Stats Final Review

A researcher compares the incomes of three different groups of pet owners (cat owners, dog owners, and gecko owners). The variability among the different individuals in the study is known as

within-groups

The F statistic increases when

within-groups variance decreases and between-groups variance increases

What are the mode, median, and mean, and when is each used?

-Mode: the most common score in the distribution: if one score dominates, if data are nominal, if dimodal or multimodal -Median: the center score: good for skewed distribution -Mean: the average of the scores in the distribution: in a symmetric distribution and with interval and ratio data

What two things does the central limit theorem tell us about the distribution of means?

1) a distribution of means will always be normally distributed even if the original distribution is not 2) the mean of a distribution of means = the population mean

What is statistical power? How does it relate to Type II errors?

A measure of the likelihood that we will reject the H0 when the H0 is false (likelihood that we will detect a real effect) -> the higher the stat power, the less chance of a Type II error

Define a random sample

A sample derived from a population in which everyone in the population had the same chance of being picked

What does a measure of central tendency indicate?

A single value used to represent a typical score in a set of scores

To make comparisons between 3 or more groups for differences on a dependent variable, use a(n)

ANOVA

Why does the standard error become smaller simply by increasing the sample size?

Because of the central limit theorem: the more scores there are, the closer to a normal distribution and less variable it will become

As they relate to comparison distributions, what is the difference between mean differences and differences between means?

Distribution of mean differences: finding individual difference scores, creating a distribution of means out of those individual scores - used for paired-samples t test Distribution of differences between means: Finding the differences between the mean of the scores of people who had first treatment and the mean of the scores of the people who took the second treatment - making that into a distribution of means by taking repeated samples (finding means and finding differences) - used for an independent samples t test

What is effect size and why is it important?

Effect size indicates the size of the difference in a way that is unaffected by sample size: it shows how much 2 sample sizes do not overlap - because it's a standardized measure, it can compare effect sizes of different studies even when the studies have different sample sizes -> it also expresses whether something that is significant is of practical importance

A scientist has conducted a one-sample experiment. What two parametric procedures are available to her? What is the deciding factor for selecting between them?

Either a single sample z test or single sample t test -> depends if she has the pop standard deviation

Write the null and research hypotheses for an ANOVA

H0: all population means are equal H1: not all population means are equal

What does a z stat tell us about a sample mean?

How close it is to the population mean?

What does a z-score indicate?

How many standard deviations away from the mean a certain score is - a location

How do you interpret a confidence interval?

If you took all possible samples of size n, the true parameter would fall in about ____% of them.

The correction of _________ is used when calculating the estimated standard deviation for the population

N-1

What is the difference between a point estimate and an interval estimate for a population value?

Point estimate: finds an estimate of a certain population parameter Interval estimate: finds a range of plausible values for a population parameter

There are 3 steps involved in creating the comparison distribution for the independent samples t test, and those steps are repeated many times. What is the sequence?

Randomly select scores and calculate their mean as the group 1 mean, randomly select another group of scores and calculate their mean as the group 2 mean, and subtract the second mean from the first

What is the difference between standard deviation and standard error?

Standard deviation is used for a distribution of scores, and a standard error is for a distribution of means

Describe a normal distribution

Symmetrical, mathematically defined frequency distribution curve Highest at the center and tapering on both sides Mean=Median=Mode -bell-shaped, unimodal, ad symmetric

If we calculate a confidence around the sample mean difference used for a paired-samples t-test, and it includes the value of 0, what can we conclude?

That there is not likely a significant difference between the two treatments

Look at the formula for the one-sample t-test. In words, what is this statistic telling us?

The t-statistic forms a ratio.The top of the ratio contains the obtained difference between the sample mean and the hypothesized population mean.The bottom of the ratio is the standard error which measures how much difference is expected by chance.With a large sample, you can say that the t-statistic is an 'estimated z score'

Look at the formula for the independent-samples t test. In words, what is this statistic telling us?

The top of the ratio contains the obtained difference between the sample statistic and the hypothesized population parameter.The bottom of the ratio is the standard error which measures how much difference is expected by chance.

What is the mathematical definition of the variance? Mathematically, how is a sample's variance related to its standard deviation and vice versa?

The variance is the mean squared deviation score. Deviation scores represent the amount of distance a score falls from the mean. The sample standard deviation is the square root of the sample variance. The formula for sample variance includes the sum of the squared deviation scores.

What is pooled variance?

The weighted average of the sample variances - a way to estimate the variance for an independent samples t test

When is a distribution of means used? Why is it useful?

Used when population distribution looks flat, if sample size is large, a sampling distribution will create a normal distribution and z scores can then be used

What do we mean when we say a distribution of mean differences?

We take the differences between the before condition and the after condition for each participant, we draw small samples of those scores and create a distribution of means with those difference scores

When is a single-sample z test used?

When the pop mean and standard deviation are known

Why is the mean called the balance point of a distribution?

because the sum of a set of deviation scores always equals zero. The mean balances the negative deviation scores on one side and the positive deviation scores on the other

A researcher compares the incomes of three different groups of pet owners (cat owners, dog owners, and gecko owners). The variability among the 3 different groups is known as

between-groups

Interested in the effects of different kinds of instruction on videogame performance, Martin asks 30 college freshmen to each play an hour of Ratchet and Klank. Participants are randomly assigned to one of three instruction groups: (1) complete the tasks as quickly as possible, (2) conserve as much health as possible (i.e., play more carefully), or (3) find gold bolts (worth lots of money in equipment and ammunition). If Martin averages the scores for each instruction group and then compares them, any differences in the means of the instruction groups reflect:

between-groups variance

The _________ is the area in the tails of the comparison distribution in which the null hypothesis can be rejected.

critical region

What is the formula for the total degrees of freedom for the independent samples t test?

dfx + dfy

What are the degrees of freedom for an independent samples t test?

dfx = nx-1 dfy = ny-1 dftotal = N-2 = dfx +dfy

The F ratio is calculated by

dividing a measure of between-groups variability by a measure of within-groups variability.

Explain the logic of the F ratio. What are the sources of error in the numerator and the denominator?

f=( Variability due to treatment effect+ variability due to individual differences)OVER(variability due to individual differences) one way ANOVA calculates the ratio of between group variability to within group variability. If there is no effect the F ratio will equal 1. As the effect of treatment grows, the numerator becomes larger than the denominator and the F ratio climbs above 1. As the F ratio increases, as it climbs higher than 1, the results are more likely to be statistically significant

Statistical power is a measure of the ability to reject the null hypothesis when it is

false

A hypothesis test for comparing two means from a between-groups design is a(n) _________

independent samples t test

A statistical ________ occurs when two or more independent variables have an effect on the dependent variable in combination.

interaction

In a two-way ANOVA, a(n) _________ occurs when one of the independent variables has an influence on the dependent variable

main effect

The measure of central tendency most likely to be distorted by outliers is the

mean

In estimating variance for an independent samples t test, variance from the larger sample counts for ________ variance than does variance from the smaller sample

more

As you increase the size of a sample, the distribution of the sample will approach the _______ as long as the underlying population is normally distributed

normal curve

The two groups compared in the single-sample t test are the sample and the

population

Effect size assesses the degree to which two a. populations overlap b. populations do not overlap c. samples overlap d. samples do not overlap

populations do not overlap

There are many t distributions, one for each possible

sample size

As sample size increases, the ________ increases

size of the test stat increases

A bigger sample size means a ________ confidence interval, a _________ z-stat, and a __________ standard error and you are more like to _________ the H0.

smaller, bigger, smaller reject the H0

Because the t test compares means, the denominator must include an estimate of variability among means called the ________.

standard error

When using a sample to estimate variability in the population, one assumes that the sample will _________ the population variability, thus requiring a "correction"

underestimate

Pooled variance involves taking the ___________ of the two variance samples.

weighted average

If the null hypothesis is true for a paired-samples t test, the mean of the distribution of mean differences is _______.

zero