Exam 2 Guide_631

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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


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