Chapter 9-11 Flashcards
When are t distributions used?
(a) when we don’t know the population sd and (b) when we compare two samples
Sample standard deviation
an estimation of the population standard deviation; the only practical different between the t test and z test
N-1
used in the sample sd to correct for the probability that it underestimates the population sd
t statistic
distance of a sample mean from a population mean in terms of the estimated standard error
single-sample t test
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
degrees of freedom
number of scores that are free to vary when we estimate a population parameter from a sample (i.e. can take on different values when a given parameter is known)
paired-samples t test
aka dependent-samples t test; used to compare two means for a within-groups design, a situation in which every participant is in both samples
replication
repetition of a study that gives us confidence that a particular observation is true
Independent-samples or between-groups t test
used to compare two means for a between-groups design, wherein each participant is assigned to only one condition
Pooled variance
a weighted average of the two estimates of variance, one from each sample in an independent-samples t test
Error bars
vertical lines added to bars or dots on a graph that represent the variability of those data and give us a sense of how precise an estimate summary statistic is
inflating alpha
the probability of a type I error increases as the number of samples increases and the number of statistical comparisons increases
What do the z, t, and f distributions have in common?
They all rely on the characteristics of the normal bell-shaped curve; f distributions are just more conservative and versatile versions of t and z distributions
Analysis of variance (ANOVA)
a hypothesis test typically used with one or more nominal, sometimes ordinal, independent variables with three groups overall and a scale dependent variable
F statistic
a ratio of two measures of variance (1) between-groups variance or the difference between sample means and (2) within-groups variance or the average of sample variances
Between-groups variance
an estimate of the population variance, based on the differences among the means
Within-groups variance
an estimate of the population variance, based on the differences within each of the three or more sample distributions; the difference between means we’d expect by chance
one-way ANOVA
a hypothesis test that includes both one nominal independent variable with more than two levels and a scale dependent variable
between-groups ANOVA
a hypothesis test in which there are more than two samples, and each sample is composed of different participants
within-groups or repeated-measures ANOVA
a hypothesis test wherein there are more than two samples, and each sample is composed of the same participants
Three assumptions for ANOVA
(1) Random selection is necessary if we want to generalize beyond a sample (2) A normally distributed population allows us to examine the distributions of the samples to get a sense of what the underlying population distribution might look like (3) Homoscedasticity assumes that the samples all come from populations with the same variance
Homoscedastic populations
those that have the same variance
Heteroscedastic populations
those that have different variances
Source table
presents the important calculations and final results of an ANOVA in a consistent and easy-to-read format
MS
the conventional symbol for variance in ANOVA; stands for means square because variance is the arithmetic mean of squared deviations for between-groups variance and within-groups variance
Grand mean
mean of every score in a study, regardless of which sample the score came from
What are the three sums of squares of ANOVA?
SSbetween, SSwithin, SStotal
R^2
an estimate of the proportion of variance in the dependent variable that is accounted for by the independent variable
Omega squared
less biased estimate of effect size for ANOVA; an attempt at correcting the bias of R^2
Post hoc test
a statistical procedure frequently carried out after the null hypothesis has been rejected in an analysis of variance; allows us to make multiple comparisons among means
Tukey HSD test or q test
a widely used post hoc test that determines the differences between means in terms of standard error; allows us to make comparisons to identify differences that are “honestly” there
