Flashcards in midterm 2 Deck (76):
central limit theorem
is a factual statement about the distribution of means. It states: given a population with mean (u) and variance (02) the sampling distribution of the mean will have a mean equal to (u).
*That as n increases the shape of the sampling distribution approaches normal.
one sample t test
standard deviation (o) is not known.
type 1 error
z score, (+- 1.96) and .05 significance. The null is rejected at the .05 level of significance whenever z exceeded 1.96.
SPSS computes the exact probability of a type 1 error, represented in the p level.
t is defined as the difference between a sample mean and a population mean, divided by the standard error of the mean.
equality of variances, it is a test on our assumption of homogeneity of variance.
power is the probability of correctly rejecting a false H when a particular hypothesis is true.
power is a function of several variables
it is a function of alpha (the probability of type 1 error), the true alternative hypothesis, the sample size, and the particular test to be employed.
power is a function of alpha
If we increase alpha, the cut off point moves to the left, thus simultaneously decreasing beta, and increasing power. But this increases the chance of a type 1 error.
(d) small .20, medium .50, large .80
there is a 20% chance of a type 2 error. *to increase power, n has to increase
it is not a very good indicator of what will happen on the next experiment.
Correlation coefficient (r)
is simply a point between -1/1 and the closer it is to either of those limits the stronger the relationship between the variables.
When the sample is small, the sample correlation will be biased. To correct for it, the adjusted correlation coefficient is calculated.
*r squared is easier to interpret as a measure of correlation than is r because it represents the degree to which the variability in one measure is attributable to variability in the other measure.
For a significant value of F, we have rejected the null hypothesis that the treatment means in the population are equal. this conclusion indicates that at least one of the population means is different from at least one other mean, but we don't know which one.
*A significant F in an analysis of variance is simply an indication that not all the population means are equal.
analysis of variance assumptions
is based on the assumption of normality, and homogeneity of variance.
when members of a set of contrasts are independent of one another, they are called orthogonal contrasts, and the sums of squares of a complete set of orthogonal contrasts sum to SStreat.
Bonferroni t test
is based on what is known as the bonferroni inequality, which states that the probability of occurrence of one or more events can never exceed the sum of their individual probabilities.
The f ratio is determined
by dividing the mean square treatment (between group variance) by mean square error (within group variance)
If between group variance is large,
then we have observed possibly both large systematic variance and larger differences due to confounds
The larger the f ratio
the greater the chance that there are large systematic effects present
If the null hypothesis for an ANOVA is false than the f ratio
should be greater than 1.00
If in a between subjects ANOV, there are four groups with 15 participants in each group,
then the df for the F-ratio is equal to 3, 56.
If a researcher reported an F ratio with df = (2, 21) for a between-subjects one way ANOVA,
then there were 3 condition in the experiment and 24 total subjects
• If a between subjects one way ANOVA produces MS between = 25 and MS within = 5,
then the f ratio would be 25/5 = 5
• One advantage of a correlated-groups design
is that the effects of individual differences have been removed
• When we manipulate more than one independent variable in a study,
we are using a factorial design
• In a study examining the effects of time of day (morning, afternoon, evening) and teaching style (lecture only versus lecture with small group discussion) on student attentiveness, how many main effects are possible? –
2 (because there are two independent variables)
• In a study examining the effects of time of day (morning, afternoon, evening) and teaching style (lecture only versus lecture with small group discussion) on student attentiveness, how many interaction effects are possible?
– 1 because there is one dependent variable.
• In a study examining the effects of time of day (morning, afternoon, evening) and teaching style (lecture only versus lecture with small group discussion) on student attentiveness, the factorial notation would be?
• A 2*4*5*6 factorial design has
4 potential main effects
• An experiment with two independent variables each with three levels
is a 3*3 design
• If the lines in a graph are not parallel,
then there is most likely a(n) interaction effect
• When the effect of one independent variable depends on the level of the other independent variable,
we have observed a(n) interaction effect
• How many conditions would there be in a factorial design with three levels of Factor A and three levels of Factor B?
• In a study with two levels of Factor A, four levels of Factor B, and 5 participants in each condition, ***
the df error would be 32
o A (2-1 = 1)
o B (4-1 = 3)
o AB (1*3 = 3)
o Error (39-1-3-3 = 32)
o Total (2*4*5 = 40 – 1 = 39)
• In a study with two levels of Factor A, 4 levels of Factor B, and 5 participants in each condition, the dfs for factors A and B, respectively,
would be 1 and 3
two independent variables, which are called factors, for ex: age and recall condition. this experiment would be called- a two-way factorial design.
an experimental design in which every level of every factor is paired with every level of every other factor is called factorial design. It is a design that includes all combinations of the levels of the independent variables.
Factorial design advantages
1. greater generalizability.
2. interaction of variables
2 independent variables two-way factorial etc...
Eysenck's study had two levels of age, and five levels of condition.
it is a 2x5 factorial design.
SSa tells us how much the differences can be attributed to variable a. and SSb tells us the same about variable b. **Whatever cannot be attributed to age or condition must be attributable to the interaction of a and b: thus SSab.
SSerror= SStotal - (SSa+SSb+SSab)
ratio scale, weight....
degrees of freedom are used when the population standard deviation is unknown
A distribution of t-scores is symmetric with a mean of 0 but are generally not normal.
per comparison error rate is the probability of making a type 1 error on a single comparison assuming the null is true.
an independent sample t test measures the distance between means when two sets of scores are uncorrelated.
a correlation coefficient represents the degree of linear association between two quantitative variables.
when a regression line is correct the SSerror is smaller than that which you would obtain from another straight line
Correlation analysis is robust to the violation of the assumption of normality as long as the sample size is large.
when the sample is more than 30, you can violate the assumption of normality.
In ANOVA when F is greater than the critical value
we can reject the null hypothesis and conclude that not all group sample means are equal.
Anova is an omnibus test...
but we know there is variation somewhere, but we don't know where. That is why there is a post hoc test.
regression is the way of predicting one value from another.
when doing an orthogonal contrast and comparison the sum of weights should always be 0.
r squared represents the proportion of variance accounted for by the regression model.
In a two-way anova and interaction effect
means that one independent variable is modified by the levels of another variable.
in a one way anova 6 groups 10 participants, what is df within?
54, n-1 for each group.
used for more than two independent variables.
for pearson's r calculation, the assumption of normality is robust to violations if
the sample size is large.
the homoscedasity assumption for regression analysis assumes that
the residuals at each level of the predictor should have the same variance.
putting an innocent person behind bars is equivalent to
rejecting a true null hypothesis.
F ratio is always postive
homogeneity of variance
assumption: Degree of variability in the two populations are equivalent
Robustness: Robust to violations with equal sample size, and to moderate violations if the sample size is large
The grand mean is the mean of all observations across all groups.
It is impossible to obtain a negative value for an F-ratio.
We wish to test the hypothesis of no difference between the means of two dependent samples. There are 30 cases in the first sample, and 30 cases in the second. The number of degrees of freedom for this test will be
The data show no significant difference between the two treatments, t(10) = 1.65, p > .05." Based on this report, you can conclude that a total of ____ individuals participated in the research study.
11. this is known because df is in the brackets. so 10+1....
A researcher reports an F-ratio with df = 3, 36 from an independent-measures research study. Based on the df values, how many treatments were compared in the study and what was the total number of subjects participating in the study?
4 and 40. Add one for each group, and one to the total groups.
A researcher reports an F-ratio with df = 2, 36 for an independent-measures experiment. How many treatment conditions were compared in this experiment? a
F-ratio with df = 2, 36 for an independent-measures experiment. How many individual subjects participated in the experiment?
39, add three to 36, one for each group
Inferential statistics are primarily concerned with
a. making inferences about a population from a sample
If the correlation between X and Y is negative, the slope of the regression equation must be