Exam 3 ch 9& 10

What is the null hypothesis in a paired-samples t test (in words)?

The null hypothesis posits no mean difference between the populations, difference between means is 0.

When should an independent-samples t test be used?

Used to compare two means for a between groups design, each participant is assigned to only one condition!!!

When do you use a paired-samples t test?

Used to compare two means for a within groups design, every participant is in both samples!!

What is the squared standard deviation equivalent to?

Variance

When is a single-sample t test used?

When we compare a sample and know the mean but not the standard deviation

single sample

X | X-M | (X-M)2 M= ∑(X-M)2 S= √∑(X-M)2 / N-1 SM= S/ √N T= M- Mm/ SM

independent

X | X-M | (X-M)2 Y| Y-M | (Y-M)2 MX= ∑(X-M)2 MY= ∑(Y-M)2 SX2= ∑(X-M)2/ N- 1 SY2= ∑(Y-M)2/ N- 1 DFX= N-1 DFY= N-1 DF TOTAL= DFX+ DFY S2 POOLED= SX2(DFX\DFTOTAL) + SY2 (DFY\DFTOTAL) S2MX= S2 POOLED/NX S2MY= S2 POOLED/NY S2DIFF= S2MX + S2MY SDIFF= √S2DIFF T= MX-MY\ SDIFF

paired sample test

X | Y | Y-X | diff- mdiff | (diff-mdiff)2 Mdiff= SS= s= √SS/ N-1 sm=S/ √N T= MM-0 / SM

What are the two populations compared in an independent-samples t test?

compares two means for a between group design, which means each participant is assigned to only one condition. the overall difference of two independent groups.

Know how to calculate degrees of freedom for an independent-samples t test. Which value is used to determine the critical values?

dfx= n -1 dfy= n -1 dftotal= dfx + dfy df total is used to determine critical cutoff

comparison distribution for independent sample

distribution of differences between the means

comparison distribution for paired sample

distribution of mean differences

Comparison distribution for single sample

distribution of means

What is the last step in computing the standard error of the comparison distribution?

divining s by the square root of N

how to determine the critical values for a two-tailed t test

in a single sample test you need to determine degrees of freedom before. df= N-1, then locate the df number on the t- distributions chart, with the certain p level under the two tailed section. in a paired sample, you do the same steps as a single samples test except the df is the number of participants and not the number of scores. in an independent samples, you do the same steps but use the df total as the df. for a two tailed the critical values will be both negative and positive numbers.

What is meant by "pooling the variance?" What is the pooled variance weighted by?

pooling the variance involves taking an average of the two sample variances while accounting for any differences in the sizes of the 2 samples. Pooled variance is an estimate of the common populations variance. The variance is weighed by the degrees of freedom.

six steps for calculating a single sample t test and

step one: identify the populations, distributions and assumptions sept two: state the null and research hypothesis in words and in symbolic notation step 3: determine the characteristics of the comparison distribution ( uM= and sM=) step 4: determine the critical values or cutoffs step 5: calculate the test statistic step 6: make a decision, reject or fail to reject the null hypothesis

Reject null hypothesis

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fail to reject

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What happens to the t distribution as the sample size gets larger? (and vice-versa?)

As the sample size gets larger, the t distribution begins to merge with the z distribution because we gain confidence as more participants are added to a study. A small sample size means that the t distribution becomes flatter and more spread out.

six steps for calculating a paired sample t test and

step one: identify the populations, distributions and assumptions step two: state the null and research hypothesis in words and in symbolic notation step three: determine the characteristics of the comparison distribution (uM= and sM=) step 4: determine the critical cutoffs step 5: calculate the test statistic step 6: make a decision

What is the symbol used to represent a standard deviation calculated by using a sample to estimate the population standard deviation? What is the symbol used to represent a standard error calculated by using a sample to estimate the population standard deviation?

S, Sm

What is the correct formula for using the sample standard deviation to estimate the population standard deviation

S= ∑(X-M)2 / N-1

What is the correct formula for calculating the standard deviation of a sample when you are not trying to estimate the population standard deviation (when calculating the standard deviation of the sample)?

SD= ∑(X-M)2 / N

What is the formula for standard error when we estimate it from a sample?

Sm = S /√N

Know all six steps for calculating an independent-samples t test

Step 1: identify populations ( P1 & P2) distributions (distribution of differences between means) assumptions (not on tests) Step 2: State null & research hypothesis Step 3: characteristics of comparison distribution: Mx, My, sx2, yx2, dfx,dfy, df total, s2pooled, s2mx, s2my, s2 diff, s diff step 4: determine the critical values or cutoffs step 5: calculate the test statistic step 6: make a decision, reject or fail to reject the null hypothesis