stats 208 final

Adding a constant changes the the mean but does not change the standard deviation.

A population has µ = 50 and σ = 5. If 10 points are added to every score in the population, then what are the new values for the mean and standard deviation?​

If one multiplies every score in a distribution by 3, then the mean and standard deviation are going to multiply by 3 as well.

A population of scores has µ = 50 and σ = 5. If every score in the population is multiplied by 3, then what are the new values for the mean and standard deviation?​

a. 3 t would be t² = 3² = 9

A repeated-measures ANOVA produced an F-ratio of F = 9.0 with df = 1, 14. If the same data were analyzed with a repeated-measures t test, what value would be obtained for the t statistic? a. 3 b. 9 c. 81 d. Cannot determine without more information

True Because dftotal = N - 1 and Because dftotal = dfbetween + dfwithin

A report shows ANOVA results: F(2, 27) = 5.36, p < .05. You can conclude that the study used a total of 30 participants.

At alpha =0.05 and two-tailed test, the cut-off z-score is 1.96. That z-score of 1.96 corresponds to a distribution that is 1.96 standard deviations above the original population mean (40). To find this distance: 1.96 σM = 1.96 (σ / √n) = 1.96 * 2 = 3.92 The critical boundary of z=1.96 corresponds to sample mean 40+3.92 = 43.92. Any sample greater than 43.92 would be in the critical region and lead to the rejection of the null. So we need to know the proportion of the NEW population (with mean of 43) that falls beyond the 43.92 cut-off point. To do this, we find need to find the corresponding z-score: Z= (M-μ)/σM = (43.92 - 43) / 2 = 0.46 Because the cut-off value (43.92) is larger than the mean of the new population (43), you would look in the proportion in tail column for a z-score of 0.46. You will see that the corresponding proportion/power is 0.3228. GW pg 255-257

A researcher selects a sample of n = 25 from a normal population with µ = 40 and σ = 10. If the treatment is expected to increase scores by 3 points, what is the power of a two-tailed hypothesis test using α = .05?

d. 2, 18

A researcher uses a repeated-measures ANOVA to test for mean differences among three treatment conditions using a sample of n=10 participants. What are the df values for the F-ratio from this analysis? a. 3, 9 b. 2, 9 c. 3, 18 d. 2, 18

Cohen's d effect size's formula (GW pg 252-253) Cohen's d = (M-μ)/σ = (63-60)/6 = 0.5

A sample of n = 16 individuals is selected from a population with μ = 60 and σ = 6 and a treatment is administered to the sample. After treatment, the sample mean is M = 63. What is the value of Cohen's d for this sample?​

Sample variance: SS/n-1 Population variance: SS/N

A set of 10 scores has SS = 90. If the scores are a sample, the sample variance is ____ and if the scores are a population, the population variance is ____.​

The easiest way to solve this problem is to use Cohen's d effect size's formula (GW pg 252-253) Cohen's d = (M-μ)/σ M= (Cohen's d * σ )+ μ = (0.5*12) + 80 = 86

A treatment is administered to a sample of n = 9 individuals selected from a population with a mean of µ = 80 and a standard deviation of σ = 12. After treatment, the effect size is measured by computing Cohen's d, and a value of d = 0.50 is obtained. Based on this information, what is the mean for the treated sample?​

True Several conditions can be compared in one test

ANOVA allows researchers to compare several treatment conditions without conducting several hypothesis tests.

50

An analysis of variance produces SStotal = 80 and SSwithin = 30. For this analysis, what is SSbetween?

false The two t values are unlikely to be the same; variance estimates (s2) differ between samples

By chance, two samples selected from the same population have the same size (n = 36) and the same mean (M = 83). That means they will also have the same t statistic.

True The t statistic does not require the population standard deviation; the z-test does

Compared to a z-score, a hypothesis test with a t statistic requires less information about the population.

The problems says that a score is 12 points above the mean, which is the deviation score. If the z-formula is: z= (x-μ)/ σ , the numerator is 12, and we know that σ=6. Therefore, z-score is 12/6 = 2

For a population with a standard deviation of σ = 6, what is the z-score corresponding to a score that is 12 points above the mean?​

Z= (95-80)/10 = 1.5

For a population with µ = 80 and σ = 10, what is the z-score corresponding to X = 95?​

how much difference there is between the two treatments

For an independent-measures research study, the value of Cohen's d or r2 helps to describe _____.

True This is an accurate interpretation

For an independent-measures t statistic, the estimated standard error measures how much difference is reasonable to expect between the sample means if there is no treatment effect.

d. SSw - SS bs

For the repeated-measures ANOVA, SSerror is found by____. a. SS total - SS between measures b. SS bt - SSw c. SSbt - SSbs d. SSw - SS bs

Size of treatment effect is near zero F-ratio is near 1.00 and indicates that the differences between treatments are random and unsystematic

If H0 is true...

Size of treatment effect is more than 0 F-ratio is noticeably larger than 1.00 and there are systematic treatment effects

If H1 is true...

False H0 is rejected when p < .05, and t > the critical value of t

If a researcher reports that t(6) = 1.98, p > .05, then H0 was rejected

False df = (n1 - 1) + (n2 - 1) = 9 + 9 = 18

If both samples have n = 10, the independent-measures t statistic will have df = 19.

If you employ an unbiased formula for sample variance and take the mean of all possible sample variances, then the mean variance should equal the population variance (in theory).

If sample variance is computed by dividing SS by df = n - 1, then the average value of the sample variances from all the possible random samples will be ____ the population variance.​

False If the null hypothesis is true, the F-ratio will have a value near 1.00

If the null hypothesis is true, the F-ratio for ANOVA is expected (on average) to have a value of 0.

a. They do not exist because the same individuals participate in all of the treatments.

In an independent-measures ANOVA, individual differences contribute to the variance in the numerator and in the denominator of the F-ratio. For a repeated-measures ANoVA, what happens to the individual differences in the denominator of the F-ratio? a. They do not exist because the same individuals participate in all of the treatments. b. They are measured and subtracted out during the analysis. c. Individual differences contribute to the variance in the numerator. d. None of the other options accurately describes individual differences in the numerator.

If you just apply the z-formula and eyeball the scores, you will see that the z-score for all exams is equal to 1. Therefore, Sarah did equally well in all exams.

Last week Sarah had exams in Math, Spanish and English. On the Math exam, the mean was µ = 40 with σ = 5 and Sarah had a score of X = 45. On the Spanish exam, the mean was µ = 60 with s = 8 and Sarah had a score of X = 68. On the English exam, the mean was µ = 70 with s = 8 and Sarah had a score of X = 78. For which class should Sara expect the better grade?​

To answer this question you would need to find the z score for each exam. Math: (45-30)/5= 3 Spanish: (68-60)/8 = 1 English: (70-70)/8 = 0 You can see that the highest z-score is 3, which means that Sarah did the best in her Math exam relative to her classmates who took the exam. Her score was just slightly higher than average for Spanish, and she was just average for English.

Last week, Sarah had exams in Math, Spanish, and English. On the Math exam, the mean was µ = 30 with s = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was µ = 60 with s = 8 and Sarah had a score of X = 68. On the English exam, the mean was µ = 70 with s = 8 and Sarah had a score of X = 70. For which class should Sara expect the better grade?​

Independent measures design

Most research studies compare two (or more) sets of data Data from two completely different, independent participant groups (an independent-measures research design or between-subjects design) Data from the same or related participant group(s) (a within-subjects design or repeated-measures research design)

Because the score (44) is lower than the mean (52), you would want a standard deviation that is as large as possible to get a better position.

On an exam with μ = 52, you have a score of X = 44. Which of the following values for the standard deviation would give you the highest position in the class distribution?​

Because your score (56) is higher than the mean (52), you would want to get away from the rest of the class as far as possible so that you can be distinguished high performing outlier. In this case, you would want to have a standard deviation that is as small as possible

On an exam with μ = 52, you have a score of X = 56. Which of the following values for the standard deviation would give you the highest position in the class distribution?​

False Post hoc tests are needed only if you reject H0 (indicating that at least one mean difference is significant)

Posttests are needed if the decision from an analysis of variance is "fail to reject the null hypothesis."

False Measures of effect size are not influenced to any great extent by sample size

Sample size has a great influence on measures of effect size.

False The assumption requires equal population variances but the test is valid if sample variances are similar

The homogeneity assumption requires the two sample variances to be equal

The null hypothesis was rejected using a sample of n = 22.

The results of a hypothesis test are reported as follows: t(21) = 2.38, p < .05. What was the statistical decision and how big was the sample?

b. 13 df error = 24 = (k-1)(n-1) = (3-1)(13-1) (3-1=2; 2/24 = 12; 12+1=13)

The results of a repeated-measures ANOVA are reported as follows, F(2,24) = 1.12, p>.05. How many individuals participated in the study? a. 25 b. 13 c. 12 d. 7

The standard deviation is going to be smaller than the range of scores

The smallest score in a population is X = 5 and the largest score is X = 10. Based on this information, you can conclude that the____.​

The greater the variance, the more spread out the distribution is and the more difficult it is to tell true difference between two distributions. Therefore, you would want the variances to be small.

There is a six-point difference between two sample means. If the two samples have the same variance, then which of the following values for the variance would make the mean difference easiest to see in a graph showing the two distributions.​

b. When there are few participants available and individual differences are large.

Under what circumstances would a study using a repeated-measures ANOVA have a distinct advantage over a study using an independent-measures ANOVA? a. When there are many participants available and individual differences are large. b. When there are few participants available and individual differences are large. c. When there are man participants available and individual differences are small. d. When there are few participants available and individual differences are small.

The z-score specifies the position of a score above or below the mean in the distribution

What position in the distribution corresponds to a z-score of z = +2.00?

is flatter and more spread out than the normal z distribution

When n is small (less than 30), the t distribution _____.

False When the value of t is near 0, the difference between M and μ is also near 0

When the value of the t statistic is near 0, the null hypothesis should be rejected.

large mean differences and small sample variances

Which combination of factors is most likely to produce a large value for the F-ratio?

a large mean difference and small sample variances

Which combination of factors is most likely to produce a significant value for an independent-measures t statistic?

b. The first stage is identical to the independent-measures analysis and the second stage removes individual differences from the denominator of the F-ratio.

Which of the following accurately describes the two stages of a repeated-measures analysis of variance? a. The first stage is identical to the independent-measures analysis and the second stage removes individual differences from the numerator of the F-ratio. b. The first stage is identical to the independent-measures analysis and the second stage removes individual differences from the denominator of the F-ratio.

Deviation is just the difference between a score and the mean. It is the numerator part of the z-formula.

Which of the following represents the deviation score?​

The mean is represented by a z-score of zero. Therefore, the close a z-score is to zero, the closer it is to the mean.

Which of the following z-score values represents the location closest to the mean?​

Standard deviation refers to the average spread of the distribution. A distribution with a small range would have a small standard deviation

Which set of scores has the smallest standard deviation?​

Experiments often require multiple hypothesis tests—each with Type I error (alpha level) Type I error for a set of tests accumulates testwise alpha experimentwise alpha testwise alpha

Why use ANOVA (if t can compare two means)?

When your score is higher than the mean, you want to get as far as way from the middle group as possible so that you can be the high scoring outlier, a distinguishing high accomplisher. In this case, your score is 75 and the mean is 70. A SD of 5 would mean that you are just part of the 70% middle pack and there is nothing special about you. A SD of 1 means that you are five SDs above the mean, which makes you the top 1% of the population and you are indeed very special. Therefore, you would want the SD to be as small as possible in this case.

You have a score of X = 65 on a math exam. The mean score for the class on the exam is μ = 70. Which of the following values for the standard deviation would give you the most favorable position within the class?​

ANOVA

_________ evaluates all mean differences simultaneously with one test—regardless of the number of means—and thereby avoids the problem of an inflated experimentwise alpha

You might use Analysis of Variance (ANOVA) as a marketer when you want to test a particular hypothesis. You would use ANOVA to help you understand how your different groups respond, with a null hypothesis for the test that the means of the different groups are equal. The real advantage of using ANOVA over a t-test is the fact that it allows you analyse two or more samples or treatments. A t-test is appropriate if you have just one or two samples, but not more than two. The use of ANOVA allows researchers to compare many variables with much more flexibility.

what is ANOVA and why do we use it

The pooled variance is indicated by a horizontal line. The pooled variance appears to be an average of the three sample variances. The exact formulas and the data for this graph are explained in subsequent sections. Most students first encounter the pooled variance in a statistics course when learning about two-sample t tests.

what is pooled variance

independent: experimental design where different participants are used in each condition of the independent variable. dependent samples design leads to less error variance than independent samples design

what is the different between dependent measures design and independent measures design

To calculate Pearson correlation, raw observations are centered by subtracting their means and re-scaled by a measure of standard deviations: It's important to remember that Pearson correlation coefficient measures linear association between variables. Pearson Correlation Coefficient is the type of correlation coefficient which represents the relationship between the two variables, which are measured on the same interval or same ratio scale. (-1 to 1)

what is the pearson correlation? (dont compute)