Statistics Exam 2

Define standard error of the mean

(sigma m) Standard deviation of sampling distributions of means, which tells us the average difference between the sample mean (M) and the population mean (mu)

Name the steps for calculating statistical power

1) Calculate M associated with critical z-value (null distribution) 2) Calculate Z for that M based on treatment distribution you expect 3) Use unit normal table to determine area in the body of the curve

What are some disadvantages of a within-subjects design?

1) Carryover effect: response in second condition could be altered by some lingering effect of first treatment (Ex drug treatments, mood induction 2) Progressive error: performance changes consistently over time (Ex fatigue or learninf

Name two characteristics of sample mean distributions

1) Cluster around the population mean (the larger the sample the closer the cluster is) 2) Form a relatively normal distribution

What factors affect the width of a confidence interval?

1) Confidence level (higher confidence level leads to larger interval) 2) Sample size (larger sample size leads to smaller interval due to decrease in standard error as n increases)

Why is the central limit theorem so important?

1) It tells us the sample means are distributed normally, which allows us to "harness the power" of the normal curve 2) Basis for inferential statistics

What are same advantages of using a within-subjects design?

1) Reduces error by making groups more similar before experiment begins 2) Eliminates individual differences that exist in an independent measures design (smaller standard error) 3) Don't need as large of a sample size to get desired significant effect

What can affect the size of standard error?

1) Sample size (as sample size increases, sigma m decreases) 2) Standard error of the population (when n=1, sigma m is the same as the standard deviation)

What factors affect statistical power?

1) Size of treatment effect (larger treatment effect means greater power) 2) Alpha level (decreasing aloha decreases power) 3) Type of test (one-tailed tests have greater power because they functionally increase alpha) 4) Sample size (increasing sample size, increases power)

What three assumptions must be true to compute an independent measures t test?

1) The observations within 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

What two things can guarantee a sample mean distribution is normal?

1) population itself is normal 2) n>30 (regardless of population shape)

How is the t statistic different from the z-score?

1) t statistic uses sample variance, whereas z-score uses actual population variance 2) t distribution changes shape with degrees of freedom, whereas z-score distribution has same shape regardless of n

What does an r^2 value of 0.5 tell you?

50% of the variability in the dependent variable is accounted for by the treatment/independent variable

What is estimation thinking?

A proposed solution to problems with null hypothesis testing. Involves effect size and confidence intervals to determine how big an effect is. "To what extent..." versus "Does effect exist?"

What is an alpha level?

AKA significance level Cutoff for determining critical region where the probability that the null hypothesis is true if very low (default is alpha=5)

Why are sampling mean distributions helpful?

Allow us to compute the probability of obtaining a sample with a particular sample mean, but ONLY when distribution meets assumptions of normality!

What is sampling error?

Amount of error between sample statistic (like Xbar) and corresponding parameter (like mu)

How does the shape of the t distribution relate to degrees of freedom?

As df decreases, t distribution become flatter or more spread out. As sample size and df increase, the t distribution more closely resembles a normal distribution

Why do we report effect size?

Because determining the effect is significant tells us nothing about the size of the effect. Which means sample size can affect whether or not an effect is significant or not

Why must we compute pooled variance?

Because if we don't we treat samples with equal weight regardless of size, when variance from a larger sample better estimates than variance from a smaller sample

Explain what the sampling distribution of means is

Collection of sample means for all possible random samples of a given size (n) that can be obtained from a population

When calculating a t statistic, where does the mu value come from?

Could be any hypothesized value related to the research question (does NOT have to be known population mean)

How is the critical value of a one-tailed test different from that of a two-tailed test?

Critical value is lower for one-tailed, so you can reject the null with a lower z-score

What is a Type 2 error?

Failure to reject a false null hypothesis

State the central limit theorem

For any population with mean mu and standard deviation sigma, the distribution of sample means for sample size n will have mean mu and standard deviation (sigma/square root of n)

When reporting results of hypothesis testing in APA style, how do you write the p part?

If you *reject* the null, p <. 05 If you *fail to reject* the null, p >.05

When do you use a one-tailed (or directional) test?

If you have an idea about the direction of the effect, *before* you collect data

Why do we compute statistical power?

If you know the size of the effect, you can figure out how many people you need to run (n) to have a certain amount of power to detect it

When do you use a one-sample t test?

If you've selected a single sample and are testing whether it's sample mean differs from a hypothesized value

What is a matched pairs design?

Match participants on potential confounding variable at an individual level

What is a Type 1 error and what determines its risk?

Rejecting a true null hypothesis. *serious error because it results in falsely reporting a treatment effect Alpha level = probability of having a type 1 error

Describe the difference between standard error and standard deviation

Standard deviation measures the standard distance between a *score* and the population mean, whereas standard error measures the distance between a *sample mean* and the population mean

What are the units of a z-score for a sample mean?

Standard error units

Define the power of a hypothesis test

The probability that the test will correctly reject the null hypothesis

How could you determine whether the homogeneity of variance assumption is satisfied when computing an independent measures t test?

Use Hartley's F-max test (s^2 of largest over s^2 of smallest

How is calculating the sum of squares for a paired t test different from usual?

Uses difference scores rather than raw scores

Why do we use t statistics instead of just using z-scores all the time?

We don't always know the standard deviation of the population, so with t statistic we can substitute sample variance in when variance of population is unknown

When do you use an independent measures t test?

When there are different people in the conditions. *aka between-subjects design*

When do you use a paired t test?

When there are the same people in the conditions *aka within-subjects design or repeated-measures design*

What does a confidence interval of 95% tell you

You're 95% confident that the population mean will fall into the estimated range