Question 1

In a two-way ANOVA,the error sum of squares can be calculated by? A)SS_E = SS_T + SS_R + SS_C B)SS_E = SS_R + SS_C - SS_T C)SS_E = SS_T - SS_R - SS_C D)SS_E - SS_R = SS_T + SS_C

Accepted Answer

In a two-way ANOVA, the error sum of squares (SSE) is calculated by subtracting the sum of squares due to rows (SSR) and the sum of squares due to columns (SSC) from the total sum of squares (SST). This is represented by the formula: SSE = SST - SSR - SSC.

Question 2

How are the degrees of freedom for interaction denoted for data displayed in columns (c)and rows (r)?
A)r - 1
B)c - 1 + r - 1
C)r(c - 1)
D)(r - 1)(c - 1)

Accepted Answer

The degrees of freedom for interaction in a two-way ANOVA, where data is displayed in columns (c) and rows (r), are denoted by (r - 1)(c - 1). This formula calculates the degrees of freedom for the interaction between the row and column factors.

Question 3

ANOVAs evaluate how likely differences between conditions are due to?
A)Sphericity
B)Normal distributions
C)Sampling error
D)Homogeneity of variance

Accepted Answer

ANOVAs evaluate how likely differences between conditions are due to sampling error, assessing the probability that observed differences among group means occurred by chance.

Question 4

Which of the following is incorrect?
A)ANOVAs are robust when used in small samples of participants.
B)ANOVAs are robust to skewed data sets.
C)ANOVAs are robust to unequal numbers of scores in different conditions.
D)All of the above.

Accepted Answer

ANOVAs are not robust when used in small samples of participants, with skewed data sets, or with unequal numbers of scores in different conditions.

Question 5

ANOVAs cannot be used when testing data collected in educational research as it cannot be applied to social science.

Accepted Answer

ANOVAs can be used in educational research as well as in other social sciences to compare means across multiple groups, making it a versatile statistical tool in these fields.

Question 6

The number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.

Accepted Answer

Degrees of freedom refer to the number of independent values or quantities which can be assigned to a statistical distribution, minus the number of parameters estimated from the same data, thus indicating the number of values in the final calculation that are free to vary.

Question 7

Which of the following distributions is used for accepting the null hypothesis?
A)Poisson
B)Chi-square
C)Binominal
D)None of the above

Accepted Answer

The concept of accepting the null hypothesis is not tied to a specific distribution like Poisson, Chi-square, or Binomial. Instead, it is related to the statistical test being performed and the resulting p-value in comparison to a predetermined significance level.

Question 8

Any difference in population means in analysis of variance will inflate the error sum of squares.

Accepted Answer

The error sum of squares in analysis of variance is influenced by the variability within groups, not by differences between the group means. Differences between group means affect the treatment (or model) sum of squares.

Question 9

In a two-way ANOVA,the interaction between factors 1 and 2 should be tested first.

Accepted Answer

In a two-way ANOVA, the interaction effect is tested first to determine if the effect of one factor depends on the level of the other factor. If the interaction is significant, it can influence the interpretation of the main effects.

Question 10

The coefficient of determination is denoted by? A)R² B)SS_E + SS_T C)(SS_E)² D)SS_R - SS_T

Accepted Answer

The coefficient of determination is denoted by R², which measures the proportion of variance in the dependent variable that is predictable from the independent variable(s).

Question 11

The probability that it is not small if bought by an administrator is?
A).505
B).612
C).999
D).002

Accepted Answer

The answer of The probability that it is not small...

Question 12

Using the same data set,the probability that a student bought the coffee is?
A).111
B).311
C).500
D).399

Accepted Answer

The correct answer is determined by analyzing the given data set and calculating the probability of a student buying coffee. The choice "B).311" likely represents the correct calculation or interpretation of the data set in question. Without the specific data, we can infer that this option was calculated based on the information provided, indicating the probability or count of students buying coffee in relation to the total or a specific condition.

Question 13

Cups of coffee are sold at the Skool Café in three sizes (S,M,L),and customers fall into three categories (academics,administrators,students).The numbers of cups sold in a working day are as follows. Small Medium Large
Academics 12 25 27
Administrators 19 26 4
Students 30 10 11
Selecting one cup sold at random,the probability that it will be a large cup is?
A).256
B).333
C).500
D).111

Accepted Answer

The answer of Cups of coffee are sold at the...

Question 14

A two-way ANOVA is conducted and the error sum of squares is worked out as 140.59.If the researcher chooses to ignore one of the factors and perform a one-way ANOVA with the same data,the error sum of squares will be smaller than 140.59.

Accepted Answer

Ignoring one of the factors in a two-way ANOVA and performing a one-way ANOVA instead generally leads to a larger error sum of squares because the variation explained by the ignored factor is now included in the error term, increasing its value.

Question 15

What does ANOVA stand for?
A)Analysis of vulnerability
B)Analysis of variance
C)Analysis of vaccination
D)Analysis of velocity

Accepted Answer

ANOVA stands for Analysis of Variance, a statistical method used to compare means among three or more groups to see if at least one differs significantly from the others.

Question 16

The calculation for the sum of squares due to column factor for one-way ANOVAs is given by? A)SS_T + SS_E B)SS_E - SS_T C)SS_T - SS_E D)SS_T × SS_E

Accepted Answer

The sum of squares due to the column factor (SSC) in one-way ANOVA is calculated by subtracting the sum of squares within groups (SSE) from the total sum of squares (SST). This is because SST represents the total variability in the data, while SSE accounts for the variability within the groups. The difference between these two gives the variability due to the treatment effect, which is the sum of squares between groups (SSC). Therefore, the correct formula is represented by the option that subtracts SSE from SST.

Question 17

Into how many rows in a two-way ANOVA is total variance partitioned?
A)1
B)2
C)3
D)4

Accepted Answer

In a two-way ANOVA, total variance is partitioned into three rows: variance due to the first factor, variance due to the second factor, and variance due to the interaction between the two factors.

Question 18

The treatment sum of squares measures the variability of the sample treatment means around the overall mean.

Accepted Answer

The treatment sum of squares quantifies the variation among the sample means from different groups or treatments, compared to the overall mean of all observations combined. It helps in assessing whether there are significant differences between group means in an analysis of variance (ANOVA).

Question 19

When sample size is large,which of the following assumptions can be ignored?
A)That each sample will have an equal variance
B)That samples have been drawn from a normal population
C)Both
D)Neither

Accepted Answer

The answer of When sample size is large,which of the...

Question 20

What type of data are best analysed in ANOVA?
A)Correlational
B)Random
C)Experimental
D)Simple

Accepted Answer

ANOVA (Analysis of Variance) is best suited for analyzing data from experimental designs where the effects of one or more independent variables on a dependent variable are being investigated. It is used to compare the means of three or more samples, assuming the data comes from an experimental or quasi-experimental research design.

Quiz 10: Comparing

In a two-way ANOVA,the error sum of squares can be calculated by?

How are the degrees of freedom for interaction denoted for data displayed in columns (c) and rows (r) ?

ANOVAs evaluate how likely differences between conditions are due to?

Which of the following is incorrect?

ANOVAs cannot be used when testing data collected in educational research as it cannot be applied to social science.

The number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.

Which of the following distributions is used for accepting the null hypothesis?

Any difference in population means in analysis of variance will inflate the error sum of squares.

In a two-way ANOVA,the interaction between factors 1 and 2 should be tested first.

The coefficient of determination is denoted by?

The probability that it is not small if bought by an administrator is?

Using the same data set,the probability that a student bought the coffee is?

A two-way ANOVA is conducted and the error sum of squares is worked out as 140.59.If the researcher chooses to ignore one of the factors and perform a one-way ANOVA with the same data,the error sum of squares will be smaller than 140.59.

What does ANOVA stand for?

The calculation for the sum of squares due to column factor for one-way ANOVAs is given by?

Into how many rows in a two-way ANOVA is total variance partitioned?

The treatment sum of squares measures the variability of the sample treatment means around the overall mean.

When sample size is large,which of the following assumptions can be ignored?

What type of data are best analysed in ANOVA?