DSOM 309 Test 1
Identify the formula used to construct a 100% confidence interval for ratio of pop variances
([s/s] 1/fa/2 ; [s/s] fa/2)
Degrees of Freedom for a CONTIGENCY TABLE is calculated as
(r-1)(c-1) 3 rows 2 columns (3-1)(2-1) = 2
the area to the left of X²a,df value is
1-a
what do we do to find F1-a and why
1/Fa(df2,df1) easier
in a 2-way ANOVA without interaction there are ___ null hypotheses tested
2
in a 2-way ANOVA with interaction there are ____ null hypotheses tested
3
Statistical inference concerning POPULATION VARIANCE is based on
Chi-Square
if two independent samples are drawn from normal populations, then teh value of the test statistic S^21/S^22 follows the
F df1,df2 Distribution
MSB/MSE
F test stat for 2 way anova
A one-way anova test is based on
Fdf1,df2 distribution
the null and alternative hypotheses for a right tailed test concerning pop variance are
Ho: @²≤@²o ; Ha:@²>@²o
null and alternate for Test of Independence
Ho: Are independent Ha: Are dependent
The null and alternative hypotheses for a GOODNESS OF FIT TEST are
Ho: Data are normal Ha: Data are not normal
what are the hypothesis of a one-way ANOVA
Ho: mean = mean = mean Ha: not all means are equal
in a two-way anova the F test statistic that determines whether differences exist between factor A means is calculated as
MSA/MSE
in two-way anova F test stat for Factor A =
MSA/MSE
The GOODNESS OF FIT test for normality is which tailed test
Right Tailed Test
SST in a 2-way ANOVA is equal to
SSA + SSB + SSE
error sum of squares
SSE weighted sum of sample variances of each trements
MSE =
SSE/(nT-c)
one-way ANOVA MSTR =
SSTR/(c-1)
in a two-way ANOVA test, SST for factor B is based on
Sum of squared differences BETWEEN the mean for each level of factor B and the GRAND MEAN
Properties of Estimators
Unbiasedness Efficiency Consistency
The null hypothesis for Jarque-Bera is a joint hypothesis that the Skewness Coeffiecient (S) and the Kurtosis Coefficient (K) are equal to
Zero
a kurtosis coefficient of ZERO means that the distribution is
as peaked as the normal distribution
confidence interval is based on
chi-square distribution
a test of independence is also called a
chi-square test of a contingency table
thhe chi-square distribution tends to the normal distribution as the
degrees of freedom gets larger
in two-way ANOVA the F test statistic for FACTOR B
determines whether significant differences exist between factor b means calculated as: MSB/MSE
ANOVA is used to determine if
differences exist between the means of 3 or more populations
X²df has the following characteristics
distribution is positively skewed distribution range from zero to infinity shapes depend on degrees of freedom
in a two tailed test if the p-value for the hypothesis test is GREATER THAN the chosen level of signicance then
do not reject Ho: population variance does not differ from Ho value since p - value = .068 > .05 = a do not reject
In a MULTINOMIAL EXPERIMENT with null Ho:p1=p2=p3=p4= .25 Value of the TEST STAT is X²₃=3.45 at the a = .05 the CRITICAL VALUE is X²₀.₀₅,₃ = 7.815 the decision rule is
do not reject Ho; cannot conclude populations differ from .25 since Test < Critical Value do not reject
In a TEST OF INDEPENDENCE if the test statistic is LESS THAN the Critical value we X²₁<X²₀.₀₅,1
do not reject Ho; cannot conclude that___ and ___ are dependent
GOODNESS OF FIT TEST for normality with a null Ho: data is normal with µ=10 and @=2 Test Statistic is 4.34 p-value is 0.1143 at the a = .05 the decision is
do not reject Ho; conclude that does follow normal distribution since the p-value = 0.1142 > .05
in ANOVA testing, if the ratio of between-treatment variability to within-treatment is significantly GREATER THAN 1
if between/within is >>>> 1 reject Ho: conclude that not all means are equal
the width of the interval
increases with the confidence level
in order to express the competing hypotheses for a GOODNESS-OF-FIT test for normality we specify the populations
mean standard deviation
when doing F distribution place the larger sample variance in the
numerator
TEST OF INDEPENDENCE compares each cells
observed frequency with expected frequency
assumptions for performing a ONE-way ANOVA
populations are normally distributed populations standard deviations are UNKNOWN but presumed equal the samples are selected independently
what skew is the chi-square distribution
positively
In a right tailed test if the test statistic is greater than the critical value
reject Ho test > crit reject and conclude that pop variance is greater than
If the hypothesized value of pop variance (@²=10) is not included in the confidence interval ([15,20]), we
reject Ho and concluded that pop variance differs
TEST OF INDEPENDENCE if the p-value is LESS THAN the a value
reject Ho: conclude are dependent reject and conclude
In a TEST OF INDEPENDENCE if the test statistic is X²₁ (5.75) GREATER THAN the critical value X²₀.₀₅,₁(3.41) then the decision is
reject Ho: conclude that ___ and ___ are DEPENDENT since X²₁ = 5.75 > 3.851 = X²₀.₀₅,₁ reject , dependent
in an ANOVA table if the p-value is LESS THAN the significance value (a) then
reject Ho: conclude that some means differ
In a two tailed test if the p-value is LESS THAN the significance value (a) then:
reject Ho: population variance differs since p-value = .027 < .05 = a we reject Ho conclude they do differ
for a X²df distributed random variable, the notation X²a,df represents a value such that the area in the
right taile of distribution is a
one-way anova is always which tail
right tailed
when conducting hypothesis test with pop variance the TEST STATISTIC depends on
sample size hypothesized value of pop variance sample variance X²df = (n-1)s²/@₂ = Test Statistic for population variance
the estimator of population variance is
sample variance or S²
a is the
signifacant value percentage
The Jarque-Bera TEST STATISTIC depends on the
skewness coefficient (S) Kurtosis Coefficient (K) Sample Size
in a two-way anova what is used to calculate sst
ssa + ssb + ssab + sse
in a ANOVA test GRAND MEAN is calculated as
sum of all observations divided by total # of observations
in ONE-way ANOVA SSTR =
sum of weighted squared differences between the samples mean and grand mean
a skewness coefficient of ZERO means that the data are
symetric about the mean
The chi-square test of contingency table is valid when
the expected cell frequencies are: at least five ≥5
the chi-square test of a CONTINGENCY TABLE is a test of independence for
two Qualitative variables
a 2-way ANOVA examines the effect of
two factors on the population mean
a one-way anova test helps reduce the risk of what type of error
type 1 error
in a one-way ANOVA within-treatments variability is based on the
variability within each sample a weighted sum of sample variances of each treatment
randomized block with NO interaction if the p-value is less than the a value then
we cannot conclude that the row means differ
in a randomized block experiment if the p-value is LESS THAN the significance level (a) then
we cannot conlude that they differ reject Ho:????
if the F number for interaction is LESS THAN a then
we conclude that there IS interaction
Values of Fdf1,df2 distribution range from
zero to infinity
