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# The Practice of Nursing Research 7^{th} Edition Grove Burns Gray Test Bank

ISBN-13: 978-1455707362

ISBN-10: 1455707368

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**Chapter 21: Introduction to Statistical Analysis**

**Test Bank**

**MULTIPLE CHOICE**

- A researcher who has conducted experimental research finds that in his 145-person hospital study the patients who are ambulated on the evening of abdominal surgery are less likely than the control group to develop postoperative pneumonia. What does the researcher infer?

a. | The control group resembled the experimental group in all important characteristics. |

b. | Early ambulation and pneumonia are strongly related. |

c. | Evening-of-surgery ambulation will prevent some cases of postoperative pneumonia in abdominal surgery patients. |

d. | Careful support of the abdomen is important for postoperative ambulation in patients who have had abdominal surgery. |

ANS: C

Statisticians use the term *inference* or *infer* in somewhat the same way that a researcher uses the term *generalize*. Inference requires the use of inductive reasoning. One infers from a specific case to a general truth, from a part to the whole, from the concrete to the abstract, from the known to the unknown. When using inferential reasoning, one can never prove things; one can never be certain. However, the rules that have been established with regard to statistical procedures so as to increase the probability that inferences are accurate. Inferences are made cautiously and with great care. Researchers use inferences to infer from the sample in their study to the larger population.

DIF: Cognitive Level: Analysis REF: Page 537

- What is this particular distribution called?

a. | Bimodal |

b. | Normal |

c. | Camelesque |

d. | Negatively skewed |

ANS: A

Another characteristic of distributions is their modality. Most curves found in practice are unimodal, which means that they have one mode and frequencies progressively decline as they move away from the mode. Symmetrical distributions are usually unimodal. However, curves can also be bimodal or multimodal. accurately reflect the shape of the population from which the sample was taken.

DIF: Cognitive Level: Application REF: Page 540

- A researcher reports that the heights of men aged 53 living in Rapid City, South Dakota, are between 5’7” and 6’0” and that the confidence interval is calculated at the
*p*<.05 level. What does this mean?

a. | If the heights of men in Rapid City, South Dakota, do not fall within the confidence interval at least 5% of the time, a type I error has occurred. |

b. | If a 53-year-old man in Rapid City, South Dakota, is measured, there is a 95% chance that his height will fall in the 5’7” through 6’0” interval. |

c. | Ninety-five percent of the 53-year-old men living in Rapid City, South Dakota, are between 5’7” and 6’0”. |

d. | The heights of the men in the sample were all between 5’7” and 6’0”, and the sample was representative of 95% of the men in town. |

ANS: B

When the probability of including the value of the parameter within the interval estimate is known, this is referred to as a confidence interval. Calculating a confidence interval involves the use of two formulas to identify the upper and lower ends of the interval. A confidence interval is actually an estimate.

DIF: Cognitive Level: Synthesis REF: Page 541

- There are four data sets:

A: 1, 1, 1, 1, 1, 10, 10, 10, 10

B: 2, 2, 2, 2, 4, 8, 8, 8, 9

C: 3, 4, 4, 5, 5, 5, 6, 6, 7

D: 1, 2, 3, 4, 5, 6, 7, 8, 9

What is the mean of the four individual data sets?

a. | 5, 5, 5, 5 |

b. | 1, 4, 5, 5 |

c. | 1, 2, 5, 5 |

d. | 5 |

ANS: A

The measures of central tendency are descriptive statistics. The statistics that represent “measures of central tendency” are the mean, median, and mode. All of these statistics are representations or descriptions of the center or middle of a frequency distribution. The mean is the arithmetic average of all of a variable’s values. The median is the exact middle value (or the average of the middle two values if there is an even number of observations). The mode is the most commonly occurring value in a data set. In a normal curve, the mean, median, and mode will be equal or approximately equal

DIF: Cognitive Level: Analysis REF: Page 538

- There are four data sets:

A: 1, 1, 1, 1, 1, 10, 10, 10, 10

B: 2, 2, 2, 2, 4, 8, 8, 8, 9

C: 3, 4, 4, 5, 5, 5, 6, 6, 7

D: 1, 2, 3, 4, 5, 6, 7, 8, 9

What is the median of the four individual data sets?

a. | 5, 5, 5, 5 |

b. | 1, 4, 5, 5 |

c. | 1, 2, 5, 5 |

d. | 5 |

ANS: B

The measures of central tendency are descriptive statistics. The statistics that represent “measures of central tendency” are the mean, median, and mode. All of these statistics are representations or descriptions of the center or middle of a frequency distribution. The mean is the arithmetic average of all of a variable’s values. The median is the exact middle value (or the average of the middle two values if there is an even number of observations). The mode is the most commonly occurring value in a data set. In a normal curve, the mean, median, and mode will be equal or approximately equal.

DIF: Cognitive Level: Analysis REF: Page 538

- There are four data sets:

A: 1, 1, 1, 1, 1, 10, 10, 10, 10

B: 2, 2, 2, 2, 4, 8, 8, 8, 9

C: 3, 4, 4, 5, 5, 5, 6, 6, 7

D: 1, 2, 3, 4, 5, 6, 7, 8, 9

What is the mode of the four individual data sets?

a. | 5, 5, 5, 5 |

b. | 1, 4, 5, 5 |

c. | 1, 2, 5, none |

d. | 1 |

ANS: C

The measures of central tendency are descriptive statistics. The statistics that represent “measures of central tendency” are the mean, median, and mode. All of these statistics are representations or descriptions of the center or middle of a frequency distribution. The mean is the arithmetic average of all of a variable’s values. The median is the exact middle value (or the average of the middle two values if there is an even number of observations). The mode is the most commonly occurring value in a data set. In a normal curve, the mean, median, and mode will be equal or approximately equal.

DIF: Cognitive Level: Analysis REF: Page 538

- Which of the following is the best example of a normally distributed data set?

a. | 1, 1, 1, 1, 1, 10, 10, 10, 10 |

b. | 2, 2, 2, 2, 4, 8, 8, 8, 9 |

c. | 3, 4, 4, 5, 5, 5, 6, 6, 7 |

d. | 1, 2, 3, 4, 5, 6, 7, 8, 9 |

ANS: C

The measures of central tendency are descriptive statistics. The statistics that represent “measures of central tendency” are the mean, median, and mode. All of these statistics are representations or descriptions of the center or middle of a frequency distribution. The mean is the arithmetic average of all of a variable’s values. The median is the exact middle value (or the average of the middle two values if there is an even number of observations). The mode is the most commonly occurring value in a data set. In a normal curve, the mean, median, and mode will be equal or approximately equal.

DIF: Cognitive Level: Analysis REF: Page 538

- One hundred students took an exam; the mean of the test was 45%, and the median was 38%; seventy students scored below the mean, but three scored more than 96%. This would represent what type of distribution?

a. | Normal |

b. | Positively skewed |

c. | Negatively skewed |

d. | Leptokurtic |

ANS: B

Any curve that is not symmetrical is referred to as skewed or asymmetrical. Skewness may be exhibited in the curve in a variety of ways. A curve may be positively skewed, which means that the largest portion of data is below the mean. A curve can also be negatively skewed, which means that the largest portion of data is above the mean. A normal curve is symmetric and has no skew. Few samples will be perfectly symmetrical; however, as the deviation from symmetry increases, the seriousness of the impact on statistical analysis increases. In a positively skewed distribution, the mean is greater than the median, which is greater than the mode. In a negatively skewed distribution, the mean is less than the median, which is less than the mode.

DIF: Cognitive Level: Analysis REF: Page 540

- In the following illustration of a negatively skewed curve, which line represents the mode?

a. | First dotted line |

b. | Second dotted line |

c. | Third dotted line |

ANS: C

In a *skewed distribution*, the mean, median, and mode are not equal. In a negatively skewed distribution, the mean will be less than the median, which will be less than the mode.

DIF: Cognitive Level: Application REF: Page 540

- Which of the following distribution curves demonstrates the least amount of variation in the scores?

a. | The least amount of variation would be in the first curve. |

b. | The least amount of variation would be in the second curve. |

c. | The least amount of variation would be in the third curve. |

d. | The amount of variation can’t be defined by the curve. |

ANS: A

*Kurtosis* explains the degree of peakedness of the distribution curve, which is related to the spread of the variance of scores. An extremely peaked curve is referred to as leptokurtic, an intermediate degree of kurtosis as mesokurtic, and a relatively flat curve as platykurtic. The less peaked the curve, the more variation is present.

DIF: Cognitive Level: Application REF: Page 541

- is the symbol for which of the following?

a. | Sample mean |

b. | Population mean |

c. | Population variance |

d. | Sample variance |

ANS: A

Use of the terms *statistic* and *parameter* can be confusing because of the various populations referred to in statistical theory. A *statistic* (such as a mean, ) is a numerical value obtained from a sample. A *parameter* is a true (but unknown) numerical characteristic of a population. For example, is the population mean or arithmetic average. The mean of the sampling distribution (mean of samples’ means) can also be shown to be equal to . Thus, a numerical value that is the mean () of the sample is a statistic; a numerical value that is the mean of the population () is a parameter.

DIF: Cognitive Level: Comprehension REF: Page 537

- A researcher conducts a statistical test that reveals that the four groups analyzed differed. The researcher wants to discover which one or ones of the four differed from the others. The researcher must then perform a post hoc analysis. What will this involve?

a. | Design of a second research study, using a new sample |

b. | Descriptive statistics about the sample demographics |

c. | Qualitative research generating new themes and ideas |

d. | A second statistical test using the original data |

ANS: D

Post hoc analyses are commonly performed in studies with more than two groups when the analysis indicates that the groups are significantly different but does not indicate which groups are different. A post hoc analysis must be performed to determine which of the three groups are significantly different. In other studies, the insights obtained through the planned analyses generate further questions that can be examined with the available data.

DIF: Cognitive Level: Application REF: Page 545

- Where would one find approximately 95% of the scores in the following example if scores are normally distributed?

Scores ranged from 30 to 68, M = 45, SD = 7.

a. | Between 37 and 61 |

b. | Between 38 and 52 |

c. | Between 31 and 59 |

d. | Between 30 and 68 |

ANS: C

The range, standard deviation, and variance are statistics that describe the extent to which the values in the sample vary from one another. The most common of these statistics to be reported in the literature is the standard deviation, because of its direct association with the normal curve. If the frequency distribution of any given variable is approximately normal, knowing the standard deviation of that variable allows us to know what percentages of subjects’ values on that variable fall between +1 and –1 standard deviation. Referring back to the hypothetical frequency distribution of pain in Figure 21-1, when we calculate a standard deviation, we know that 34.13% of the subjects’ pain scores were between the mean pain score and 1 standard deviation above the mean pain score. We also know that 34.13% of the subjects’ pain scores were between the mean pain score and 1 standard deviation below the mean. The middle 95.44% of the subjects’ scores were between –2 standard deviation and +2 standard deviations.

DIF: Cognitive Level: Evaluation REF: Page 541

- If a researcher wishes to predict with 97.5% accuracy, the level of significance would be

a. | .05 |

b. | .01 |

c. | .25 |

d. | .025 |

ANS: D

If one wishes to predict with 95% accuracy, the level of significance *(p)* is 1 minus 95% = .05. In nursing research, alpha is usually set at 0.05, meaning that the researcher will allow a 5% or lower chance of making a type I error.

DIF: Cognitive Level: Application REF: Page 535

**MULTIPLE RESPONSE**

- A researcher states in an article that a new experimental treatment, trialed in the outpatient setting in a tri-physician practice in northern Oregon, produces better outcomes than the control treatment for patients with COPD. The
*p-*value given is*p*<.05. What does this mean? (Select all that apply.)

a. | There is better than a 95% chance that at the research site mentioned in the article the experimental treatment really DOES produce better outcomes for patients with COPD. |

b. | The probability of error is 95%. |

c. | There is very little chance that the intervention is effective—less than a 5% chance, in fact. |

d. | There is better than a 95% chance that the experimental treatment will produce better outcomes for all COPD patients. |

e. | There is less than a 5% chance that the researcher has reached this conclusion in error. |

ANS: A, D, E

Probability theory addresses statistical analysis as the likelihood of accurately predicting an event or the extent of an effect. In probability theory, the meaning of statistical results is interpreted by the researcher in light of his or her knowledge of the field of study. Probability is expressed as a lowercase *p*, with values expressed as percentages or as a decimal value ranging from 0 to 1.

DIF: Cognitive Level: Synthesis REF: Page 535

- A null hypothesis is stated. The null hypothesis is, “There is no difference between 10 mcg and 20 mcg of vitamin D
_{3}in prevention of osteoporosis.” What are the implications of this statement, concerning that hypothesis and type I error? (Select all that apply.)

a. | Rejecting the null hypothesis when it actually is false means that the researcher has made a type I error in concluding that there is a difference between 10 mcg and 20 mcg of vitamin D_{3} in preventing osteoporosis. |

b. | Making the statement is itself a type I error. |

c. | Whether the null hypothesis is true or not makes no difference in terms of type I error. |

d. | Whether or not the researcher rejects the null hypothesis makes no difference in terms of type I error. |

e. | Rejecting the null hypothesis when it actually is false means that the researcher concludes that there is a difference between 10 mcg and 20 mcg of vitamin D_{3} in preventing osteoporosis, and there is no error. |

f. | Rejecting the null hypothesis when it actually is true means that the researcher concludes that there is no difference between 10 mcg and 20 mcg of vitamin D_{3} in preventing osteoporosis, but the researcher thinks there is and has made a type I error. |

ANS: E, F

Type I error is the probability of rejecting the null hypothesis when it is in fact true. It is also called alpha [α]. In nursing studies, this is usually .05, which equals 5%. To test the null hypothesis, the researcher consults a statistics website or book, to discover the decision point or cutoff point, which is the value at which rejecting the null hypothesis would be the wrong decision only 5% of the time. Then the researcher calculates the statistic, based on the data. If the value of the statistic is less than the cutoff point, the null hypothesis stands—it is not rejected. If the value of the statistic is more than the cutoff point, the null hypothesis is rejected. This will be the correct decision 95% of the time.

DIF: Cognitive Level: Analysis REF: Page 535

- A null hypothesis is stated. The null hypothesis is, “There is no difference between one baby aspirin every day and no baby aspirin at all in prevention of myocardial infarction.” What are the implications of this statement, concerning that hypothesis and type II error? (Select all that apply.)

a. | Accepting the null hypothesis when it actually is true means that the researcher has made a type II error in concluding that there is no difference between 10 mcg and 20 mcg of vitamin D_{3} in preventing osteoporosis. |

b. | Making the statement is itself a type II error. |

c. | Whether the null hypothesis is true or not makes no difference in terms of type II error. |

d. | Whether or not the researcher rejects the null hypothesis makes no difference in terms of type II error. |

e. | Accepting the null hypothesis when it actually is true means that the researcher concludes that there is no difference between 10 mcg and 20 mcg of vitamin D_{3} in preventing osteoporosis, and there is no error. |

f. | Accepting the null hypothesis when it actually is false means that the researcher concludes that there is no difference between 10 mcg and 20 mcg of vitamin D_{3} in preventing osteoporosis, when there actually IS a difference. The researcher has therefore made a type II error. |

ANS: E, F

Type II error is the probability of retaining the null hypothesis when it is in fact false. In nursing research, type II error is usually set at .20. This means that a type II error, failure to detect a difference when it indeed exists, will occur 20% of the time. One minus beta [ß] equals the power of the study. This is the research study’s power to detect a difference when it indeed *does* exist.

DIF: Cognitive Level: Analysis REF: Page 535

- As researcher designs a study to measure the effect on patient satisfaction of the nurse stating to the patient at least once a day, “You’re a good person.” The researcher sets the alpha (type I error) for the study at
*p*<.10 because the intervention is free, it needs next to no time to enact, and it is harmless. If the alpha is set at .10, what is the effect on the beta [*β*] and on type II error? (Select all that apply.)

a. | Beta [ß] stays the same. |

b. | Type II error becomes less likely. |

c. | Type II error becomes more likely. |

d. | Beta [ß] decreases. |

e. | Beta [ß] increases as well. |

f. | Type II error stays the same. |

ANS: B, D

The researcher chooses the probability of making a type I error when setting alpha [α], and if the researcher sets the probability of making a type I error quite low, perhaps only 1%, the probability of making a type II error, [ß], increases. By the same token, if the researcher sets the probability of making a Type I error quite high, perhaps 10%, the probability of making a type II error decreases.

DIF: Cognitive Level: Analysis REF: Page 536

- In statistical hypothesis testing, which of the following occur before the data are collected? (Select all that apply.)

a. | The beta (type II error) is set. |

b. | A power analysis is conducted. |

c. | The null hypothesis is accepted or rejected. |

d. | The alpha (type I error) is set. |

e. | The primary null hypothesis is stated. |

ANS: A, B, D, E

The following steps outline each of the components of statistical hypothesis testing. The null hypothesis is stated. The study alpha (type I error) is set. The study beta (type II error) is set. A power analysis is performed. The study is conducted. The statistic is computed, based on the data obtained. The obtained statistic is compared with the critical value for the alpha chosen. If the obtained statistic is greater than the critical value, the null hypothesis is rejected; if the obtained statistic is less than the critical value, the null hypothesis is accepted.

DIF: Cognitive Level: Analysis REF: Page 535

- If beta, ß, is the probability of making a type II error, what is 1 minus ß? (Select all that apply.)

a. | Alpha [α] |

b. | A relationship exists |

c. | The power of the study |

d. | The likelihood that the null hypothesis is incorrect |

e. | The probability of not making a type II error |

ANS: C, E

Power is the probability that a statistical test will detect an effect when it actually exists. Therefore, power is the inverse of type II error and is calculated as 1 – ß. Recall that type II error is the probability of retaining the null hypothesis when it is in fact false. When the researcher sets type II error at 0.20 prior to conducting a study, this means that the power of the planned statistic has been set to 0.80. In other words, the statistic will have an 80% chance of detecting an effect if it actually exists.

DIF: Cognitive Level: Analysis REF: Page 536

- A researcher is concerned about the power of his study. His planned interventional study examines the effect upon depression of instituting twice-yearly trips with a Road Scholar program for widows and widowers who have, 1 to 2 years before, lost a spouse to a long illness. What strategies could make type II error less likely? (Select all that apply.)

a. | Decreasing the effect size |

b. | Increasing the alpha from .05 to .10 |

c. | Increasing the beta from .20 to .30 |

d. | Decreasing the beta from .20 to .10 |

e. | Decreasing the alpha from .05 to .025 |

f. | Increasing the sample size |

ANS: B, D, F

Power is the probability that a statistical test will detect an effect when it actually exists. Therefore, power is the inverse of type II error and is calculated as 1 – ß. Recall that type II error is the probability of retaining the null hypothesis when it is in fact false. When the researcher sets type II error at 0.20 prior to conducting a study, this means that the power of the planned statistic has been set to 0.80. In other words, the statistic will have an 80% chance of detecting an effect if it actually exists. Often, reported studies failing to reject the null hypothesis (in which power is unlikely to have been examined) will have a low power level to detect an effect if one exists. Until recently, the researcher’s primary interest was in preventing a Type I error. Therefore, great emphasis was placed on the selection of a level of significance but little on power. This point of view is changing. Power analysis involves determining the required sample size needed to conduct the study. Cohen identified four parameters of power: (1) significance level, (2) sample size, (3) effect size, and (4) power. If three of the four are known, the fourth can be calculated by using power analysis formulas. Effect size is a constant; it is “the degree to which the phenomenon is present in the population or the degree to which the null hypothesis is false.” Consequently, if the researcher wants to increase a study’s power, the sample size must be increased, or the level of significance must be set at a less stringent level.

DIF: Cognitive Level: Analysis REF: Page 536

- Findings can be statistically significant be clinically not significant. Which of the following studies with statistically significant findings exemplify this? (Select all that apply.)

a. | Seventy-five seconds of UV light daily can completely reverse the symptoms of allergic dermatitis. |

b. | Eating a cup of salad greens daily increases one’s life expectancy by 2 years. |

c. | Petting a cat for five minutes daily increases one’s endorphin levels. |

d. | Exercise Program Delta causes weight loss of 6.3 pounds per year in morbidly obese women. |

e. | Talking to a crying baby calms the baby more than ignoring it; picking up the baby calms it more than talking to it. |

f. | Medication R15B, taken daily from age 13, completely controls cystic acne by age 23. |

ANS: C, D, E, F

The findings of a study can be statistically significant but may not be clinically important. For example, one group of patients might have a body temperature 0.1° F higher than that of another group. Data analysis might indicate that the two groups are statistically significantly different. However, the findings have little or no clinical importance due to the small difference in temperatures between groups. Persons with dermatitis would find the UV light treatment almost miraculous. Two extra years of life may be clinically important to those with good quality of life. Increasing endorphins is not due only to petting cats, so this study is not particularly significant, clinically. A weight loss of 6.3 pounds per year is not large enough to make a significant difference in the life of a morbidly obese woman. Picking up crying babies is something that even one’s grandmother knows; this is not clinically useful. A medication that controls cystic acne ten years later is of little use to the adolescent who is miserable with acne.

DIF: Cognitive Level: Analysis REF: Page 537

- A measured value is within two standard deviations of the mean but not within one standard deviation, and it is greater than the mean. The distribution is very close to a normal distribution. What does this signify? (Select all that apply.)

a. | This particular value is not an outlier. |

b. | In the data set, almost 2/3 of the values are closer to the mean than this one is. |

c. | The data point falls within the majority of the measured values, in terms of its closeness to the mean. |

d. | In the data set, at least 4% of the values are further from the mean than this particular value is. |

e. | In this data set, between 65% and 95% of the values are smaller in value than this one is. |

ANS: A, B, D, E

The range, standard deviation, and variance are statistics that describe the extent to which the values in the sample vary from one another. The most common of these statistics to be reported in the literature is the standard deviation, because of its direct association with the normal curve. If the frequency distribution of any given variable is approximately normal, knowing the standard deviation of that variable allows the reader to know what percentages of subjects’ values on that variable fall between +1 and –1 standard deviation. In a normal distribution, when a standard deviation is calculated, 34.13% of the values are between the mean score and 1 standard deviation above the mean. Similarly, 34.13% of the values are between the mean score and 1 standard deviation below the mean. The middle 95.44% of the subjects’ scores are between +2 standard deviations and –2 standard deviations.

DIF: Cognitive Level: Synthesis REF: Page 541

- Which of the following are true about a type II error? (Select all that apply.)

a. | It is more likely to occur when p <.01 rather than when p <.05. |

b. | It is extremely likely to occur when p <.001. |

c. | It occurs when the null hypothesis is true but rejected. |

d. | It is a possibility only when there are statistically nonsignificant results in a study. |

e. | It is a possibility only when there are statistically significant results in a study. |

ANS: A, B, D

The probability of retaining the null hypothesis when it is in fact false is a type II error. In nursing research, beta is frequently set to 0.20, meaning that the researcher will allow for a 20% or lower chance of making a type II error, when the alpha is set at .05. If the alpha decreases (becomes more stringent) (.025, .01, and so forth), decreasing the possibility of type I error, the consequence is that the beta rises, making type II error much more likely. When a statistical test in a research study shows that a result is not statistically significant, the discerning reader will evaluate the sample size and the level of significance, in order to determine the possibility that a type II error occurred. It is not possible to decrease both types of error simultaneously without a corresponding increase in sample size.

DIF: Cognitive Level: Analysis REF: Page 535

- A teacher administers an exam. The exam seemed relatively easy for the students, and the majority of the scores are at the high end of the scale, although several students received low scores. In statistical terms this represents what? (Select all that apply.)

a. | Positive skew |

b. | Negative skew |

c. | Asymmetrical distribution |

d. | Symmetrical distribution |

e. | A normal curve |

f. | A non-normal curve |

ANS: B, C, F

Any curve that is not symmetrical is referred to as skewed or asymmetrical. Skewness may be exhibited in the curve in a variety of ways. A curve may be positively skewed, which means that the largest portion of data is below the mean. A curve can also be negatively skewed, which means that the largest portion of data is above the mean. A normal curve is symmetric and has no skew.

DIF: Cognitive Level: Synthesis REF: Page 540

- A researcher is attempting to decide whether to hire a statistician to assist with the statistical aspects of the study. If the researcher cannot perform which of the following for a quantitative study, a statistician should be contacted? (Select all that apply.)

a. | Provide sample demographics using descriptive statistics. |

b. | Perform reliability testing of the study instruments. |

c. | Design and perform analyses to answer research questions and test hypotheses. |

d. | Design and perform an exploratory analysis of the data. |

e. | Hand-compute all statistical calculations. |

f. | Prepare the data for analysis. |

g. | Perform a power analysis. |

h. | Interpret the results obtained by all statistical computations. |

ANS: A, B, C, D, F, G, H

To perform statistical analysis of data from a quantitative study, one must be able to (1) determine the necessary sample size to adequately power your study, (2) prepare the data for analysis, (3) describe the sample, (4) test the reliability of measures used in the study, (5) perform exploratory analyses of the data, (6) perform analyses guided by the study objectives, questions, or hypotheses, and (7) interpret the results of statistical procedures. If the researcher is not able to do all of these, a statistician is consulted. Descriptions of the sample demographics are made statistically.

DIF: Cognitive Level: Application REF: Page 534

- Why might nonparametric statistical methods be used for analysis?

a. | The level of measurement of the variables is nominal. |

b. | The researcher prefers to use these statistical tests. |

c. | The null hypothesis is absent. |

d. | The sample is small or lacks a normal distribution. |

ANS: A, D

The most commonly used type of statistical analysis is parametric statistics. The analysis is referred to as parametric statistical analysis because the findings are inferred to the parameters of a normally distributed population. These approaches to analysis require meeting the following three assumptions before they can justifiably be used: (1) normal distribution and variance can be calculated, (2) level of measurement at least interval, or ordinal with an approximately normal distribution, and (3) data that can be treated as a random sample. Nonparametric statistical analysis, or distribution-free techniques, can be used in studies that do not meet the first two assumptions of normal distribution and at least interval level data.

DIF: Cognitive Level: Analysis REF: Page 542

- Which of the following should a reader of a research article be able to do, in order to decide whether the article’s statistics are correctly selected and applied? (Select all that apply.)

a. | Understand the discussion section of the article. |

b. | Make a judgment as to whether the author’s interpretations of the data are correct. |

c. | Make some judgment about whether the statistical procedures used were the correct ones for the level of measurement used for the study variables. |

d. | Make some judgment about whether the statistical procedures used were the correct ones for the research question. |

e. | Agree with the study’s stated limitations. |

f. | Find the names of the statistical procedures the author used. |

ANS: A, B, C, D, F

To critically appraise the results section of a quantitative study, the reader needs to be able to (1) identify the statistical procedures used, (2) judge whether these statistical procedures were appropriate for the hypotheses, questions, or objectives of the study and for the data available for analysis, (3) comprehend the discussion of data analysis results, (4) judge whether the author’s interpretation of the results is appropriate, and (5) evaluate the clinical importance of the findings.

DIF: Cognitive Level: Comprehension REF: Page 534

- Which of the following are true in a skewed distribution? (Select all that apply.)

a. | Mean, mode, and median are not equal. |

b. | The curve is asymmetrical. |

c. | There is bimodal distribution. |

d. | There is no mode. |

e. | More than 50% of the values lie to one side of the mean. |

ANS: A, B, E

Any curve that is not symmetrical is referred to as skewed or asymmetrical. A curve may be positively skewed, which means that the largest portion of data is below the mean. A curve can also be negatively skewed, which means that the largest portion of data is above the mean. In a skewed distribution*,* the mean, median, and mode are not equal. In a positively skewed distribution, the mean is greater than the median, which is greater than the mode. In a negatively skewed distribution, the mean is less than the median, which is less than the mode.

DIF: Cognitive Level: Analysis REF: Page 540

- Why can type I error and type II error not be
*both*present for one given hypothesis?

a. | Power analysis makes one type of error less likely. |

b. | One refers to rejecting the null hypothesis when it is true and the other to accepting it when it is false. |

c. | As beta rises, alpha falls. |

d. | The researcher sets both the alpha level and the beta level. |

e. | Qualitative research does not use power analysis. |

ANS: B, C

The researcher sets the values of two theoretical probabilities: (1) the probability of rejecting the null hypothesis when it is in fact true (alpha [α]; type I error), and (2) the probability of retaining the null hypothesis when it is in fact false (beta [ß]; type II error). In nursing research, alpha is usually set at 0.05, meaning that the researcher will allow a 5% or lower chance of making a type I error. The beta is frequently set to 0.20, meaning that the researcher will allow for a 20% or lower chance of making a type II error. A type II error occurs if the null hypothesis is regarded as true when, in fact, it is false.

DIF: Cognitive Level: Comprehension REF: Page 535

- A data set shows that the mean, median, and mode are the same. This means which of the following? (Select all that apply.)

a. | The distribution is bimodal. |

b. | The data are normally distributed. |

c. | The variables are dichotomous. |

d. | All data points are identical. |

e. | The kurtosis is symmetrical. |

f. | This may describe the normal curve. |

ANS: B, D, F

The theoretical normal curve is an expression of statistical theory. It is a theoretical frequency distribution of all *possible* scores. This theoretical normal curve is symmetrical and unimodal and has continuous values. The mean, median, and mode are equal. The distribution is completely defined by the mean and standard deviation. The data are normally distributed. If all data points are identical, their mean, median, and mode will be the same.

DIF: Cognitive Level: Analysis REF: Page 538