BNAD 277 Concepts Exam 1
What word indicates a two-tailed test?
"differ"
How do you calculate expected frequencies for each cell in a contingency table?
(row total)(column total)/sample size
What are the assumptions for a one-way ANOVA test for testing c population means?
-population means are normally distributed -the population standard deviations are unknown but assumed equal -the samples are selected independently
What are the two ways that multinomial experiment hypothesis tests can be set up?
-set them all equal to each other (p1=p2=p3=p4=.25) -set them all to predetermined rate (p1=.4, p2=.3, p3=.2, p4=.1)
Multinomial experiments consist of a series of n independent trials such that:
-there are k possible outcomes called categories -the probability (pi) associated with the (ith) category remains the same -the sum of the probabilities is 1
The sum of expected "probabilities" in a G.O.F always equals?
1
How do you locate the chi-square values in the lower tail?
1- alpha
How do you find left tail values for F distribution?
1/ F(alpha, df2, df1)
How many qualitative variables are there in a test for independence?
2
ANOVA is used when at least how many populations are under consideration?
3
How many components make up the SST for a Two-Way ANOVA without interaction?
3 (SSA + SSB + SSE)
An ANOVA procedure is applied to data obtained from 5 samples where each sample contains 10 observations. The df's for the critical value of F are?
4, 45
Statistical inferences regarding variance are based on what distribution?
Chi-square
Typically Factor A refers to what in a Two-Way ANOVA?
Columns
ANOVA tests are based on what distribution?
F distribution
Testing for the difference of two population variances is based on what distribution?
F distribution
How does a G.O.F. and test for independence differ?
G.O.F examines a single qualitative variable, while a test for independence assesses the relationship between TWO qualitative variables
What is the alternate hypothesis for a goodness-of-fit test?
Ha: not all population proportions equal their hypothesized values
What is the hypothesis test for Jarque-Bera test?
Ho: S=0 AND K=0 Ha: S doesn't equal 0 OR K doesn't equal 0
What is the hypothesis test for two-way ANOVA with interaction?
Ho: There is no interaction between factors A and B Ha: There is interaction between factors A and B
What is the hypothesis test for a test for independence?
Ho: the two qualitative variables are independent Ha: the two qualitative variables are dependent (meaning there is a relationship to one another)
What is the null hypothesis to test whether or not there is a difference between treatments A, B, C, and D?
Ho: u1=u2=u3=u4 Ha: at least one of the hypothesized values differs
What is the hypothesis test for one-way ANOVA?
Ho: u1=u2=u3=u4=uc Ha: not all population means are equal
The trials in a multi-nomial experiment must be what?
Independent
Fisher's LSD vs Tukey's HSD
LSD type 1 error increases as number of comparisons increase, while HSD ensures the probability of type 1 error equals alpha by making each interval slightly wider than the Fisher counterpart
The Chi-squared distribution is derived from what distribution?
Normal Distribution
What is the alternate hypothesis for a Two-Way ANOVA without interaction?
Not all population means are equal... or "not so"
For a Chi-square test, what are the conditions for rejecting Ho based on p-value approach and critical value approach?
P < alpha test statistic > critical value
Chapter 11 is concerned with inferential statistics concerning what?
Population Variance
What do you find SST in two-way ANOVA with interaction?
SSA + SSB + SSAB + SSE
How do you find SST in two-way ANOVA without interaction?
SSA + SSB + SSE
How do you calculate MSA and MSB?
SSA/c-1 or SSB/r-1
What is the alternate hypothesis when using the F test statistic: MSAB/MSE?
There is interaction between factors A and B
What is different about the randomized block design for a two-way ANOVA without interaction and a two-way ANOVA with interaction?
a two-way ANOVA with interaction needs at least two observations for each combination of A and B
What is a requirements for a two-way ANOVA test?
all groups must have the same sample size
In a Chi-square distribution, the upper right tail contains ______.
alpha
In the F distribution, the upper (right) tail of the distribution is what?
alpha (like chi-square)
What does ANOVA stand for?
analysis of variance
How do you know if data is balanced or unbalanced?
balanced: n1=n2=nc unbalanced: ni does not equal nj
Treatments refers to ________, within refers to _________.
between, error
Tukey's method uses the studentized range of distribution, where the tails are _________ than those of the t distribution.
broader, flatter, and thicker
How can a left-tailed test easily be converted into a right-tailed test?
by interchanging the variances of the two populations
What does treatments identify in ANOVA?
c populations being examined
What is another name for a test for independence?
chi-square test of a contingency table
What table is used for G.O.F.?
chi-squared because it is right tailed
What is the shortcut to determine the df for a contingency table?
cross off one column and one row and count the boxes left
In inferential statistics, sample variance is an ______________ for population variance.
estimator (or point estimator)
In a goodness-of-fit test, we compare what kind of frequencies?
expected and observed
What does HSD stand for in Tukey's method?
honestly significant differences
What does the chi-square statistic measure in a G.O.F.?
how much the observed frequencies differ from the expected frequencies
What do the abbreviations in the test statistic for goodness-of-fit test stand for? (k, oi, ei)
k=categories oi=observed frequencies ei=expected frequencies
What do kurtosis and the skewness coefficient mean?
kurtosis measures whether a distribution is more or less peaked than a normal distribution skewness of zero indicated that the data is symmetric about its mean
What does LSD stand for in Fisher's method?
least significant difference
MSE stands for what?
mean square error
We prefer to use to ______ rather than the ________ to get a more accurate reflection of the typical income.
median, mean this is because data gets messed up when distributions are skewed
The sum of expected "frequencies" in a G.O.F. always equals?
n
As df increases, the Chi-square distribution becomes more like what?
normal distribution
What degrees of freedom does the F distribution depend on?
numerator and demoninator
What are the two independent estimates of the common population variance in an ANOVA test attributed to?
one estimate is attributed inherent differences between the c populations, and the other is attributed to chance
Why is the one-way ANOVA test better than using the two-sample t approach?
one-way ANOVA reduces type 1 error (incorrectly rejecting the null)
What is the difference between a one-way ANOVA and a two-way ANOVA?
one-way compares population means based on ONE categorical factor, two-way analyzes the effects of TWO factors simultaneously
What is the formula for pi, given ei and n?
pi= ei/n
What number do we place in the numerator of the F statistic and why?
place the larger sample variance in the numerator so that the value only focuses on the upper tail of the distribution
The ratio of the sample variance is a what for the ratio of the population variances?
point estimator
A one-way ANOVA compares what?
population MEANS based on one categorical variable or factor
What does a one-way ANOVA test compare?
population means based on ONE categorical variable or factor
All the values in the chi-square distribution are? (positive or negative)
positive
The F distribution is ______ skewed with values ranging from ____ to ____, but becomes increasingly _________ as both dfs increase.
positively, 0 to infinity, symmetric (just like chi-square distribution)
The Chi-squared distribution is _________ skewed, with the extent of skewness dependent on the _________.
positively, degrees of freedom
Tukey's HSD procedure uses what statistic?
q statistic from the studentized range distribution
If the difference between expression 1 and expression 2 is nonzero, then _________ Ho.
reject
If the confidence interval does not include "0" when the hypothesized value is "0", then what conclusion is reached?
reject Ho
The mean return evaluates ________ and the standard deviation assesses ______.
reward, risk
Where is all of the alpha found in a chi-square distribution?
right tail
ANOVA tests are always what kind of test?
right-tailed
What kind of test is a test for independence implemented as?
right-tailed test
G.O.F. are always implemented as __________ tests.
right-tailed. however, rejection of null doesn't indicate which proportions differ from these values
We use _______ as an estimator for the population mean, and ________ as an estimator for the population variance.
sample mean, sample variance
The formula for the confidence interval for the ratio of two population variances is valid if what?
sample variances are computed from independently drawn samples from two normally distributed populations
What is a contingency table?
shows frequencies for two qualitative variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values
What is the formula for SSA and SSB?
sum of (factor A or B means per column or row - grand mean)^2
How do you find the test statistic for a test for independence?
sum of all the (observed-expected)^2/expected
What does SSE mean?
sum of squares due to error, it provides a measure of the degree of variability that exists even if all population means are the same
What does a completely randomized design indicate?
that it is a one-way ANOVA
What is the purpose of Fisher's LSD and Tukey's HSD method?
the ANOVA test determines whether or not they differ but gives no insight on which ones differ, and these methods determine which means significantly differ from one another
What is the p-value?
the area under the curve beyond the calculated test statistic
How is df defined?
the number of squared standard normal random variables included in the summation
In general, what is the F distribution?
the probability distribution of the ratio of two independent chi-square variables, where each variable is divided by its own degree of freedom
In general, what is the Chi-square distribution?
the probability distribution of the sum of several independent squared standard normal random variables
How are the t distribution and chi-square distribution similar? What about the F distribution?
the t and chi-square distribution are each characterized by a family of distributions, and each distribution depends on their df. the F distribution is also characterized by a family of distributions, but each distribution depends on TWO degrees of freedom
Why would we use a two-way ANOVA test with interaction?
to capture the possible relationship between factors A and B
When do we use an ANOVA test?
to determine in differences exist between the means of three or more populations under independent settings
The ANOVA test is a generalization of what test?
two-sample t test with equal but unknown variances
What is the null hypothesis for a test concerning ratio of variances for a two-tailed, right-tailed, and left-tailed test?
two-tailed- Ho: ratio equals 1 right-tailed- Ho: ratio less than or equal to 1 left-tailed- Ho: ratio greater than or equal to 1
What is the null hypothesis for a test concerning variance for a two-tailed, right-tailed, and left-tailed test?
two-tailed- Ho: variance= hypothesized variance right-tailed- Ho: variance less than or equal to hypothesized variance left-tailed- Ho: variance greater than or equal to hypothesized variance
What is a randomized block design?
two-way ANOVA where table is laid out according to blocks (matched set of observations across the treatments)
Tukey's HSD method protects against an inflated risk of _______________.
type 1 error
What happens to type 1 error as we compare more means?
type 1 error becomes inflated
What is the meaning of between-treatments?
variability between sample means, denoted by MSTR
What does SSA mean?
variability between the levels of factor A in a two-way ANOVA
What is the meaning of within-treatments?
variability of data within each sample (variability due to chance), denoted by MSE
The population variance is used in quality-control studies to measure the variability of what?
weight, size, or volume of a product
What are between-treatments based on?
weighted sum of squared differences between the sample means and the overall mean of the data set (grand mean)
When does chi-square equal zero in G.O.F.?
when observed frequency equals its expected frequency
When can we use LSD or HSD?
when the ANOVA test rejects the null hypothesis of equal means
When can you reject the null hypothesis of equal means?
when the between-treatments are significantly greater than the within-treatments
When is the goodness-of-fit test valid?
when the expected frequencies for each category are five or more. combine categories if this requirement isn't satisfied
When is the test statistic for population variance valid?
when the population is normally distributed
When is the confidence interval for population variance valid?
when the random sample is drawn from a normally distributed population
What does G.O.F test determine?
whether two or more population proportions equal each other or any predetermined set of values
What is different between SSA and SSB for two-way ANOVA with/without interaction?
with interaction you multiply the formula for SSA and SSB by the number of observations per cell
What are the skewness and kurtosis coefficients equal to in a normal distribution?
zero
The values of the Chi-square distribution range from ___ to ____.
zero, infinity
