Final Exam - Weeks 5 & 6

Question 1

Sample size calculation and choosing how many people should be sampled for a quantitative study depends on what factors?

Answer 1

• Research question
• How data will be analyzed
• Level of statistical significance
• Statistical power
• The effect size

Question 2

The level of statistical significance is usually chosen at ________ or _________.

Answer 2

0.05 or 0.01

Question 3

Why should the needed sample size be calculated before doing a study?

Answer 3

Make sure it is possible to recruit enough people into the study to detect a difference if it exists (have enough power to detect a difference).

Question 4

In quantitative sampling the goal is to select a representative sample so you can generalize to the larger study population = good _______________________

Answer 4

external validity

Question 5

Explain the 5 steps in sampling for quantitative studies.

Answer 5

1. Define population: by specifying criteria
2. Develop sampling plan: select the sampling method, try to minimize systematic error, simple random sampling, systematic, stratified, cluster
3. Determine sample size: will depend on a number of factors, including the size of the population, the level of precision you require, and the amount of variability in the population.
4. Implement sampling procedures:
5. Compare critical values of sample to population

Question 6

Explain systematic sampling.

Answer 6

Systematic sampling is a method of probability sampling where every nth member of a population is selected to be part of the sample. The process of selecting the sample involves selecting a random starting point from the population, and then selecting every nth element after that starting point.

Question 7

Explain stratified random sampling.

Answer 7

Stratified random sampling is a method of probability sampling where the population is divided into smaller subgroups, or strata, based on certain characteristics that are relevant to the study. Then, a random sample is selected from each stratum, proportional to the size of that stratum within the population. This ensures that each subgroup is represented in the sample, allowing for more accurate estimates of population characteristics.

Question 8

_______________ sampling has the advantage of ensuring that each subgroup is represented in the sample, allowing for more accurate estimates of population characteristics. It also reduces sampling error and increases precision.

Answer 8

Stratified random sampling.

Question 9

Explain cluster sampling.

Answer 9

Cluster sampling is a method of probability sampling where the population is divided into clusters or groups, and a random sample of those clusters is selected for inclusion in the study. This method is often used when the population is spread out over a large geographical area or is difficult to access.

Question 10

Suppose you want to conduct a study on the health of children in a particular region of a country. The region is divided into 20 school districts, and you want to select a sample of 400 children. What type of sampling might you use?

Answer 10

Cluster sampling (multistage sampling)

Question 11

When it is not feasible to get a probability sample, or a sampling frame of the population is not available then ___________ methods are used.

Answer 11

non-random.

Question 12

What is a sampling frame?

Answer 12

A sampling frame is a list or representation of the population from which a sample is selected. It serves as a basis for identifying and selecting the sample.

Question 13

Name some types of non-probability sampling.

Answer 13

Convenience sampling, purposive sampling, snowball sampling.

Question 14

Explain convenience sampling.

Answer 14

Individuals or units are selected for inclusion in the study based on their availability and willingness to participate. It is one of the easiest and least expensive methods of sampling, but it is also one of the least reliable.

Question 15

Explain purposive sampling.

Answer 15

Involves selecting individuals or units for inclusion in the study based on specific criteria or purpose. In this method, the researcher selects the sample based on their knowledge and understanding of the population and the research question (deliberate selection of participants based on certain criteria).

Question 16

Explain snowball sampling

Answer 16

Technically this type of sampling is a subtype of purposive sampling. Snowball sampling involves selecting participants based on referrals from other participants. The researcher starts with a few individuals who meet the selection criteria and then asks them to refer others who may also meet the criteria.

Question 17

What is methodological rigor and why is it important?

Answer 17

Methodological rigor refers to the degree to which a research study is designed and conducted with high standards of quality and rigor, such that the study can be trusted to produce valid and reliable results.

Methodological rigor is essential in research because it ensures that the study is conducted in a way that minimizes bias and maximizes the accuracy and generalizability of the findings. This includes designing the study with appropriate research questions and hypotheses, selecting appropriate research methods and measures, using appropriate statistical analyses, and ensuring that the sample is representative and the data is reliable.

Question 18

Explain what a priori hypothesis is.

Answer 18

A hypothesis based on assumed principles and deductions from conclusions of previous research, and are generated prior to a new study taking place.

Question 19

The two levels of quantitative statistical analysis are:

Answer 19

1. Descriptive: used to summarize the data
2. Inferential: used to draw conclusions about population parameters based on data from sample

Question 20

Frequency distribution, measures of central tendency, and measures of dispersion/variability are all what type of measure?

Answer 20

Descriptive measurements.

Question 21

What are measures of central tendency?

Answer 21

Statistics that describe the location of the center of the distribution of numerical and ordinal measurements (mean, median, mode).

Question 22

What are measures of dispersion/variability?

Answer 22

Statistics that describe the degree of dispersion of the differences among scores (range, standard deviation, variance, coefficient of variation, percentiles).

Question 23

Explain the difference between median, mean, and mode.

Answer 23

The mean is also known as the average and is calculated by adding up all the values in a set of data and dividing by the total number of values in the set.

The median is the middle value in a set of data that has been arranged in numerical order. If the data set has an even number of values, the median is calculated as the average of the two middle values.

The mode is the most frequently occurring value in a set of data. It is the value that appears the most number of times and can be used to describe the most common value in a data set.

Question 24

Explain normal distribution.

Answer 24

Normal distribution is a statistical concept used to describe the distribution of a set of data. It is a continuous probability distribution that is symmetrical around the mean, with most of the data falling close to the mean and fewer data points occurring away from the mean.

The normal distribution is characterized by two parameters: the mean and the standard deviation. The mean is the center of the distribution , and the standard deviation measures the spread of variability of the data around the mean.

Question 25

Explain skewed distribution.

Answer 25

A skewed distribution is a type of distribution in which the data is not evenly distributed around the mean, and is not symmetrical around the center of the distribution. One tail of the distribution is longer than the other, resulting in a lopsided or asymmetrical shape.

There are two types of skewed distributions: positively skewed (or right-skewed) and negatively skewed (or left skewed).

Skewed distributions can occur for various reasons, such as outliers or extreme values in the data, or because data in inherently skewed by nature.

Question 26

Skewed distributions can have a significant impact on statistical analysis, as they can affect the accuracy of measures of central tendency, such as the mean, median, and mode. In a skewed distribution, the mean is typically shifted towards the direction of the longer tail, and is not representative of the typical value of the data. Therefore, in such cases, the ________________ may be a more appropriate measure of central tendency.

Answer 26

median

Question 27

When conducting statistical analysis using continuous data, it is essential to examine the distribution of the data to determine whether it is appropriate to use certain statistical methods, why?

Answer 27

This is because the distribution of the data can have a significant impact on the validity and reliability of statistical tests.

In general, statistical methods assume that the data is normally distributed, meaning that it follows a bell-shaped curve, with most of the data clustering around the mean and fewer data points at the extremes. If the data is not normally distributed, it may be skewed or have outliers, which can affect the validity of statistical tests.

Question 28

What is continuous data?

Answer 28

Continuous data is data that can take on any value within a range, and is typically measured on a scale, such as time, weight, or height.

Question 29

If the data is __________________ distributed, statistical methods such as t-tests, ANOVA, and correlation can be used with confidence, as these methods are robust to normality assumptions. However, if the data is not _________________distributed, it may be necessary to use non-parametric methods, such as the Wilcoxon rank-sum test, the Kruskal-Wallis test, or Spearman’s rank correlation, which do not require normality assumptions.

Answer 29

normally

Question 30

Explain symmetrical distribution.

Answer 30

In statistics, a symmetrical distribution refers to a probability distribution where the values of the variable are evenly distributed on both sides of the mean, resulting in a mirror image when the distribution is folded in half. In other words, the left half of the distribution is a mirror image of the right half.

Examples of symmetrical distributions include the normal distribution (also known as the Gaussian distribution) and the uniform distribution. In a normal distribution, the mean, median, and mode are all equal and the distribution is perfectly symmetrical around the mean. In a uniform distribution, all values have an equal probability of occurring, resulting in a symmetrical distribution.

Question 31

When data is _______________ distributed, the mean and median are equal, and the standard deviation can be used to determine the variability of the data.

Answer 31

symmetrically

Question 32

For skewed distribution why is it more appropriate to use the range of values and the median to describe the distribution of the data?

Answer 32

The range of values represents the spread of the data and gives an idea of how far apart the values are from each other. The median, on the other hand, is the middle value in the data set and is not affected by extreme values.

Using the median and range of values allows us to describe the central tendency and variability of the data in a more robust and accurate way than relying solely on the mean. For example, if the data is positively skewed, the mean will be greater than the median, and if it is negatively skewed, the mean will be less than the median. In such cases, using the median and range of values can give a more accurate picture of the distribution.

Question 33

The median is not affected by extreme values , true or false?

Answer 33

True.

Question 34

What are measures of association?

Answer 34

Measures of association are statistical techniques used to describe and quantify the relationship between two or more variables. These measures help determine the strength and direction of the association between variables. There are different types of measures of association, including correlation coefficients, contingency coefficients, and regression coefficients.

Question 35

A symmetrical distribution of numerical data used in most statistical tests, if sample size is >100 this distribution is usually used.

Answer 35

Normal distribution.

Question 36

A probability distribution similar to the standard normal distribution, used to test hypotheses involving numerical data for small sample sizes (N<30).

Answer 36

T-distribution.

Question 37

When distribution is not normal, and non-parametric methods are used.

Answer 37

Skewed distribution.

Question 38

Explain correlation coefficients and in particular Pearson’s correlation coefficents.

Answer 38

A measure of association. Correlation coefficients are used to describe the strength and direction of the relationship between two continuous variables.

Pearson’s correlation is used with interval data and reflects the linear relationship between two variables.

+1 = perfect positive correlation (linear relationship)
-1 = perfect negative correlation (linear relationship)
0 = no linear relationship

Question 39

Explain Spearman Rank Correlation (what is it?).

Answer 39

A measure of association. Non-parametric measure of the strength and direction between the association between two variables. It is used when the variables are measured on an ordinal or continuous scale and the assumption of normality or linearity is violated.

Question 40

Is odds ratio and relative risk a measure of association?

Answer 40

Yes, both are considered a measure of association as they measure the relationship between two categorical variables.

Question 41

Explain ANOVA.

Answer 41

ANOVA stands for analysis or variance. It is a statistical method for comparing the means of two or more groups or populations. ANOVA tests whether the means of the groups are significantly different from each other, based on the variation in the data.

Question 42

_____________ is commonly used when comparing the means of more than two groups, and is an extension of the t-test for two groups. __________ can be used with both categorical and continuous variables, and can also be used to determine whether there is an interaction effect between two or more variables.

Answer 42

ANOVA

Question 43

When you do ANOVA you get a test statistic called the ______________ this _____________ is associated with a particular p-value, this p-value will tell you whether the means are statistically different.

Answer 43

F statistic.

Question 44

The basic idea behind ANOVA is to divide the total variation in the data into two components: _________________ and __________________.

Answer 44

Variation between groups and variation within groups.

If the variation between groups is greater than the variation within groups, then there is evidence that the means of the groups are significantly different from each other.

Question 45

Explain the F-statistic.

Answer 45

ANOVA produces an F-statistic, which is calculated by dividing the variation between groups by the variation within groups. If the F-statistic is large enough, indicating that the variation between groups is significantly larger than the variation within groups, then we reject the null hypothesis of no difference between the groups.

Question 46

If the populations from which data to be analyzed by ANOVA violate one or more of the assumptions, the results of the analysis may be incorrect of misleading, what are these assumptions?

Answer 46

• Independence: measures are independent of each other (no association), if not true then one-way ANOVA is not appropriate.
• Normality: measures are normally distributed, if not true then ANOVA may not be able to detect a difference when it exists.

Question 47

The __________ the sample, the less variance and the more power to detect differences.

Answer 47

larger

Question 48

____________________ determines whether a null hypothesis can be rejected.

Answer 48

Statistical significance.

Question 49

The researcher calculates a p-value (based on the distribution of values), which is the probability of observing an effect given that the ______________ is true.

Answer 49

Null hypothesis.

Question 50

The null hypothesis is rejected if the p-value is __________ than the significance level.

Answer 50

less

Question 51

If a research question states:
“Do adults 65 and older who receive occupational therapy services on restorative care units have higher levels or leisure activity participation post-discharge than those who do not receive these services?”

What might the null hypothesis and alternative hypothesis be?

Answer 51

H0 (null hypothesis): There is no difference in leisure activities in the first month post-discharge between older adults who receive OT services and those who do not”

HA (alternative hypothesis): Older adults who receive OT services will participate in significantly more leisure activities post-discharge in the first month than those who do not receive OT services.

Question 52

The lower the p-value, the ______________ the statistical significance of the observed difference.

Answer 52

Lower.

Question 53

A _________ is a measure of the probability that an observed difference could have occurred just by random chance.

Answer 53

p-value

Question 54

P-value greater than or equal to 0.05

Answer 54

Not enough evidence to reject the null hypothesis, statistically non-significant.

Question 55

P-value lesser than or equal to 0.05

Answer 55

Enough evidence to reject the null hypothesis, statistically significant.

Question 56

Sample size needed to test a hypothesis depends on four factors:

Answer 56

1. Expected difference between the two groups
2. Variability of the data
3. Power of the study (usually at least 80%)
4. Level of significance accepted (usually 5%)

Question 57

In research the sample size should be large enough to avoid Type I and Type II error, explain these types of error.

Answer 57

Type I error is the incorrect rejection of a true null hypothesis.

Type II error is the failure to reject a false null hypothesis.

Question 58

p-value=0.07

Is this result statistically significant?

Answer 58

No, the p-value is larger than 0.05