Chapter 10 - Independent Samples t Test
paired
a logical value specifying that we want to compute a paired t test
var.equal
a logical variable indicating whether to treat the two variances as being equal. if TRUE then the pooled variance is used to estimate the variance otherwise the Welch test is used.
researchers need to be very cautious when interpreting null results because
it might occur due to a problem with the study's experimental procedure
the two-tailed research hypothesis states that the two means are
different
if the null hypothesis is false, the obtained t should be
far from 0
when you are doing a one-tailed t test, the critical region is always on the side of the t distribution that is predicted by the
research hypothesis
alternative
the alternative hypothesis. allowed value is one of "two.sided" (default), "greater" or "less".
when computing the standard error of the mean difference, the equation calls for using
the sample sizes from each group
independent t test degrees of freedom formula
(n1 - 1) + (n2 - 1)
conceptual formula for the independent samples t
(samples' mean difference - populations' mean difference expected if null is true) / (mean difference expected due to sampling error)
numeric vectors
(x,y)
an independent t test can be used to compare differences between people that
-are created by the researcher by providing different IV levels -already exist in different populations of people
in general, what are the two samples supposed to represent in an independent samples t test?
-one sample is intended to represent the control condition -another sample is intended to represent the experimental condition
the estimated standard error of the mean difference is
-used to find the critical value for the t test -an estimate of how different the two sample means are expected to be due to sampling error
which alpha value has a lower risk of making a type I error?
.01
which alpha value has a lower risk of making a type II error?
.05
if the null hypothesis is true, the obtained t should be
0
when computing the numerator of the independent samples t test, the population mean difference will always be
0
T/F: the standard error of the mean difference can never be negative
T
in most cases, what is the best assumption to have when calculating expected sampling error when doing an independent t test?
assuming equal variances
why will the population mean difference always be 0?
assuming the null hypothesis is true, it is very rare that a specific difference would not result in 0
based on the results of the Levene's test, you will
choose between the t test that assumes equal variance or the one that does not
what does computing the pooled variance assume?
homogeneity of variance
levene's test will help you determine
if the two conditions have similar variances or variances that are very different
when determining if an effect size is small, medium, or large, you should
ignore the size of the computed effect size and use its absolute value
the two-tailed null hypothesis states that the two means are
not different
what sign should you use for a two-tailed research hypothesis?
not equal
when writing your results, if you failed to reject the null hypothesis and your sample size was small, you should
point this out to the readers so that your report does not mislead them
the independent t test is a ratio of the difference between two sample means over an estimate of
sampling error
R syntax for single-sample t test and mean difference confidence interval
t.test(dataset, mu = populationmean, alternative = "two.sided")
R syntax for independent samples t test
t.test(x, y, alternative = "two.sided", var.equal = FALSE)
R syntax for related samples t test
t.test(x, y, paired = TRUE, alternative = "two.sided")
whenever you failed to reject the null hypothesis and yet the effect size is medium or large, you should conclude
that your sample size was too small and you should rerun the study with a larger sample size
how is the appropriate measurement of variables assumption met in an independent samples t statistic?
the IV defines two independent samples and the DV is measured on an interval/ratio scale
what is the objective of the independent samples t test?
to determine if the difference between the two sample means is likely or unlikely to be due to sampling error
the numerator of the independent samples t test is the difference between
two sample means
when should you use the independent samples t test?
when you need to compare two sample means that are unrelated
why is it best to pool variances if they are similar when computing sampling error?
you are using more data to estimate the populations' variances; makes your significance test more accurate
