Question 1

The t-test may be expressed as:&#10;A) difference between means standard deviation&#10;B) standard error of difference difference between means&#10;C) difference between means standard error of the difference&#10;D) standard error of the difference standard deviation

Accepted Answer

The t-test involves comparing the difference between the means of two groups to the standard error of that difference. Therefore, the correct choice is the one that presents this formula: "difference between means standard error of the difference", which is C. The other choices either miss a component of the formula or include irrelevant variables.

Question 2

When tests of significance are needed for more complex experimental designs, which of the following statistical instruments is used:&#10;A) standard deviation&#10;B) t-test&#10;C) chi-square&#10;D) analysis of variance

Accepted Answer

Analysis of variance (ANOVA) is used when multiple groups are being compared, which is often the case in more complex experimental designs. It allows for comparison of more than two means and can determine whether any of the groups are significantly different from each other. ANOVA also takes into account the variability within each group and between groups, and calculates an F-ratio to determine if the differences observed are statistically significant. Standard deviation is a measure of variability within a single group, while t-test is used to compare two groups. Chi-square is often used for categorical data and is not typically used in complex experimental designs.

Question 3

A test of significance reports the probability that:&#10;A) the observed differences are a result of the real world&#10;B) the observed differences are a result of sampling fluctuations&#10;C) the observed differences are important&#10;D) the observed differences are false

Accepted Answer

A test of significance is used to determine whether the observed differences between groups or variables are likely due to chance (sampling fluctuations) or if they were caused by a real-world effect. Therefore, the probability reported by the test of significance refers to the likelihood of the observed differences being due to sampling error alone. Answer A is incorrect because it reverses the meaning of the test; the observed differences would only be caused by the real world if the probability reported by the test is very low, indicating that they are unlikely to be due to chance. Answer C is incorrect because the test of significance does not directly assess the importance of the observed differences, but only their statistical significance. Finally, answer D is incorrect because the test of significance does not determine whether the observed differences are false or not, only whether they are likely due to sampling fluctuations or not.

Question 4

Which of the following represents an instance where tests of significance are not appropriate:&#10;A) when a total population is being studied&#10;B) when non-probabilistic sampling has been employed&#10;C) where there is a substantial non-participation rate in the study&#10;D) all of the above&#10;E) none of the above

Accepted Answer

Tests of significance are not appropriate when the total population is being studied because the entire population is being examined, and there is no need to generalize the findings to a larger group. Non-probabilistic sampling is also inappropriate for tests of significance because it lacks randomness and may not reflect the larger population accurately. In cases where there is a substantial non-participation rate in the study, the results may not be representative of the desired population. Therefore, in all these instances, tests of significance are not appropriate.

Question 5

When executing control analyses, a test of significance after the original relationship has been tested is:&#10;A) vital&#10;B) relevant if the relationship is spurious&#10;C) of limited use only&#10;D) inappropriate

Accepted Answer

The answer of When executing control analyses, a test of...

Question 6

If the probability of an observed difference being a result of sampling error is less than 5%, then:&#10;A) the null hypothesis is usually accepted&#10;B) the null hypothesis is usually rejected&#10;C) the null hypothesis is always rejected&#10;D) the null hypothesis is always accepted

Accepted Answer

If the probability of an observed difference being a result of sampling error is less than 5%, it suggests that the difference is statistically significant and unlikely to happen by chance. Therefore, the null hypothesis (which states that there is no difference between the groups being compared) is usually rejected in favor of the alternative hypothesis.

Question 7

Normally, within a chi-square test, the dependent variable is:&#10;A) ratio&#10;B) ordinal&#10;C) interval&#10;D) nominal

Accepted Answer

The dependent variable in a chi-square test is nominal, as it consists of categorical data that cannot be ordered or measured numerically. The chi-square test is used to analyze the relationship between two or more categorical variables.

Question 8

The ANOVA test of the F distribution may be expressed as:&#10;A) F = random error + possible treatment effects random error&#10;B) F = possible treatment effects + systematic error systematic error&#10;C) F =  &#10;D) F = Ax + By + c

Accepted Answer

The ANOVA test of the F distribution compares the variance between groups to the variance within groups. This is expressed as the F-statistic, which is calculated as the ratio of the mean square between groups to the mean square within groups. Therefore, the correct formula for the F-statistic is F = between-group variation / within-group variation, which can be expressed as F = possible treatment effects + random error / random error.

Question 9

To accept the null hypothesis when using a between-subjects t-test, which of the following conditions must satisfied:&#10;A) having too little variance within the group&#10;B) having too little between group variation compared to within group variation&#10;C) having too little variation within the 5% zone of rejection&#10;D) having no variation within the 5% zone of rejection

Accepted Answer

When using a between-subjects t-test, the null hypothesis assumes that there is no significant difference between the means of two groups. Therefore, to accept the null hypothesis, there should be little between-group variation compared to within-group variation. This can be assessed by calculating the F-statistic, which is the ratio of between-group variance to within-group variance. If this ratio is small, it suggests that most of the variability is accounted for by within-group variation, and the null hypothesis should be accepted. Option A is incorrect because too little variance within the group is not necessary for accepting the null hypothesis. Option C is also incorrect since the 5% zone of rejection refers to the critical value where it is improbable to obtain the observed test statistic if the null hypothesis is true, and is not related to variation within the data. Option D is incorrect because if there is no variation within the 5% zone of rejection, it suggests that the null hypothesis is false, and the alternative hypothesis should be accepted instead.

Question 10

The distribution associated with the analysis of variance is:&#10;A) the normal distribution&#10;B) bi-modal distribution&#10;C) platykurtic distribution&#10;D) F distribution

Accepted Answer

The distribution associated with the analysis of variance is the F distribution.

Question 11

Analysis of variance is typically used when:&#10;A) the dependent variable is of the ratio level&#10;B) the treatment variable has 2 or more levels&#10;C) the researcher wants to determine if there are statistically significant differences between the groups&#10;D) all of the above

Accepted Answer

The answer of Analysis of variance is typically used when:&#10;A)...

Question 12

When conducting a two-tailed test, the rejection area is:&#10;A) two 5% zones&#10;B) two 2.5% zones&#10;C) one 2.5% zone&#10;D) one 5% zone

Accepted Answer

The answer of When conducting a two-tailed test, the rejection...

Question 13

The chi-square test is based on:&#10;A) a comparison of the independent and the dependent variables&#10;B) a comparison of the observed and expected frequencies&#10;C) the concept of a linear relationship&#10;D) the null hypothesis

Accepted Answer

The answer of The chi-square test is based on:&#10;A) a...

Question 14

The null hypothesis states that:&#10;A) there will be no relationship between the 2 variables&#10;B) there will be a significant relationship between the 2 variables&#10;C) there will be a spurious relationship between the 2 variables&#10;D) there will be a confounding variable involved in the relationship

Accepted Answer

The answer of The null hypothesis states that:&#10;A) there will...

Question 15

A t-test is used when:&#10;A) the dependent variable is of the ratio level&#10;B) only when sample sizes are large (over 30)&#10;C) group assignment has been done on a non-random basis&#10;D) the treatment variable has only one level

Accepted Answer

The answer of A t-test is used when:&#10;A) the dependent...

Question 16

If no prediction concerning the direction of the relationship is made, then:&#10;A) a one-tailed test is being conducted&#10;B) a two-tailed test is being conducted&#10;C) the test is not valid or scientific&#10;D) a theory is not being tested

Accepted Answer

The answer of If no prediction concerning the direction of...

Question 17

The chi-square, represented by x², is expressed by which of the following: A) B) C) D)

Accepted Answer

The answer of The chi-square, represented by x², is expressed...

Question 18

In conducting a test of significance, the researcher is determining whether the results of one sample fall outside the null hypothesis zone, which usually is:&#10;A) within the 95% zone&#10;B) outside of the 5% zone&#10;C) within the 68% zone&#10;D) outside of the 95% zone

Accepted Answer

The answer of In conducting a test of significance, the...

Question 19

ANOVA is used when:&#10;A) the research design employs multiple dependent variables&#10;B) the independent variable has multiple treatment levels&#10;C) the dependent variable is of the nominal level of measurement&#10;D) all of the above

Accepted Answer

The answer of ANOVA is used when:&#10;A) the research design...

Question 20

To calculate the degrees of freedom, one must employ which of the following:&#10;A) (# of rows - # of columns) 2&#10;B) (# of rows - 1) x (# of columns - 1)&#10;C) (# of rows - 1) (# of columns - 1)&#10;D) _ (# of rows - 1) (# of columns - 1)2

Accepted Answer

The answer of To calculate the degrees of freedom, one...

Deck 9: Three Tests of Significance