Psy 10 exam 3

What are the two ways the estimated standard error can be interpreted for an independent samples t test?

1- it is the standard or average distance between sample statistic and population parameter. 2- the estimate standard error produces a simplified version of the independent measures t statistic

What are the three assumptions of the independent measures t test?

1-observations in each sample MUST be independent 2- the two populations from which the samples are selected must be normal 3- the two populations from which the samples are selected must have equal variances

Describe the t statistic.

A statistic used to test hypotheses about an unknown population mean, μ, when the value of σ is unknown.

What is a repeated measures design?

Aka within subjects design- a single sample of individuals is measured more than once on the same dependent variable

What are two items in the independent samples t test that are structurally different from the single sample t test?

All of the elements of the single sample t test are doubled, the independent measures uses the difference between two sample means to evaluate a hypothesis about the difference between two population means

What is the main advantage of a repeated measures design?

Because it uses the same participants, there is no risk of individual differences between groups interfering with the measurements

When making a decision for an independent measures t test, what numbers do you look at and when do you reject the null?

Compare the calculated t statistic to the critical value obtained for the selected alpha level- if t is bigger, reject the null.

In an independent measures t test, if we reject the null, what needs to be done after that?

Compute cohen's d and r2

What would a symbolized null hypothesis look like for an independent measures design look like?

H0 = µ1 - µ2 = 0

What would a symbolized alternative hypothesis look like for an independent measures design?

H0 = µ1 - µ2 ≠ 0

What is the symbolized null hypothesis for a repeated measures design?

H0 = µD = 0

What is the symbolized alternative hypothesis for a repeated measures design?

H0 = µD ≠ 0

What does sample size n approximate?

How many bodies were made up the sample

What does pooled variance do for the estimated standard error in an independent measures t test?

It corrects the bias in the standard error by combining the two sample variances into a single value

Why is the symbol for estimated standard error sM if it is the standard error for the population?

It indicates that the estimated value is computed from sample data rather than from the actual population parameter

What is a limitation on the estimated standard error for the independent-measures t test?

It is limited to situations in which the two samples have the same sample size

What is the estimated standard error used for?

It is used as an estimate of the real standard error when the value of σM is unknown

What does the standard error (in the denominator of t formula) measure in an independent samples test?

It measures the amount of error when you use a sample difference to represent a population mean difference.

What does standard error provide us?

It provides us a measure of how well a sample mean approximates the population mean by describing how much difference is reasonable to expect between M and µ

What is the formula for the t statistic?

M - µ/ sM

What is the formula to calculate cohen's d in an independent samples t test?

M1 - M2/√ sp2

What is the formula to calculate the t statistic for a related samples t test?

MD - µD/ sMD

How do you calculate cohen's d for a related samples design?

MD/√s2

Notation: D

Notation: D

How is the t statistic for a repeated measures design different than the independent measures design?

Repeated uses the Difference scores (D) rather than the raw scores (X)

What is the estimated standard error formula for independent measures test?

S(M1-M2) = √s12/n1 + s22/n2

What is the formula for sample variance?

SS /n-1

What are the four steps to a hypothesis test for independent measures designs?

Same as others: 1- state the hypothesis and select alpha level 2-calculate df to determine critical region 3-obtain data and compute test statistic 4- Make a decision

Rewrite the t formula to reflect where the data comes from.

Sample mean - population mean (from the data) - (from the null hypothesis)/ estimated standard error (computed from the sample data)

What is the t formula for the independent measures test?

Sample mean difference - population mean difference/estimated standard error AKA (M1 - M2) - (µ1 - µ2)/ S(M1-M2)

What is the shape of the t distribution?

The exact shape of a t distribution changes with degrees of freedom. As df gets very large, the t distribution gets closer in shape to a normal z-score distribution

What happens to the sample variance as the df increases?

The larger the df, the better the sample variance represents the population variance, and the better the t statistic approximates the z score

What is the major difference between a non-directional and a directional hypothesis test for independent measures designs?

The null and alternative hypothesis are set up with < or > or ≥ or ≤ and you conduct a one tailed not a two tailed test

In an independent measures test situation where the sample sizes are different, what formula can be used to fix this?

The pooled variance: sp2= SS1 + SS2/df1 + df2

What is the general difference in shape from the normal distribution and the t distribution?

The t distribution tends to be flatter and more spread out, whereas the normal z distribution has more of a central peak

How is the t distribution table read?

The two rows at the top of the table show proportions of the t distribution contained in either one or two tails, depending on which row is used. The first column of the table lists degrees of freedom for the t statistic. Finally, the numbers in the body of the table are the t values that mark the boundary between the tails and the rest of the t distribution.

What is the purpose of an independent measures research design?

To evaluate the mean difference between two populations (or treatment conditions)

Why do we use the z-score statistic?

To quantify our inferences about the population (comparing the obtained sample mean with the hypothesized population mean)

What is a matched-subjects research design and why is it used?

When subjects are matched based on various factors (age, IQ, gender, etc), used to try to approximate the advantage of a repeated measures design

For sum of squares what is (∑x) 2

add up all the values then square it

Define the estimated standard error.

an estimate of the real standard error, σM , when the value of σ is unknown. It is computed using the sample variance or sample standard deviation and provides an estimate of the standard distance between a sample mean, , and the population mean, μ.

What does the sample mean M approximate?

approximates an unknown pop mean (u)

Notation: d

cohen's d

What is symbol for degrees of freedom and how do you calculate it?

df; n-1

Notation: s(M1-M2)

estimated standard error for two independent samples

Describe why we use sample variance to calculate the estimated standard error.

it is an unbiased statistic; on average, the sample variance provides an accurate and unbiased estimate of the population variance . Therefore, the most accurate way to estimate the standard error is to use the sample variance to estimate the population variance.

What do you do if your df is not on the t table?

look up the critical t value for both the one smaller and the one larger and then use the larger t value. If your sample t statistic is greater than the larger value listed,

Notation: N

number of scores in a population set

Notation: n

number of scores in the sample set

Notation: r2

percentage variance accounted for by treatment

Notation: sp2

pooled variance

Notation: µ

population mean

How is sM calculated?

s/ √n

What is the symbol for sample variance?

s2 (s squared)

What is the symbol for the estimated standard error?

sM

How do you calculate r2 for a related samples design?

same as for independent design: t2/ t2 + df

For sum of squares what is ∑x2 (squared)

square each value and add it up

What is the formula for calculating r2 in an independent samples t test?

t2/t2 + df

Describe the t distribution

the complete set of t values computed for every possible random sample for a specific sample size (n) or a specific degrees of freedom (df). The t distribution approximates the shape of a normal distribution, especially for large samples or samples from a normal population.

Describe degrees of freedom.

the number of scores in a sample that are independent and free to vary. Because the sample mean places a restriction on the value of one score in the sample, there are degrees of freedom for a sample with n scores

What is the difference between the t statistic and the z-score formulas?

the z-score uses the actual population variance, σ2 (or the standard deviation), and the t formula uses the corresponding sample variance (or standard deviation) when the population value is not known.

If you are calculating a t, and the table doesn't list the df you have, why would you use the larger critical value listed?

then you can be certain that the data are in the critical region, and you can confidently reject the null hypothesis

What do we do in a hypothesis testing situation with the t statistic?

we begin with a population with an unknown mean and an unknown variance, often a population that has received some treatment. The goal is to use a sample from the treated population (a treated sample) as the basis for determining whether the treatment has any effect.