## Question

# Question 1 Hemoglobin level data for three independent groups are associated with the summary statistics reported in the table below. Given summary statistics in the

**Question 1**

Hemoglobin level data for three independent groups are associated with the summary statistics reported in the table below.

*Given summary statistics in the table, answer questions number 1-5.*

Group | Number of Subjects n | Sample Mean | Sample Standard Deviation |

1 | 10 | 13.0 | 2.0 |

2 | 10 | 12.0 | 2.0 |

3 | 10 | 11.0 | 2.0 |

An investigator is trying to test hemoglobin level differences in these three populations. The hypothesis are

Group of answer choices

H01=2=3vsHA123

H01=2=3vsHA12or13or23

**Flag question: Question 2**

The test which is used to test hemoglobin level difference in these three population is

Group of answer choices

z-statistics test

t-statistics test

F-statistics test

**Flag question: Question 3**

ANOVA is analysis of variance. It requires data to meet certain conditions. The following three conditions are frequently used in statistics tests. 1. Sampling independence within and among groups 2. Normality of sampling distribution of means 3. Equal variances in the source populations The conditions for ANOVA are

Group of answer choices

1 and 2

1 and 3

2 and 3

only 3

all 1, 2 and 3

None of these three conditions

**Flag question: Question 4**

Pair-wise comparisons among these three groups are called post hoc comparisons. If the ANOVA test fails to reject the null hypothesis in question 1, post hoc comparisons are not needed.

Group of answer choices

True

False

**Flag question: Question 5**

Post hoc multiple comparisons will increase

Group of answer choices

Type I error

Type II error

Both Type I and II errors

None of above

**Flag question: Question 6**

*Given incomplete ANOVA table for Hemoglobin level data below, answer question number 6-10.*

Sum of Squares | df | Mean Square | F-value | P-value | |

Between Groups | 20.0 | 2 | |||

Within Groups | 108.0 | 27 | |||

Total | 128.0 | 29 |

The mean square between groups is

Group of answer choices

20.0

2.5

10.0

4.0

**Flag question: Question 7**

The mean square within groups is

Group of answer choices

20.0

2.5

10.0

4.0

**Flag question: Question 8**

The F-value for testing hemoglobin level difference in these three population is

Group of answer choices

20.0

2.5

10.0

4.0

**Flag question: Question 9**

Given a critical value ofF2,27(0.95)=4.20, the null hypothesis is

Group of answer choices

Reject

Retain

Can not be determined

**Flag question: Question 10**

The P-value for testing hemoglobin level difference in these three population is

Group of answer choices

Larger than 0.05

Less than 0.05

Can not be determined

**Flag question: Question 11**

In a research study, descriptive statistics of BMI for three-group and all pair-wise comparisons are summarized in two tables below.

Table I

Group | n_{i} | x_{i}bar (mean) | s_{i}(standard deviation) |

1 | 8 | 24 | 2 |

2 | 8 | 26 | 2 |

3 | 8 | 28 | 2 |

Table II

Mean Diff | Std Error | ||

(i) group | (j) group | (i-j) | SE |

1 | 2 | -2 | 1 |

3 | -4 | 1 | |

2 | 1 | 2 | 1 |

3 | -2 | 1 | |

3 | 1 | 4 | 1 |

2 | 2 | 1 |

Critical t value and alpha level from Table (C)

t | alpha-level |

2.080 | 0.05 |

Based on above three tables, please answer the questions 11-25

The t-statistic for mean difference between group 1 and group 2 (group 1 - group 2)

Group of answer choices

2

1

4

-1

-2

-4

**Flag question: Question 12**

The t-statistic for mean difference between group 1 and group 3 (group 1 - group 3)

Group of answer choices

2

1

4

-1

-2

-4

**Flag question: Question 13**

The t-statistic for mean difference between group 2 and group 1 (group 2 - group 1)

Group of answer choices

2

1

4

-1

-2

-4

**Flag question: Question 14**

The t-statistic for mean difference between group 2 and group 3 (group 2 - group 3)

Group of answer choices

2

1

4

-1

-2

-4

**Flag question: Question 15**

The t-statistic for mean difference between group 3 and group1 (group 3 - group 1)

Group of answer choices

2

1

4

-1

-2

-4

**Flag question: Question 16**

The two-sided p-value of comparing means between group 1 and group 2

Group of answer choices

larger than 0.2

between 0.1 and 0.2

between 0.05 and 0.1

between 0.01 and 0.05

less than 0.01

**Flag question: Question 17**

The two-sided p-value of comparing means between group 1 and group 3

Group of answer choices

larger than 0.2

between 0.1 and 0.2

between 0.05 and 0.1

between 0.01 and 0.05

less than 0.01

**Flag question: Question 18**

The two-sided p-value of comparing means between group 2 and group 1

Group of answer choices

larger than 0.2

between 0.1 and 0.2

between 0.05 and 0.1

between 0.01 and 0.05

less than 0.01

**Flag question: Question 19**

The two-sided p-value of comparing means between group 3 and group 2

Group of answer choices

larger than 0.2

between 0.1 and 0.2

between 0.05 and 0.1

between 0.01 and 0.05

less than 0.01

**Flag question: Question 20**

The two-sided p-value of comparing means between group 3 and group 1

Group of answer choices

larger than 0.2

between 0.1 and 0.2

between 0.05 and 0.1

between 0.01 and 0.05

less than 0.01

**Flag question: Question 21**

95% confidence interval for the mean difference between group 1 and group 2 (group 1- group 2)

Group of answer choices

(-4.080, 0.080)

(-6.080, -1.920)

(-0.080, 4.080)

(1.920, 6.080)

**Flag question: Question 22**

95% confidence interval for the mean difference between group 1 and group 3 (group 1- group 3)

Group of answer choices

(-4.080, 0.080)

(-6.080, -1.920)

(-0.080, 4.080)

(1.920, 6.080)

**Flag question: Question 23**

95% confidence interval for the mean difference between group 2 and group 1 (group 2- group 1)

Group of answer choices

(-4.080, 0.080)

(-6.080, -1.920)

(-0.080, 4.080)

(1.920, 6.080)

**Flag question: Question 24**

95% confidence interval for the mean difference between group 2 and group 3 (group 2- group 3)

Group of answer choices

(-4.080, 0.080)

(-6.080, -1.920)

(-0.080, 4.080)

(1.920, 6.080)

**Flag question: Question 25**

95% confidence interval for the mean difference between group 3 and group 1 (group 3- group 1)

Group of answer choices

(-4.080, 0.080)

(-6.080, -1.920)

(-0.080, 4.080)

(1.920, 6.080)

**Flag question: Question 26**

Bonferroni's method ensures that the family-wise error rate is less than or equal to the design level such as 0.05 after all possible pairs-wise comparisons have been made. Three groups have 3 possible pairs-wise comparisons. Four groups have 6 possible pairs-wise comparisons.

*Please answer following questions 26-29 based on this method.*

A study has three groups. Given an overall design error rate 0.05, a pairs-wise comparison can be claimed statistically significant difference when the p-value less than

Group of answer choices

0.05

0.017

0.15

0.008

0.3

**Flag question: Question 27**

A study has four groups. Given an overall design error rate 0.05, a pairs-wise comparison can be claimed statistically significant difference when the p-value less than

Group of answer choices

0.05

0.017

0.15

0.008

0.3

**Flag question: Question 28**

A study has three groups. An investigator wants to claim a statistically significant difference if a pairs-wise comparison p-value less 0.05. The overall design error rate for this study could be as large as

Group of answer choices

0.05

0.017

0.15

0.008

0.3

**Flag question: Question 29**

A study has four groups. An investigator wants to claim a statistically significant difference if a pairs-wise comparison p-value less 0.05. The overall design error rate for this study could be as large as Group of answer choices

0.05

0.017

0.15

0.008

0.3

**Flag question: Question 30**

If a study has only two groups, a statistician uses ANOVA to compare means between these two groups, the conclusion from ANOVA is

Group of answer choices

same as two-sample t-test with unequal variance.

same as two-sample t-test with equal variance.

Can not be determined

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