t-tests 1

For independent-samples t-tests, in SPSS, the grouping variables are usually ____________ variables.

are usually discrete variables - meaning there are exactly two levels of the variable (pass/fail). Continuous variables can be used if divided into two levels.

What is the purpose of the independent t-test?

compare the means of two groups

The independent samples t-test

compares the means of two different samples that share some variable of interest in common, but there is no overlap between membership of the two groups.

For independent-samples t-tests, in SPSS, the test variables are _____________ variables.

continuous variables.

What are the assumptions of the independent t-test?

1. independence of observations 2. normal distribution of the DV for each level of the IV 3. homogeneity of variance

How do you assess normal distribution?

1. look at the histogram 2. skewness/std. error of skewness < 2

What t-test would be used for: Does a course offered to college seniors result in a GRE score greater or equal to 1200?

A one-sample t-test

What t-test would be used for: students' scores on the first quiz vs. the same students' scores on the second quiz?

A paired-samples t-test

t test formula

sample mean - pop mean/estimte SE

z test for hypothesis testing - single score

score - mean/ SD

The paired-samples t-test

t is based on groups of individuals who experience both conditions of the variables of interest.

What t-test would be used for: the difference between males and females on an exam score?

An independent samples t-test

What assumptions are made with a t-test?

Assumptions of normal distribution if a parametric tests is used. Otherwise a non parametric test should be used.

How do you assess independence of observations?

Check for an appropriate study design (random selection, random assignment)

What is the effect size commonly reported for t?

Cohen's d

The three different types of t-tests are ____________

Independent sample, paired-sample, and one-sample

Confidence Interval formula

Sample mean +- t (from table) x estimete SE

Estimate Standard Error formula

Sample standard deviation/ square root of number of scores

Calculated t score LARGER than score on table

Significant

Standard Error formula

Standard deviation of the population/ Square root of number of scores

What is the null hypothesis of the independent t-test?

There is no difference between the means of the groups.

Why would a one-sample t-test be used to test if a course offered to college seniors results in a GRE score greater or equal to 1200?

because the sample mean is compared to a single fixed value.

Small Confidence interval

high precision

The one-sample t-test

is designed to test whether the mean of a distribution differs significantly from some preset value.

The only computational value of a one-tailed and a two-tailed test of significance is

is that the p-value of a two-tailed is twice as much as the p-value of a one-tailed test of significance.

The t-value

is the difference between means divided by the standard error.

z test for hypothesis testing - mean scores

mean score - population mean / SE

How do you assess homogeneity of variance?

non-significant Levine's test

The f-value

of the two distributions differ significantly with each other.

When using t-tests

the one-tailed or two-tailed test of significant measures the probability associated with the difference between groups

A t-test compares samples means to see if _________________

to see if there is sufficient evidence to infer that the means of the corresponding population distributions also differ.

Two sample t-Test

unequal sample sizes - best way to compare 2 means. One dependent variable is involved Df = (n1 + n2 - 2)

ONE SAMPLE t test

one sample compared with a known population

t test stepS

1 Calculate mean & SD 2 calculate standard error - SD/ square root of number of scores 3 calculate t score - sample mean - pop mean/ estimated SE 4 - Work out df (N-1) and look up on table (0.05) - if calculated score is higher than score on table = SIGNIFICANT

What is the nonparametric equivalent of the independent t-test?

Mann-Whitney U

How do we choose the type of t-test?

Look at distribution. Look at data is the data paired (same group before and after) in which case use a paired t-test. Is it two group one on placebo the other on a drug in which case the independent sample t-test is used.

The Mann-Whitney U-test

The grouping variable is dichotomous. The measures of each value of the variable, which measure the characteristic of interest, constitute an independent random sample. The measurement scale of the variable, which measures the characteristic of interest, is at least ordinal. The total sample size is at least 8.

What variables are analysed with a t-test?

The t-test is of a categorical nature e.g. it compares people within two groups (medication A vs placebo, before or after intervention). The dependent variable is a continuous interval or ratio.

Research articles using t-Tests

Usefulness of aspirin therapy in high-risk pregnant women..

Paired t-Test

a group of individuals are measured at the beginning of a period of time and again later --- comparisons test t = (X1 - X2)/S.E...... S.E. = (Sd/n^.5) Df = n-1 (number of pairs) When? measure clinical outcome for a same group of study subjects who received one treatment vs. another OR measure a clinical outcome for a same group of treatment Advantages = minimize differences so that the differences between therapies can be evaluated - minimize background noise

Heteroschedasticity is the ____________ test.

f-value

Z-curve vs. t-curve

t-curve is wider and a little shorter than the normal distribution

Standard error

- The extend to which means of means (second in hierarchy) vary from the population mean - The standard deviation of the sample means

Interpreting t score

- calculate df - Look up df and .05 - if calculater t score is larger than score on table = Significant

Why would a paired-samples t-test be used for students' scores on the first quiz vs. the same students' scores on the second quiz?

A paired-samples t-test would be used for the same students' scores on the first quiz vs. the same students' scores on the second quiz because the same group experiences both levels of the variable.

How are t-tests interpreted?

For the t test a t statistics is found from a t table. To find the t statistics you need the degrees of freedom (for a t test the degrees of freedom are found from the sum of persons in both groups minus 2). The confidence interval for the means should not include 0 if the null hypothesis is rejected as we are testing the hypotheses of difference between means in the sample.

The independent t test

The grouping variable is dichotomous. The variable measuring the characteristic of interest is normally distributed and continuous. The measures of each value of the variable, which measures the characteristic of interest, constitute an in

When would you use a t-test?

The t-tests looks at the differences in two samples and examines their means relative to the spread or variablity of the scores. It is used when comparing within subjects (dependent sample) or between different subjects (independent sample).

Why would an independent samples t-test be used for the difference between males and females on an exam score?

because there is no overlapping membership between the "male" and "female" groups.

One sample t-Test

can be used to estimate population mean OR compare sample mean to expected population mean t = (X - u)/S.E. X = sample mean; S.E. = estimated standard error of the mean (s/n^.5); u = population mean

A t-test is a procedure used for ____________

used for comparing sample means.

t-Tables

used to adjust the z-values of a normal distribution to account for sample sizes