for
experimental alpha
The testwise alpha level is simply the alpha level you select
for each individual hypothesis test
Matching through experimental manipulation is typical
for experiments in which the researcher manipulates the traits or characteristics used to match the participants
post hoc tests control
for experimentwise alpha
Critical values _______ as sample size ______
get smaller; increases (p.233)
The tails of a t distribution are thicker, which reflects the
greater variability in values resulting from not knowing the population variance
F ratio is equal to 0 when
group means exactly the same
Between subjects design want to see if the
groups meaningfully different on average on a certain D.V
There are different degrees of freedom associated with the ANOVA: to account for each source of variance
have to have degrees of freedom between groups (numerator) and have to have degrees of freedom error (denominator)
The estimation formula for two independent samples is used to
identify the confidence limits within which the difference between two population means is contained
The ANOVA process divides the total variability
in the entire data set into two basic components
Confidence intervals are rooted
in the idea of estimation
Pre-post design: Type of repeated measures design
in which researchers measure a dependent variable for participants before (pre) and following (post) some treatment
proportion of variance (η2, ω2)
is a measure of effect size in terms of the proportion or percentage of variability in a dependent variable that can be explained or accounted for by a treatment.
Matched pairs design
is less common for psychology
Why does the t distribution have greater variability in the tails as compared to the normal distribution? Because the sample variance
is not always equal to the population variance (p.230)
Null hypothesis for a between- subjects design: The DV
is not different between groups
The estimated standard error for difference scores
is placed in the denominator of the t statistic for related samples formula
It is crucial that the variances are equal because
it would be hard to gage overlap with a large dispersion among two groups
Degrees of freedom in numerator for 1 way ANOVA
k-1
when ANOVA is significant, end up
knowing there are significant differences across groups but do not know which groups are significantly different from one another
What is the size of the effect if d = .82?
large
The F statistic is used to determine how
large the differences are between group means compared to the variance expected to occur by chance
Equal variances regarding Two-Independent-Sample t Test is satisfied when
larger s^2/smaller s^2 < 2
Two-Way ANOVA: A statistical procedure used to examine
mean difference between groups that have been split on two factors
The formula for the 1 way ANOVA test statistic is:
mean square (or variance) between groups divided by the mean square (or variance) within groups
the variances measured in an ANOVA test are computed as
mean squares, or variance
Key for pre-post design
measure dv before and following treatment
Equal sample sizes then the pooled variance is the
midpoint of the two variances
As the sample size increases, sample variance
more closely resembles population variance
The less overlap between the scores of two groups, the _____ likely we are to find that the _____________
more; two groups are significantly different
The notation to identify the sample size for an ANOVA is different from the notation used to describe sample size with the t test For the ANOVA:
n = number of participants per group N = number of total participants in a study k = number of groups
The t distribution is like a ______ but with _______
normal distribution; greater variability in the tails
Two assumptions made to compute related sample t test
normality and independence between groups
Three assumptions regarding a one-sample t test
normality, random sampling, and independence
Assumptions of independent t tests
normality, random sampling, independence, and equal variances
Assumptions for Two-Independent-Sample t Test
normality, random sampling, independence, equal variances
Assumptions for the one-way between-subjects ANOVA:
normality, random sampling, independence, homogeneity of variance
A researcher computes the following test statistic for a one-independent-sample t test, t(16) = 2.900, p < .05. What is the proportion of variance for this test using the formula for omega squared?
not enough information
Type of Anova determined through
number of factors being tested (color of walls effect on test scores) versus (color of walls and lighting effect on test scores) and how participants are observed across each level of a factor
Levels of a 2 way Anova are identified
numerically
The power of the one-way within-subjects ANOVA is largely based upon the assumption that
observing the same participants across groups will result in more consistent responding, or changes in the dependent variable, between groups
Difference score regarding related samples t test
obtained prior to computing the test statistic
The test statistic, is used to determine the number
of standard deviations in a t distribution that a sample deviates from the mean value or difference stated in the null
There are many research projects focusing
on using 3 groups or more
One-Way Within-Subjects ANOVA: Statistical procedure used to test hypotheses for
one factor with two or more levels concerning the variance among group means. This test is used when the same participants are observed at each level of a factor and the variance in any one population is unknown.
Eta-squared tends to
overestimate proportion of variance explained by treatment
Use test statistic to see extent of ______ between the two groups
overlap
Post hoc comparisons are used in one-way ANOVA to see which
pair or pairs of group means significantly differ
Two types of estimation
point estimation and interval estimation
Hypotheses are always
population based since we want to generalize to populations. Thus we use Mu instead of sample mean
With a t test, _____________ is ___________
population standard deviation; not known
Two types of Repeated Measures designs include
pre-post design and within-subjects design
Matching through natural occurrence is typical for
quasi-experiments
Participants can be related through
repeated measures design or matched-pairs design
the increased power of the within-subjects design is only true when
responding between groups is consistent
Suppose a researcher observes 16 participants and measures a sample mean equal to 0. If the null hypothesis is that the mean equals 0, then what is the decision for a one-sample t test at a .05 level of significance?
retain the null hypothesis
In a repeated measures design, the
same group is tested in all of the different treatment conditions (p.394)
Repeated measures
same group of participants at multiple points in time
A large value for the F statistic provides evidence that the
sample mean differences are larger than would be expected if there were no treatment effects
Treatment: Any unique characteristic of a
sample or any unique way that a researcher treats a sample
What value is placed in the denominator of the formula for estimated Cohen's d for the one-sample t test?
sample standard deviation
Hedges' correction uses the __________, plus ______
sample standard deviation; a correction factor
Estimated standard error basically substitutes the
sample variance for the population variance (p. 230)
The means are insufficient to
see the differences. Rather we have to see the overlap to really understand the differences between groups
Ideally the sample size in a 1 way between subjects ANOVA
should be equal in each group
Hypotheses for one way between subjects ANOVA
sigma sub mu = 0: Group means do not vary in the population sigma sub mu >0: Group means in the population do vary
As the number of separate tests increases,
so does the experiment-wise alpha level (p. 395)
The within-subjects design is associated with more power to detect an effect than the between-subjects design because
some of the error in the denominator of the test statistic is removed
Matched pairs design: Must measure
some trait or characteristic before matching
When conduct Post hoc tests overall alpha level
split among the number of groups
Estimated standard error: An estimate of the
standard deviation of a sampling distribution of sample means selected from a population with unknown variance
Estimated standard error is an estimate of the
standard distance that sample means deviate from the value of the population mean stated in the null hypothesis
An analysis of variance (ANOVA), also called the F test, is a
statistical procedure used to test hypotheses for one or more factors concerning the variance among two or more group means, where the variance in one or more population(s) is unknown
In the one-way within-subjects ANOVA, the between persons variation is measured and then
subtracted from the error term in the denominator- reducing the error term in the denominator, thereby increasing the power of the test
Similarly to the normal distribution, the t distribution is
symmetrical and asymptotic, and its mean, median, and mode are all located at the center of the distribution (p. 230)
F statistic, or F obtained: The
test statistic for an ANOVA.
To summarize the results of a one-way between subjects ANOVA test: ◦ Report the
test statistic, df, and p-value, effect size for significant analyses
T tests limited to
testing for differences in one or between two groups
Levene's test for equality of differences
tests to see if there is equal variances. We need to apply a correction if the variances are significantly different from one another.
Example APA Write-Up for ANOVAs Results of a one-way within-subjects ANOVA suggest
that turnover significantly differs across employees experiencing low (M=3.43,SD=.40), moderate (M=3.30,SD=.33), and high (M=2.98,SD=.43) stress, F(2,27)=3.52,p<.05. Further, results of a Tukey HSD post hoc test shows that the low stress group significantly differs from the high stress group in their intent to turnover (p<.05)
To report the results of a t test, which of the following is not reported?
the critical values
A researcher observes 15 students and reports the following result for a one-sample t test: t(29) = 3.52, p < .05. If this is a two-tailed test at a .05 level of significance, then what must be incorrect with this result?
the degrees of freedom
The degrees of freedom for a t distribution are equal to
the degrees of freedom for sample variance
Two independent-Sample t test is a statistical procedure used to test hypotheses concerning
the difference between two independent groups
The variance between groups in an ANOVA is really measuring
the differences between sample means
The Hedge's g statistic is used to measure
the effect size for the difference between means ( https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/hedgeg.htm)
the t distribution is a sampling distribution in which
the estimated standard error is computed using the sample variance in the formula (p. 231)
Page 401 (supplementary textbook): For an analysis of variance, the systematic treatment effects in a study contribute to the _________ and appears in the ______ of the F-ratio
variance between treatments; numerator
The test statistic for ANOVA is _______ to the ______ statistics
very similar; t
When focusing on 3 groups or more
we shift to analyzing variance
Unequal sample sizes then the pooled variance is
weighed by the degrees of freedom
A pooled standard deviation is a
weighted average of the standard deviation (variances) from two or more groups of data when they are assumed to come from populations with a common standard deviation
When is a post hoc test necessary
when k>2
Confounds due to individual differences are eliminated
when using the same group of participants
Within-subjects design: Type of repeated measures design
where researchers observe the same participants across many treatments but not necessarily before and after a treatment
Substitute the population variance
with the sample variance in the formula for standard error
Like a t test we have both options to have
within or between subjects design
Interval estimate: An interval or range of possible values
within which a population parameter is likely to be contained
A sample of 25 mothers rated how important they thought patience was for being a good mother. Women reported an average rating of 1.1 ± 1.0 (M ± SD) on a rating scale from −3 (not important at all) to +3 (very important). If the null hypothesis is that the rating equals 0, then test whether or not women find patience important at a .05 level of significance (two-tailed test).
women rated patience as being significantly important, t(24) = 5.50, p < .05
A researcher reports the following result for a t test at a .05 level of significance: t(40) = 3.02, p < .05 (d = .22). Is this result significant?
yes, the p value is less than 5%
If the confidence intervals cross 0, it means that
zero; no difference between groups and within the realm of possibility.
H0: for 1 way ANOVA
σμ2 = 0 - group means (μ) do not vary (σ2) in the population
H1: for 1 way ANOVA
σμ2 > 0 - group means in the population do vary