Chapter 8 and 9 Flashcards
What is an interval estimate?
■■An interval estimate is based on a sample statistic and provides a range of plausible values for the population parameter.
What is a confidence interval?
■■A confidence interval is an interval estimate based on the sample statistic; it includes the population mean a certain percentage of the time if we sample from the same population repeatedly.
What is a Point Estimate?
8.1: We can use a sample to calculate a point estimate — one plausible number, such as a mean — for the population. More realistically, we also can use a sample to calculate an interval estimate — a range of plausible numbers, such as a range of means — for the population.
What is the formula for estimating the standard deviation of a sample?
9-1: The formula for standard deviation when estimating from a sample is: s = √∑ (X-M)2 / (N-1) We subtract 1 from the sample size in the denominator to correct for the probability that the sample standard deviation slightly underestimates the actual standard deviation in the population.
What is Statistical power
8.4: Statistical power is the likelihood of rejecting the null hypothesis when we should reject the null hypothesis. Researchers consider a probability of 0.80—an 80% chance of rejecting the null hypothesis if we should reject it—to be the minimum for conducting a study.
When do we use t distributions?
> We use t distributions when we do not know the population standard deviation and are comparing only two groups.
What two groups can we use t distributions on?
> The two groups may be a sample and a population, or two samples as part of a within groups design or a between-groups design.
Is the formula for a single-sample t test the same as a z statistic?
> The formula for the t statistic for a single-sample t test is the same as the formula for the z statistic for a distribution of means, except that we use estimated standard error in the denominator rather than the actual standard error for the population.
What is the denominator?
> We calculate estimated standard error by dividing by
N - 1, rather than dividing by N, when calculating standard error.
What are degrees of Freedom?
MASTERING THE CONCEPT
9.2: Degrees of freedom refers to the number of scores that can take on different values when a given parameter is known. For example, if we know that the mean of three scores is 10, only two scores are free to vary. Once we know the values of two scores, we know the value of the third. If we know that two of the scores are 9 and 10, then we know that the third must be 11.
What are the formulae for confidence intervals?
MASTERING THE FORMULA
9-5: The formula for the lower bound of a confidence interval for a single-sample t test is
Mlower = -t(sM) + Msample
The formula for the upper bound of a confidence interval for a single-sample t test is
Mupper = t(sM) + Msample
The only differences from those for a z test are that in each formula z is replaced by t, and M is replaced by sM.
What is the formula for estimated standard error from a sample?
MASTERING THE FORMULA
9-2: The formula for standard error when we estimate from a sample is: sM = s / √N. It only differs from the formula for standard error we learned previously in that we use s instead of because we’re working from a sample instead of a population.
What happens when sample size increases?
MASTERING THE CONCEPT
8.2: As sample size increases, so does the test statistic (if all else stays the same). Because of this, a small difference might not be statistically significant with a small sample but might be statistically significant with a large sample.
What happens to the t distribution as sample size increases?
MASTERING THE CONCEPT
9.3: As sample size increases, the t distributions more and more closely approximate the z distribution. You can think of the z statistic as a single-blade Swiss Army knife and the t statistic as a multi-blade Swiss Army knife that includes the single blade that is the z statistic.
What are the APA requirements for conducting a hypothesis test?
MASTERING THE CONCEPT
9.4: Whenever researchers conduct a hypothesis test, the APA encourages that, if possible, they also calculate a confidence interval and an effect size.
