Chapter 8 & 9- t tests (One sample, Independent Measures Design)

Question 1

estimated standard error

Answer 1

an estimate of the standard deviation of a sampling distribution of sample means selected from a population with an unknown variance. It is an estimate of the standard error or standard distance that sample means deviate from the value of the population mean stated in the null hypothesis.

Question 2

t statistic, known as t observed or t obtained

Answer 2

an inferential statistic used to determine the number of standard deviations in a t distribution that a sample mean deviates from the mean value or mean difference stated in the null hypothesis.

Question 3

t distribution, or Student’s t,

Answer 3

a normal-like distribution with greater variability in the tails than a normal distribution because the sample variance is substituted for the population variance to estimate the standard error in this distribution.

Question 4

degrees of freedom (df)

Answer 4

for a t distribution are equal to the degrees of freedom for sample variance for a given sample: n − 1. Each t distribution is associated with specified degrees of freedom; as sample size increases, the degrees of freedom also increase.

Question 5

one-sample t test

Answer 5

a statistical procedure used to compare a mean value measured in a sample to a known value in the population. It is specifically used to test hypotheses concerning the mean in a single population with an unknown variance.

Question 6

estimated Cohen’s d

Answer 6

a measure of effect size in terms of the number of standard deviations that mean scores shift above or below the population mean stated by the null hypothesis. The larger the value of estimated Cohen’s d, the larger the effect in the population.

Question 7

proportion of variance

Answer 7

a measure of effect size in terms of the proportion or percent of variability in a dependent variable that can be explained or accounted for by a treatment.

Question 8

treatment

Answer 8

In hypothesis testing, a treatment is any unique characteristic of a sample or any unique way that a researcher treats a sample.

Question 9

Estimation

Answer 9

a statistical procedure in which a sample statistic is used to estimate the value of an unknown population parameter. Two types of estimation are point estimation and interval estimation.

Question 10

point estimate

Answer 10

the use of a sample statistic (e.g., a sample mean) to estimate the value of a population parameter (e.g., a population mean).

Question 11

interval estimate

Answer 11

often reported as a confidence interval, is an interval or range of possible values within which a population parameter is likely to be contained.

Question 12

Level of confidence

Answer 12

the probability or likelihood that an interval estimate will contain an unknown population parameter (e.g., a population mean).

Question 13

between-subjects design

Answer 13

a research design in which different participants are observed one time in each group or at each level of one factor.

Question 14

independent sample

Answer 14

a type of sample in which different participants are independently observed one time in each group.

Question 15

two-independent-sample t test

Answer 15

a statistical procedure used to compare the mean difference between two independent groups. This test is specifically used to test hypotheses concerning the difference between two population means, where the variance in one or both populations is unknown.

Question 16

estimated standard error for the difference

Answer 16

an estimate of the standard deviation of a sampling distribution of mean differences between two sample means. It is an estimate of the standard error or standard distance that mean differences can be expected to deviate from the mean difference stated in the null hypothesis.

Question 17

pooled sample variance

Answer 17

the mean sample variance of two samples. When the sample size is unequal, the variance in each group or sample is weighted by its respective degrees of freedom.

Question 18

pooled sample standard deviation

Answer 18

(√ s 2/p)
is the combined sample standard deviation of two groups or samples. It is computed by taking the square root of the pooled sample variance. This measure estimates the standard deviation for the difference between two population means.

Question 19

Eta-Squared (η2)

Answer 19

Eta-squared is a measure of proportion of variance that can be expressed in a single formula based on the result of a t test:

n²= t²/( t²+df)

Question 20

Omega-Squared (ω2)

Answer 20

Omega-squared is also the variability explained by a treatment, divided by the total variability observed. The change in the formula of proportion of variance is that 1 is subtracted from t2 in the numerator:

w2= t²-1 / (t²+df)

Subtracting 1 in the numerator reduces the estimate of effect size. Hence, omega-squared will always give a smaller or more conservative estimate of effect size, making it less biased than eta-squared

Question 21

Effect Size compared

Answer 21

Description of Effect

d

η2

ω2

Trivial

—

η2 < .01

ω2 < .01

Small

d < 0.2

.01 < η2 < .09

.01 < ω2 < .09

Medium

0.2 < d < 0.8

.10 < η2 < .25

.10 < ω2 < .25

Large

d > 0.8

η2 > .25

ω2 > .25

Question 22

INFERRING SIGNIFICANCE AND EFFECT SIZE FROM A CONFIDENCE INTERVAL

Answer 22

If the value stated by a null hypothesis is inside a confidence interval, the decision is to retain the null hypothesis (not significant).

If the value stated by a null hypothesis is outside the confidence interval, the decision is to reject the null hypothesis (significant).

Question 23

For a two-independent-sample t test concerning two population means, we make four assumptions:

Answer 23

Normality. We assume that data in each population being sampled are normally distributed. This assumption is particularly important for small samples because the standard error is typically much larger. In larger sample sizes (n > 30), the standard error is smaller, and this assumption becomes less critical as a result.

Random sampling. We assume that the data we measure were obtained from samples that were selected using a random sampling procedure. It is generally considered inappropriate to conduct hypothesis tests with nonrandom samples.

Independence. We assume that each measured outcome or observation is independent, meaning that one outcome does not influence another. Specifically, outcomes are independent when the probability of one outcome has no effect on the probability of another outcome. Using random sampling usually satisfies this assumption.

Equal variances. We assume that the variances in each population are equal to each other. This assumption is usually satisfied when the larger sample variance is not greater than two times the smaller

Question 24

What are the three steps to compute an estimation formula?

Answer 24

Step 1: Compute the sample mean and standard error. Step 2: Choose the level of confidence and find the critical values at that level of confidence. Step 3: Compute the estimation formula to find the confidence limits.