Stats Final

If the null hypothesis is true for paired sample t-test the mean of the mean difference is

0

For a sample of 35 people, with a standard deviation of 4.67, the standard error is

0.789

The variance calculated on 40 scores is equal to 21.08. The standard deviation is

4.59

What does a measure of central tendency indicate?

A measure of central tendency refers to the center or most typical score of a distribution

To make comparisons between three 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 standard error is standard deviation/=square root of sample size when sample size increases, the denominator of the equation increases which will make standard error smaller

· Why should Fobt equal 1 if the data represent the null hypothesis?

If Fobt equals 1, that means that mean squared within and mean squared between are the same.

· When would you use an independent samples t test?

It is used when we do not know the population parameters and are comparing two groups composed of unrelated participants or observations

Type 1 error

Rejecting null hypothesis when it is true

· Explain why the standard error for the distribution of sample means is smaller than the standard deviation of sample scores.

Standard error is smaller because in order to get standard error, you have to divide standard deviation by the square root of N.

Why do we divide by N - 1 (instead of N) when estimating the population standard deviation from a sample?

The sample standard deviation will underestimate true population variability and dividing by N-1 corrects the sample standard deviation.

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

The standard deviation is not known, so it has to be estimated.

To decide whether to to reject the null hypothesis, we compare the test statistic to the ____________ values

critical

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

critical region

Values of a test statistic beyond which one rejects the null hypothesis are called _______

critical values

Values of a test statistic beyond which one rejects the null hypothesis are called ________

critical values

The formula for the total degrees of freedom for the independent-samples t test is:

dfx+dfy

type 2 error

failing to reject a false null hypothesis

one way chi square

goodness of fit looking at one nominal variable expected frequencies based on what we know about the population

What does a z-score indicate?

how many standard deviations a particular score is from the mean

The most frequently occurring score in a distribution is the

mode

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

more

with large sample sizes, the shape of the distribution of the means will be _________

normal

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

Numbers based on a(n) _________ are called parameters

population

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

population

Effect size assesses the degree to which two

populations do not overlap

When alpha increases, both ________ and ________ increase.

power; the probability of a Type 1 error

A(n) ________ sample occurs when everyone in the population has the same chance of being selected.

random

If a researcher finds that the groups he studied differed from each other more than would be expected by chance alone, the researcher _________ the null hypothesis

rejects

Numbers based on a(n) _________ are called statistics

sample

There are many t distributions, one for each possible

sample size

As sample size increases

size of the test statistics increases.

For a normal distribution with a given mean and standard deviation, a score of 14 will result in a __________ z score than a mean of 14 based on a sample from the distribution

smaller

The range of raw scores contained in an 80 percent confidence interval will be ______ the range of raw scores contained in a 95 percent confidence interval

smaller than

The F statistic increases when:

within-groups variance decreases and between-groups variance increases

Define random sample

when each case in the population has an equal chance of being selected

When is a Z test used?

when the dependent variable is a scale variable, participants are randomly selected and the population of interest is normally distributed

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 variability

What is the difference between a point estimate and an interval estimate for a population value? How do you interpret a confidence interval?

A point estimate is a summary statistic that is used as an estimate of the population parameter such as the mean. An interval estimate provides a range of plausible values for the population parameter such as confidence intervals. For confidence intervals - Draw normal curve with sample mean in the center - Indicate bounds on the interval on either end and record the percentage under each segment of the curve - Look up z-stats for lower and upper ends - Convert z-stats back into raw means for each end and check answer

· Explain why it is easier to reject the null hypothesis when sample size increases.

Because when sample size increases, it becomes less likely that an event occurred due to chance. When sample size increase, standard error decreases and test statistic increases.

What are critical values and critical region?

Critical region is the area in the tails of the comparison distribution in which the null hypothesis can be rejected Critical values are points on the test distribution that are compared to the test statistic to determine whether to reject the null hypothesis

· What is effect size and why is it important?

Effect size indicates the size of a difference and it is important because it is unaffected by sample size and tells us how much two populations do not overlap. - When two populations are farther apart, the overlap of the distributions is less and the effect size is bigger - When two populations decrease their spread, the overlap of the distributions is less and the effect size is bigger - Because effect size is a measure based on scores rather than means, we can compare effect sizes on different studies with one another, even when the studies have different sample sizes

Why are effect sizes rather than test statistics used when comparing study results?

Effect sizes, unlike test statistics, are not affected by sample size and thus ensure a fair comparison

· Write the null and research hypotheses for an ANOVA.

H0: u1=u2...=uk Ha: not all u's are equal

· 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?

If an interval contains 0, then 0 is a plausible mean difference and we fail to reject the null hypothesis.

· What are the three different F statistics in a two-way ANOVA?

The three statistics are main effect for A, main effect for B and AxB interaction.

· If a significant F-ratio is obtained, why is it necessary to do post-hoc comparisons?

It is necessary to do post hoc comparisons because they are needed to discover where the significant differences exist between the groups. We compare all possible pairs of means from a factor, one pair at a time, to determine which means differ significantly.

Why does the Z stat (a z score based on a distribution of means) tell us about the sample mean?

It tells us how many standard errors a sample mean is from the population mean. It is a Z-stat when the z-score represents a mean and not an actual score

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

N-1

The________ level is the probability used to determine the critical values, or cutoffs, in hypothesis testing.

P

Numbers based on a population are called ______.

Parameters

· What is pooled variance?

Pooled variance is a weighted average of the two estimates of variance. If the sample sizes are equal, the pooled variance would be the average of two variance estimates.

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

Statistical power is a measure of likelihood that we will reject the null hypothesis when the null hypothesis is false- the likelihood that we will detect a real effect. If the statistical power is high, the probability of a Type 2 error occurring goes down.

Distinguish between statistical significance and practical importance.

Statistical significance relates to whether an effect exists or not and practical importance relates to the magnitude of the effect

What does statistically significant mean to statisticians?

Statistically significant indicates the results are too unlikely to occur by chance.

· Explain the concept of sum of squares.

Sum of squares is all squared values added together. Deviations from the mean will always add up to 0. When you square these deviations, they will no longer add up to 0. These sums of squares are measures of variability of scores from the mean.

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

Tells us whether there is statistical evidence that the associated population means are significantly different.

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

The F ratio is the ratio of the between group variance to the within group variance. The sources of error in the numerator and denominator are they are measuring random, unsystematic factors. F= Ms between/MS within

· Explain what a main effect is. Explain what an interaction means. There are three factors for main effect.

The Main Effect for Factor A: The mean differences between the levels of factor A are obtained by computing the overall mean for each row in the matrix. The Main Effect for Factor B: The mean differences between the levels of factor B are obtained by computing the overall mean for each column in the matrix. The A x B Interaction: Often two factors will "interact" so that specific combinations of the two factors produce results (mean differences) that are not explained by the overall effects of either factor. An interaction is when your observations indicate that there is a difference in increase or decrease amongst groups.

What is the standard size of the critical region used by most statisticians?

The convention is to set the cutoffs to a level of .05.

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

The degrees of freedom for an independent-samples t test is N-1. Use n-1 for X and Y and add the two together to get Df total.

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

The distribution for the paired-samples t test is made up of mean differences, which are the average of many different scores. The distribution the independent-samples t test is made up of differences between means, which are the differences we can expect to see between group means if the null hypothesis is true.

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

The mathematical definition of the variance is the average of the squared deviations from the mean. The variance is the standard deviations squared, making the standard deviation the square root of the variance

What are the mean and the standard deviation of the z distribution?

The mean is 0 and the standard deviation is 1

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

The mean is the average of a group of scores and the most commonly reported measure of central tendency, It is calculated for interval or ratio data. It is most commonly used for symmetric distributions. The median is the middle score of all scores in the sample when arranged in order from least to greatest. Used for skewed distributions Mode most frequent occurring number One particular score dominates a distribution, the distribution is uni modal or bi modal or when the data is normal

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?

The student can either perform a one-tailed t test or a two-tailed t test. The deciding factor is whether the student is predicting a difference or not. If he/she thinks or predicts an increase or decrease against the null, a one-tailed test would be used. If he/she makes a prediction to reject the null but does not specify a prediction on whether there is any increase or decrease, then it would be a two-tailed t test.

There are many t distributions, one for each possible __________.

There are many t distributions, one for each possible sample size

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

This would mean you are taking groups of individuals, getting the mean from each group and comparing the different means to one another. An example of this would be asking several groups that have 10 people each to perform problems, and taking the mean of each group of 10 people to compare to the other groups.

When a researcher rejects the null hypothesis but the null hypothesis is in fact true, the researcher has made a(n) _____________ error

Type 1

When a researcher fails to reject the null hypothesis but the null hypothesis is false, the researcher has made a ________ error

Type 2

· Recognize when a situation calls for a paired-samples instead of an independent-samples t test.

Unlike an independent samples test, a paired-samples test will have two scores for every participant. We take the difference between the two scores before calculating the sample mean difference that will be used in the t test.

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

When N is large, a distribution of sample means approximates the distribution even if the original population is not normally distributed. Also tells you how large N is

· When would you use a one-way ANOVA? Why is it better to perform a one-way ANOVA instead of multiple t-tests?

You would use a one-way ANOVA when you have one nominal variable with more than two levels and a scale dependent variable. If you use multiple t tests when there are more than two means, it leads to an increase in experiment-wise error rate, which is the probability of making a Type 1 error. Using ANOVA allows us to compare the means from all levels of the factor and keep the experiment-wise error rate equal to alpha

normal distribution

a bell-shaped curve, describing the spread of a characteristic throughout a population uni modal and symmetric percentage of cases that fall in specific areas under the curve

Random ________ is what researchers do with participants once they have been recruited into a study

assignment

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

because the scores always balance around the mean for any sample

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

between groups variability

Distribution of means? when is it used? Why is it useful?

distribution composed of many means that are calculated from all possible samples of a given size, all taken from the same population. It is used to reduce the influence of individual outliers It is useful because it is less variable than a distribution based on individual scores

The F ratio is calculated by:

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

If an extreme score is added to a data set, increasing the range of data, the standard deviation will

increase

Increasing sample size does NOT:

increase effect size

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

independent samples t-test

A confidence interval is a(n) _________ that includes the population mean a certain percentage of time with repeated

interval estimate

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

it is false

A distribution of means is _______ variable than a distribution of scores

less

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

main effect

The arithmetic average of a set of data is the

mean

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

mean

The middle score of an ordered distribution is the

median

Independent samples t-test 3 steps

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

A statement that two populations are different from one another is a __________ hypothesis

research

What is the difference between standard deviation and standard error?

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

Because the t test compares means, the denominator must include as estimate of variability among means called the ____________

standard error

The standard deviation of a distribution of means is called the ________.

standard error

If the data differ from what one would expect if chance was the only thing operating, the finding is called

statistically significant

Two-way chi square

test for independence two categorical variables not looking at populaton expected values row total, column total

What is the difference between a null hypothesis and a research hypothesis?

the null indicates there is no change, no difference, or no relationship between two groups. The research hypothesis indicates that there is a difference between the two groups.

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

underestimate

A measure that describes variability in squared units is

variance

Standard deviation is computed by taking the square root of

variance

What are the two decisions or conclusions we can make about our hypotheses, based on the data?

we can either reject the null hypothesis or fail to reject the null hypothesis

Pooled variance involves taking the _________ of the two variance samples

weighted average

What does hypothesis testing tell us?

what results are significant, but no details regarding the means

Know how to use z-scores to compare scores from 2 different distributions .

you standardize the raw scores on two different scores on two different scales, converting both scores to z-scores and we then can compare the scores directly

A _______ is a z computed on a sample mean rather than a raw score

z stat

A person who scored exactly at the mean of the distribution of raw scores would have a z score of ____________

zero