Chapter 8 and 9 Flashcards Preview

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Flashcards in Chapter 8 and 9 Deck (30):
1

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.

2

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.

3

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.

4

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.

5

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.

6

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.

7

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.

8

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.

9

What is the denominator?

> We calculate estimated standard error by dividing by
N - 1, rather than dividing by N, when calculating standard error.

10

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.

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.

12

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.

13

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.

14

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.

15

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.

16

When do we use a t distribution?

MASTERING THE CONCEPT
9.1: We use a t distribution instead of the z distribution when sampling requires us to estimate the population standard deviation from the sample standard deviation.

17

What are the z distribution formulae for confidence intervals?

MASTERING THE FORMULA
8-1: The formula for the lower bound of a confidence interval using a z distribution is
Mlower = −z(σM) + Msample

and the formula for the upper bound is

Mupper = z(σM) + Msample

The first symbol in each formula refers to the mean at that end of the confidence interval. To calculate each bound, we multiply the z statistic by the standard error, then add the sample mean. The z statistic for the lower bound is negative, and the z statistic for the upper bound is positive.

18

What is the formula for Cohen's d of a z statistic?

MASTERING THE FORMULA

8-2: The formula for Cohen’s d for a z statistic is: Cohen’s d = (M-μ) / σ

It is the same formula as for the z statistic, except we divide by the population standard deviation rather than by standard error.

19

What is the formula for degrees of freedom?

MASTERING THE FORMULA
9-4: The formula for degrees of freedom for a single-sample t test is: df = N - 1. To calculate degrees of freedom, we subtract 1 from the sample size.

20

What is the formula for Cohen's d of a t statistic?

MASTERING THE FORMULA
9-6: The formula for Cohen’s d for a t statistic is: Cohen’s d = (M-μ) / s
It is the same formula as for the t statistic, except that we divide by the population standard deviation (s) rather than by the population standard error (sM).

21

What is meta-analysis?

■■A meta-analysis is a study that involves the calculation of a mean effect size from the individual effect sizes of many studies.

22

What is a point estimate?

■■A point estimate is a summary statistic from a sample that is just one number used as an estimate of the population parameter.

23

What is a single-sample t test?

■■A single-sample t test is a hypothesis test in which we compare a sample from which
we collect data to a population for which we know the mean but not the standard deviation.

24

What are degrees of freedom?

■■Degrees of freedom is the number of scores that are free to vary when we estimate a population parameter from a sample.

25

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.

26

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.

27

What is Cohen's d?

■■Cohen’s d is a measure of effect size that assesses the difference between two means in terms of standard deviation, not standard error.

28

What is a dot plot?

■■The dot plot is a graph that displays all the data points in a sample, with the range of scores along the x-axis and a dot for each data point above the appropriate value.

29

What is a t statistic?

■■The t statistic indicates the distance of a sample mean from a population mean in terms of the estimated standard error.

30

What is an effect size?

8.3: Because a statistically significant effect might not be an important one, we should calculate effect size in addition to conducting a hypothesis test. We can then report whether a statistically significant effect is small, medium, or large.