Statistics in HC - Final Exam

Sampling bias

Not all members of the population are equally likely to be selected

Sampling error

A misrepresentation of an association between an exposure and the outcome of a study due to using too small a sample size. The larger the sample, size, the more valid the research.

Simple random sampling

A quick and convenient way to select a random sample by giving each member of the population a number then using a method of unknowingly choosing a number for use in the sample.

Cluster sampling

Choosing a random sample by dividing the population into groups, and then selecting a set of groups.

Systematic sampling

A method of choosing a random sample by selecting every nth person until the desired amount has been chosen.

A study was done to determine the age, number of times per week, and duration residents use a local park. The first house in the neighborhood around the park was selected randomly and then every eighth house in the neighborhood around the park was interviewed. The **sampling method** used in this scenario is known as __?

Systematic

A study was done to determine the age, number of times per week, and the duration residents use a local park. The first house in the neighborhood around the park was selected randomly and then every eighth house in the neighborhood around the park was interviewed. The **population** is __?

All the residents in all of the houses in the neighborhood that use the local park.

A study was done to determine the age, number of times per week, and the duration residents use a local park. The first house in the neighborhood around the park was selected randomly and then every eighth house in the neighborhood around the park was interviewed. **Duration** is what type of data?

Quantitative continuous

A study was done to determine the age, number of times per week, and the duration residents use a local park. The first house in the neighborhood around the park was selected randomly and then every eighth house in the neighborhood around the park was interviewed. **Number of times per week** is what type of data?

Quantitative discrete

Define ratio.

A comparison of two or more **unrelated**, independent variables.

Define proportion.

A comparison of two **related** parts of a whole.

How are ratios and proportions similar and different?

They are similar because they are both comparative and describe a situation in terms of numbers and amounts. They are different because ratios compare independent variables while proportions compare one variable to the entire group.

If a table is given with percentages of students who use computers at home, and it is given that the number of students who have and use 1 computer at home is 87% and those who have and use 2 computers at home is 75%, what percent of students do not have any computer at home?

13% (100-87)

How can the flow of statistics be described?

From simple, unclustered, unsupervised to complex, clustered, and supervised.

Is statistics an exact science?

No

Is convenience sampling a method of random sampling?

No

What is the difference between a control group and a placebo group?

A control group is a group that receives no treatment or a standard treatment, while a placebo group receives a fake treatment that has no therapeutic effect. The purpose of a control group is to provide a baseline for comparison, while a placebo group is used to test the effectiveness of a new treatment.

Define lurking variables.

Variables that are not anticipated in an experiment that could have affected the results.

Descriptive statistics refers to a sample and not a proportion. True/False

True

Mean, median, mode, and percentiles are measures of __.

Central tendency

Standard deviation, range, span, and variance are measures of __.

The spread of the data/variation

What are some non-numerical examples of descriptive statistics?

Box & Whisker plots, quartiles, IQR, outliers, pie charts, bar charts, histograms, pareto charts

What is the difference is uses for bar charts and histograms?

Bar charts are used for fewer n, qualitative categories, and have separated bars. Histograms are used for over 100 n, frequency or relative frequency data, and the bars are connected.

What is a pareto chart?

A bar chart in an ascending or descending order.

Contingency table

A tool used by statisticians to organize data in order to determine frequency of different variables.

Equally likely events

Experiments or events that have the same theoretical probability of occurring.

Mutually exclusive events

Outcomes that cannot be shared between sample space subsets at the same time.

Probability

The likelihood of something happening; the extent that something is likely to occur.

Sample space

A set that is concerned with all of the possible, unique outcomes of a probability experiment.

What is the notation for an AND compound probability?

The notation for an AND probability is represented by the symbol "∩".

What is the notation for an OR compound probability?

The notation for an OR compound probability is represented by the symbol "∪".

Given a Venn diagram, to find the set of an OR compound probability, what do you do?

List all of the elements of all circles involved in the OR probability, and use only the elements that are **unique.**

What is the test for independent events?

P(A|B) = P(A)

P(B|A) = P(B)

P(A and B) = P(A) x P(B)

Only one has to be true to be independent.

What is the test for mutually exclusive events?

P(A and B) = 0

What is the assumption for events before testing for independence and mutual exclusivity?

Assume the events are **dependent** and are **not** **mutually exclusive.**

List 3 distinct applications for using the normal and/or standard normal distributions.

1. Finding outliers
2. Finding percentiles
3. Determining variance in a data set

The empirical rule accounts for a total of __ % of the area under a bell-shaped curve.

99\.7

Unlike a uniform distribution, where we can use geometry to determine the area (probability) of a continuous random variable occurring, we require tables, a calculator, or software to provide areas (probabilities) under bell-shaped normal or standard normal distributions. True/False

True

A positive z-score value tells us how many __ the value x is above (or to the right of) the population mean.

standard deviations

By convention, probabilities calculated from x- or z-scores are those areas located to the LEFT of our value of interest. True/False

True

One good reason for sketching bell-shaped curves is to assess probability direction (and predicted values) relative to our x- or z-value of interest. True/False

True

Calculations of percentiles are an additional application for the central limit theorem, but are easier to calculate via programmable calculator or software. True/False

True

The calculated value of the term σ/√n is called the standard error of the mean. (It’s the population standard deviation divided by the square root of the sample size). True/False

True

Given an adequately large history of sample invoices, n, we could conceivably use the central limit theorem for sums to predict the probability that a lab manager goes on a wild spending spree and exceeds his average monthly budget limit. True/False

True

The population mean lifetime for prosthetic hips is 15.25 years. A medical device company has implemented some improvements in the manufacturing process and believes that the lifetime is now linger. A sample study of 49 new devices reveals a mean lifetime of 18.75 years with a standard deviation of 8.6 years. Identify the relevant variables.

Sample mean (x̄): 18.75

Population mean (μ): 15.25

Sample size (n): 49

Population (in this case it’s actually the sample) standard deviation (σ): 8.6

The central limit theorem states that __ and __ form their own normal distributions as sample sizes, n, increases.

Means and sums

If in calculating the probability of an event occurring using z-scores, you need to calculate the probability that an event occurs is **greater than or equal to** a value, you will need to subtract the calculated probability from 1 to get your final answer. True/False

True

The standard error term for a single x value distribution is only the standard deviation, while the standard error term for a sampling distribution of means is the standard deviation divided by the square root on n. True/False

True

List 3 point estimates AND their corresponding population parameters.

1\.) x̄ > μ

2\.) s > σ

3\.) p’ > p̂

List 3 commonly-used confidence levels AND their corresponding statistical significance values.

1\.) 0.90 sig. = 0.1

2\.) 0.95 sig. = 0.05

3\.) 0.99 sig. = 0.01

A hospital is trying to cut down on emergency room waiting times. It is interested in the amount of time patients must wait before being called back to be examined. An investigation committee randomly surveyed 263 patients. The sample mean was 0.75 hours with a sample standard deviation of 0.25 hours. Identify the variables and their corresponding vales and the EBM that was used given that the 95% CI is (0.12, 1.38).

x̄: 0.75

s: 0.25

n: 263

EBM: 0.63 (0.75+x=1.38)

If given that z(sub)(a/2), do you divide the given critical value by 2?

No

What are the two common critical values (do not divide by 2)?

1\.) 95% CL > 1.96

2\.) 99% CL > 2.053

A hypothesis test of a single population proportion, p, muse meet the conditions for __.

A binomial distribution.

Hypothesis testing can be regarded as a 5-step process that can involve all of the following EXCEPT __.

Directly testing the alternative hypothesis statement.

The preset or preconceived a (alpha) is a “significance level” that is also the probability of a Type I error. True/False

True

Hypothesis testing for matched or paired samples requires that the two samples are **independent** of each other. True/False

False

The **decision** step of hypothesis testing depends upon direct comparisons between __.

A calculated **p-value** and the a (alpha) value.

If the p-value is lower than the alpha, do you reject or not reject the null hypothesis?

REJECT

When writing the null and alternative hypotheses, you must include symbols (or written words) that are the __ of each other. Give an example.

Opposite

Ho: x̄ __

When does a Type 1 error occur?

When the null hypothesis is actually true but rejected.

When does a Type II error occur?

When the null hypothesis is actually false but NOT rejected (or accepted).

A student’s t-distribution is best used when the sample size is __.

Less than 30.

Can a student’s t-distribution be used when the sample size, n, is greater than 30?

Yes

A student’s t-distribution requires a degree of freedom value, which is n-1. True/False

True

In a student’s t-distribution with as sample sizes increase, what happens to the sample standard deviation?

Become constant

What is the first step in quality control?

1. Set up two contradictory hypothesis statements.

What is the second step in quality control?

2. Collect and sort sample data (throw out outliers)

What is the third step in quality control?

3. Determine correct distributions to perform hypothesis test.

What is the fourth step in quality control?

4. Analyze sample data (perform probability calculations (p-value) and make a decision based on the p-value and the alpha value.

What is the fifth/last step in quality control?

5. Write a meaningful conclusion.

Homogeneity test

Compared distributions need not be known

Independence test

Expected values are calculated from a contingency table

Variance test

Comparing the squared standard deviation of both a sample and its population

Goodness-of-fit test

Differences between (theoretical or given) expected values and observed (or actual) values

Absolute Risk

A subtracted difference between an exposed group and an un-exposed group

Relative Risk

A ratio of ratios

Odds Ratio

Determines an adverse condition as a fold-difference

Relative Risk, Absolute Risk, and the Odds Ratio are three calculations that similarly consider __.

The numbers of an adverse condition relative to a control group and a ratio or proportion relative to a control group

Which of the following is NOT a Chi-square test?

Test of Two Variances

What are the Chi-square tests?

Goodness-of-Fit, Independence, Single Variance, Homogeneity

Chi-square hypothesis tests necessarily consider __.

degrees of freedom, sums of each data set’s differences, and differences between observed and expected values

The most common and easiest way to determine if a new data set may be appropriate for a linear regression would be to __.

Construct a scatter plot

Linear regression outliers are determined from the differences in **y, the dependent variable.** True/False

True

If a hypothesis test concludes the correlation coefficient, r, is significantly different from zero, we say the correlation coefficient is “significant”. This implies a significant linear relationship between x and y and therefore we may use a regression line to model its linear relation in the population. True/False

True

The value of r is always __.

\-1 __

Is the coefficient of determination the same as r?

No

The coefficient of determination, when expressed as a percent, represents the percent of variation in the independent variable x that can be explained by variation in the dependent variable y using a line-of-best-fit. True/False

False

Given y = 33.27 + 0.152, where it has been determined that y shall not be a cost beyond $175 and where x is a range between 0 and 900 pages, determining the cost of a textbook with x=755 pages is an example of __.

interpolation and prediction

A good rule of thumb with regard to graphically and/or numerically determining outliers is by looking for points/values beyond __.

2 standard deviations from a line-of-best-fit

A line-of-best-fit __.

Is known as the Least-Squares Line, necessarily underestimates actual y data values above it and overestimates actual y values below it, and necessarily will have residuals that could be positive or negative

Which Chi-square test does not require you to know the distribution beforehand?

Homogeneity

Which Chi-square tests require contingency tables?

Independence and homogeneity

What is the purpose of a Cohen’s d?

Testing the effect of sample size

Is extrapolation and estimation reliable?

No

What does the correlation value (Pearson) indicate?

The strength and direction of the slope

What is the formula for the coefficient of determination? How is it expressed?

r^2; as a percent of y that can be explained by x

When is ANOVA best used and why?

When there are 3+ groups to compare to avoid multiple Type I errors

If the null hypothesis in an ANOVA test is **false**, one or more differences between groups is significant among all data groups tested. True/False

True

With independent samples and using proportions, the population must be ______ times the sample size, assume a normal distribution and uses pooled samples.

10-20; normal