Independent Samples & Paired Samples t-tests

Use the ________________________ of the t-statistic and the degrees of freedom, to refer to a t-table and find whether the ratio is significant.

absolute value

Related-samples design:

Dependent samples don't have to be scores from same individuals, but they must somehow be related, e.g., marriage partners, best friends. Samples are dependent because 1st man is married to 1st woman and ith man is married to ith woman.

Step 5: _________________________

make a decision about the hypotheses. Will we reject or fail to reject the null hypothesis?

The larger the observed difference between our two means, the greater _______________________________.

our confidence that the null hypothesis be rejected

The t-test can be applied to answer each research question when the independent variable is _____________________ with only two groups and the dependent variable is continuous.

dichotomous

A (-) in front of your t-value indicates _________________________.

direction, NOT a negative value

We look at the difference between the sample statistic and the population parameter and _________________________.

divide by the estimated standard error (standard deviation of the sampling distribution)

Step 3: ________________________ It is almost impossible to study the full population. Thus, we use a sample's result as a basis for making our inference about the population parameter. i.e., We take two random samples of 50 rats each who are either injected with the drug or with a placebo, and their response time is measured. The mean (M1) response time is 1.05 for rats (n1 = 50) injected with the drug. The SD is 0.5 The mean (M2) response time is 1.2 seconds for rats (n2 = 50) injected with the placebo. The SD is 0.7

drawing the sample

When group sizes are NOT equal (but the assumption of normality is met) one should use the _______________________ column.

equal variances not assumed

Because the mean differences between the two samples could be based on _______________, we need to estimate the chances that a difference between means could be due to random error.

error

Paired (Dependent) Samples t-tests: _____________________

half of the scores are dependent on the other half That is, members of one group are statistically related to members of the other group, e.g., wife's drinking may be dependent on husband's drinking.

The t-statistic tells us ___________________________________.

whether our obtained result is an unlikely one to be obtained in random sampling from a population in which the null is true

repeated measures t-statistic compares ___________________________.

1 sample measured on 2 occasions

independent samples t-statistic compares _______________________.

2 independent samples

The one-sample t-test addresses the question:

Is the population mean (on the variable we are studying) = <specified value>. The null hypothesis is that the population mean = <specified value>.

The test used to check for normality is the ______________________________.

K-S test

Dependent Samples t-test: Step 5:

Make a decision. Will we reject or fail to reject the null hypothesis?

3 Paired Samples Designs:

Pretest-Posttest Related-Samples Matched Pairs

The Paired Samples t-test is often used in a ________________________.

Repeated Measures or Within-Subjects design

Pretest-Posttest design:

Same individuals measured twice. The ith score in 2nd sample depends on ith score in 1st sample.

Dependent Samples t-test: Step 2:

Set the criterion One-tailed or two-tailed test? α = ? Df = n-1 Critical value for t = ?

Dependent Samples t-test: Step 1:

State the hypotheses (Define the problem) i.e., Motor and cognitive skills are unaffected by alcohol There is no difference between the two matched/paired/dependent samples on number of cones hit. H0: μD = 0 H1: μD ≠ 0

Dependent Samples t-test: A Difference Score (D) is calculated between subjects' scores. It is computed as _________________________________.

X2-X1, where X2 is the subjects' score after the treatment and X1 is the subjects' score before treatment. We use the same sample of difference scores to estimate the population of difference scores (μD).

The generic formula for these inferential statistics is:

Z or t = (sample statistic - population parameter)/standard error

Four inferential statistics:

Z-score statistic One-sample t-statistic Independent samples t-statistic Dependent samples t-statistic

z-score statistic compares ___________________________.

a sample to a population when the population σ is known

t-statistic compares ________________________.

a sample to a population when the population σ is unknown

It is almost impossible for us to study the full population of interest. Thus, we use _________________________.

a sample's result as a basis for making our inference about the population parameter

Independent Samples t-tests: _______________________

all scores are unrelated

We have to estimate the standard error using the sample standard deviation or variance. If there are 2 samples, we must _______________ the two sample variances.

average

In an independent samples t-test, we are interested in the difference between two independent groups. As such, we are ______________________________.

comparing two populations by evaluating the mean difference

Step 4: ____________________________ For the independent samples t-test: t = (X1-X2)-(μ1 - μ2)/S x1-x2 S x1-x2 = sq. root of (S2 pooled/n1 + S2 pooled/n2) Degrees of freedom (df) for the Independent t statistic = n1 + n2 - 2 (or df 1 +df 2)

compute the t-statistic

Paired Samples t-test: We are not looking at just one score, we are looking at one score's RELATION to another score. Therefore, __________________________.

each score MUST remain with it's own pair

If the samples comes from the same population, we expect the means to be roughly _________________.

equal

The reason for hypothesis testing is to _____________________________.

gain knowledge about an unknown population

In order to compare the difference between means to the standard error of the difference, we find out ____________________________.

how far apart (in terms of the standard error of the difference) are the two group means

We must be conservative when using data based on small sample sizes because with small samples, a difference between means of more than two standard errors of the difference may _________________________________.

not be statistically significant (whereas it might be with a larger sample)

If neither assumption (normality and equal variance) is met, one must ___________________________.

not use the independent samples t-test

Paired (Dependent) Samples t-tests can only be used with _____________________.

one DV (continuous) and one IV with two levels

The Paired Samples t-test uses the ______________________________.

same sample of subjects measured on two different occasions

The __________________________ is one where one IV is manipulated in only two ways (i.e., 2 conditions), and only one DV (outcome ) is measured.

simplest form of experimentation

The t-ratio =

the difference between means divided by the standard error of the difference (OR otherwise stated the difference between the means divided by an index of random error).

Estimated Standard Error of the Difference gives us the _____________________ involved in using 2 sample means to estimate 2 population means.

total amount of error

An independent samples t-test must have ________________________ that is continuous to compare them on.

two independent groups (i.e. samples) and one dependent variable

Dependent Samples t-test Assumptions:

- Independent observations (i.e., no practice effects) - Normal distribution

Assumptions of the Independent Samples t-test:

- Participants in the two groups are randomly assigned and independent of one another. - Data are at the interval level of measurement - The dependent variable is normally distributed

Reporting Results:

- State the type of test you used and what you were evaluating. = State whether or not the test was significant and include your t, df, and p values. = State your results for both levels of your IV and include mean and standard deviation for each.

Dependent Samples t-test: Step 4:

Calculate the t-statistic

Dependent Samples t-test: Step 3:

Collect sample data, calculate D (X2-X1) Once the difference score is obtained, all further computations are done on D.

The t-test statistic is _____________________________.

Group 1 Mean - Group 2 Mean/Standard Error of the Difference

When comparing two groups, use _________________________ as the measure of degrees of freedom.

N-2 (or n1 + n2 - 2)

Matched pairs design:

Participants measured on same variable and then subjects with most similar scores are paired off: highest score with 2nd highest, 3rd highest with 4th highest, and so on. By random decision, one of each pair assigned to 1st group and the other to the 2nd group. Used to "control" for an extraneous variable by spreading a characteristic equally among groups. For example, reading ability controlled when studying GRE effects.

Comparing maze-running abilities of rats raised in normal conditions and in deprived conditions is known as _________________________________.

an independent sample design

We perform ____________________________ to determine if there is a significant difference in hourly wage ('hourwage') between positions (hospital nurses and office nurses).

an independent-sample t-test

The Estimated Standard Error of the Differences tells us the _______________________ between the sample difference (x1-x2) and the population difference (µ1-µ2).

average distance

When n1 = n2 [equal sample sizes], the violation of this assumption has been shown to be unimportant (Zimmerman, 2004), and one can use the ____________________ column.

equal variances assumed

Step 2: ___________________________ We set an alpha level. Let alpha = .05 Say n=50. Calculate the df. Df = n1 + n2 - 2 = 98 Look up the critical value that would be needed to accept/reject the null hypothesis. Table value of t at df = 98, alpha = .05 is t = 1.96.

establishing the criterion that will determine whether our result is an unlikely one

The Paired Samples t-test is used when we are interested in finding out ____________________________________.

how much difference exists between subjects' scores before the treatment and after the treatment

If we could collect an infinite number of samples from both populations and we computed the ___________________________ in each sample, we would find that the mean of the sampling distribution of mean differences would be zero.

mean difference

With large enough samples - the distribution of the difference between means would be ____________________________.

normally distributed

Independent samples t-test is applied when we have two independent samples and want to make a comparison between two groups of individuals. The _________________________ are unknown.

population parameters

In order to evaluate the mean difference between two populations, we ______________________________.

sample from each population and compare the sample means on a given variable

The standard unit of variability for the distribution of the differences between means is NOT the ________________________. Instead, it is the standard error of the difference between means.

standard deviation or the standard error

We compare the difference between our two sample means to what we would expect to obtain if the null hypothesis were true, using the ________________________ as a gauge of the variability between means.

standard error

The standard error of the difference between means - measures TWO unstable estimates - therefore it is larger than the _______________________________.

standard error of a single mean

Step 1: ____________________________ The independent samples t-test addresses the question: Do the two groups in our sample come from the same population? i.e., they have the same population mean. H0: μ1 - μ2 = 0 H1: ?

state the hypotheses

Use a __________________________ to figure out how likely it is that two means could differ by that many standard errors of the difference.

t-distribution

Looking at the different between the sample statistic and the population parameter gives us a ____________________________.

t-statistic that can be looked up under a t probability distribution.

Paired (Dependent) Samples t-tests determines the likelihood that ______________________________.

the differences found between groups are true differences or are due to chance

Research question: Do women lose more weight than men on a special low-fat diet? Alternative hypothesis:

the means for weight loss will be significantly different for men and women

Research question: Do women lose more weight than men on a special low-fat diet? Null hypothesis:

the samples come from the same population, and we expect the means to be roughly equal

Random assignment and independence are important because _____________________________.

the t-statistic is estimating random error

If the t statistic you calculated is greater than the one indicated in the table, then your results are statistically significant at the .05 level, which indicates that ___________________________, and you can be reasonably sure that there is a difference between the two groups.

there is less than a 5% chance that the difference between your groups is solely due to chance

A significance test allows us to make an inference about the ____________________________. The inference is based on the value of the corresponding sample statistic.

value of a population parameter

Data need to be at the interval level of measurement because _____________________________.

we are calculating means

In order to check that the DV is normally distributed, _________________________________.

we examine skewness and kurtosis (peak) of distribution.

Pooled Variance is the average of the two sample variances, allowing the larger sample to be ___________________________.

weighted more heavily