# Statistics GCU Essay

Explain the importance of random sampling. What problems/limitations could prevent a truly random sampling and how can they be prevented? Probability sampling, also known as random sampling, requires that every member of the study population have an equal opportunity to be chosen as a study subject. For each member of the population to have an equal opportunity to be chosen, the sampling method must select members randomly. Probability sampling allows every facet of the study population to be represented without researcher bias.

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Four common sampling designs have been developed for selection of a random sample: simple random sampling, stratified random sampling, cluster sampling, and systematic sampling (Burns & Grove, 2007). Simple random sampling is achieved by random selection of members from the sampling frame. The random selection can be accomplished many different ways, but the most common is using a computer program to randomly select the sample. Another example would be to assign each potential subject a number, and then randomly select numbers from a random numbers table to fulfill the required number of subjects for the sample.

Stratified random sampling is used when the researcher knows some of the variables within a population that will affect the representativeness of the sample. Some examples of variables include age, gender, ethnicity, and medical diagnosis. Thus, subjects are selected randomly on the basis of their classification into the selected stratum. The strata ensure that all levels of the variable(s) are represented in the sample. For example, age could be the variable, and after stratification, the sample might include equal numbers of subjects in the established age ranges of 20–39, 40–59, 60–79, and over 80.

Researchers use cluster sampling in two different situations: (1) when the time and travel necessary to use simple random sampling would be prohibitive, and (2) when the specific elements of a population are unknown, therefore making it impossible to develop a sampling frame. In either of these cases, a list of institutions or organizations associated with the elements of interest can often be obtained. To conduct cluster sampling, a list of all the states, cities, institutions, or organizations associated with the elements of the population is developed.

The states, cities, institutions, or organizations are then randomly selected from the list to form the sample. Of note is the fact that subjects obtained from the same institution are likely to be somewhat correlated, thus not completely independent (Burns & Grove, 2005). Systematic sampling requires an ordered list of all of the members of the population. Individuals are selected through a process that accepts every kth member on the list using a randomly selected starting point. k is calculated based on the size of population and the sample size desired.

For example, if the population has 1,000 potential subjects and a sample size of 100 is desired, then k = 1,000 ? 100 = 10. The initial starting point must be random for the sample to be considered a probability sample. Also, steps must be taken to ensure that the original list was not ordered in any way that could affect the study. (Grove 57-58) A problem with random sampling would be if you’re looking for specific information about your chosen subject and the people whom give you results for your study don’t have any knowledge or conditions that relate to your topic. Grove, Susan K.

Statistics for Health Care Research: A Practical Workbook. W. B. Saunders Company, 022007. Jeanette, I agree with you regarding if samples in studies are not taken randomly then they would result in possible biases with in the community. Asking someone in person to take a survey could also be biases in regards to the location you are trying to promote people to answer the survey such as a mall or grocery store. It truly seems difficult to do a random survey in regards to people being selected and people participating. It seems everywhere we go these days want a survey to be completed.

Cheryl, Great example you provided. It sounds like a great example of probability sampling which is also called random sampling where each person chosen to participate each have equal opportunity to be selected. When choosing the random sampling they have to be chosen without any bias towards the results that are being studied. Jan 7th 05:03pm Cheryl, I agree with your posting that when dealing with a larger population obtaining participants can be a very time consuming process and it needs to be taken in account for when performing your population selection.

If we are surveying a certain element of a reportable disease process I wonder if using the local county infectious disease data would be possible. Laisamma, It sounds like using the stratified random sampling would be a good choice for using a particular group of people. In stratified random sampling the individuals conducting the research know some things about the community that is providing date such as age, gender, ethnicity, and medical diagnosis. This is also a good option when there is a time restraint to obtain the information that is being gathered.

The survey would also have to be ensured it is written in a way that the average person can clearly understand the question to get a proper answer. DQ2 Explain each sampling technique discussed in the “Visual Learner: Statistics” in your own words, and give examples of when each technique would be appropriate. Stratified sample: Puts a population of people in two or more groups that have common characteristics then gain a population from each group. An example would be a group of nursing students at different local schools and choosing a few from each school to create a comprehensive study group.

Cluster sampling: A population is divided into “clusters”, and one whole “cluster” is chosen. An example could be taking each floor of a hospital and call them a cluster, then the whole third floor is chosen to evaluate housekeeping efforts. Random sample: Each person selected with no particular commonality considered. An example is walking through the downtown area randomly asking the community to take a survey. Simple random sample: There is a group of people put together but have equal odds of being selected.

An example is if we were leaving GCU campus and the safety patrol began to ask the students how they felt about safety. Jan 9th 8:08pm Carrie, Great response to the original posting, I agree that even in the example of simple random sampling there could be some example of basis such as age, ethnicity, religion, and educational background. It appears that every option for choosing a sample of individuals has pro’s and con’s for each. I am certainly going to think about articles differently now after learning how the participants are chosen. Jan 10th 07:28 a Victor,

Thank you for your response, I would have to agree with you that it is nearly impossible to study the entire population that you are interested in. I believe the largest flaw with this sort of selection is there is a larger chance that the people will have no relation to what it is you’re seeking a survey type of answer from. For example if you are studying the relation the Native Americans and their risk factors for diabetes and cirrhosis and the sample is taken from non-native American populations. WEEK FIVE DQ1 Explain when a z-test would be appropriate over a t-test.

T test is used if measuring a limited survey size and variables are evenly distributed, a T test could be an optimal choice if you don’t know the standard deviation, and there are less than 30 results. Using the Z test is a good choice if you know the standard deviation, and you have more than 30 participants. The test statistic used to determine the significance of a regression coefficient may be t (from t-test) or F (from ANOVA). Small sample sizes decrease the possibility of obtaining statistical significance. (Burns,2011) Burns, Grove.

Understanding Nursing Research, 5th Edition. W. B. Saunders Company, 2011. Toni, I agree with you that a T-test is an optimal choice when there is a sample size of less than thirty individuals. A good example of when a T-test would be sufficient in representing a sample size would be if all the freshmen in a selected high school were asked to do a survey but only one home room class completed the survey. Shija, Thank you for responding to my posting and adding the important information regarding the difference of the two different types of T tests.

The two different types of T tests have two different means to compare, this can be an important objective of there are more than one thing the owner of the survey is attempting to gather data upon. Thank-you again. DQ2 Researchers routinely choose an alpha level of 0. 05 for testing their hypotheses. What are some experiments for which you might want a lower alpha level (e. g. , 0. 01)? What are some situations in which you might accept a higher level (e. g. , 0. 1)? To test the assumption of no difference, a cutoff point is selected before data collection.

The cutoff point, referred to as alpha (? ), or the level of statistical significance, is the probability level at which the results of statistical analysis are judged to indicate a statistically significant difference between the groups. The level of significance selected for most nursing studies is 0. 05. This means that if the level of significance found in the statistical analysis is 0. 05 or less, the experimental and comparison groups are considered to be significantly different (members of different populations). In some studies, the more rigorous level of significance of 0.

01 may be chosen. This may be written as ? = 0. 01, particularly in tables and figures. (Burns, 2011) An example where a lower alpha level such as 0. 01 would be if you’re studying the death rate of anything, and an example where you may accept a higher alpha level than 0. 1 would be the results of side effects of medication interactions. Burns, Grove. Understanding Nursing Research, 5th Edition. W. B. Saunders Company, 2011. THE PEOPLE THAT RESPONDED TO MY SECOND DQ QUESTION Laisamma, Thank you for reminding me about the high alpha level is also related with high type one error and vise-versa.

I agree with you that when you’re experimenting with something delicate the type one error should be as low as possible. I also believe that when the risk of type one error is a possible outcome there should be several studies done to prove there is in fact a low error ratio. Angela, I agree with you that it seems logical for the alpha to be at a certain level of low depending on what the consequences are. It would make since that a higher level would be acceptable if it is related to a type of weight loss measure.

It is also logical that a low as possible alpha number is more acceptable when it is related to the possibility of death or major bodily harm. DQ2 Jan 13th 03:04 pm Annie, I agree that when researching the effectiveness of a new drug and its side effects the lower alpha number is more desirable in order to determine if the new drug is in fact effective. The alpha number should also be lower for the risk of death as a result of the medication. The alpha number could be higher with other side effects that are experienced such as upset stomach and other random complaints associated with the use of the drug.

DQ 1 January 15th 05:23p Daisy, Thank you for your informative posting. I agree with you that measuring the variable of a population can be stressful and time consuming for the researcher. It makes more since that a T test is selected in order to test a hypothesis that could require a smaller sample to be surveyed. The explanation of a Z test showing it is a larger population with a standard deviation because the results can have a larger scale of responses make more since. WEEK SIX DQ1 How would you explain the analysis of variance, assuming that your audience has not had a statistics class before?

If I were to explain variance to an individual that has never had statistics I would remind them the math concept of mean, mean and median. I would then elaborate on the mean and how majority of survey participants could answer a particular question one way but the difference of how far from the median is measured by variance. Analysis of variance (ANOVA) tests for differences between means of dependent variables. ANOVA is more flexible than other analyses, because it can be used to examine data from two or more groups.

There are many types of ANOVA, some developed for analysis of data from complex experimental designs, such as those using blocking or repeated measures (Burns & Grove, 2009). Rather than focusing just on differences between means, ANOVA tests for differences in variance. One source of variance is the variance within each group, because individual scores in the group will vary from the group mean. This variance is referred to as the within-group variance. Another source of variation is variation of the group means around the grand mean, which is referred to as the between-group variance.

The assumption is that if all of the samples are drawn from the same population, these two sources of variance will exhibit little difference. When these two types of variance are combined, they are referred to as the total variance. The test for ANOVA is always one-tailed. (Burns, 2011) Burns, Grove. Understanding Nursing Research, 5th Edition. W. B. Saunders Company, 2011. DQ2 What is an interaction? Describe an example and identify the variables within your population (work, social, academic, etc. ) for which you might expect interactions?

Hypothesis stating the specific nature of the interaction or relationship between two or more variables. (Burns,2011). Investigators use correlational analyses to identify relationships between or among variables. The purpose of the analysis may be to describe relationships between variables, clarify the relationships among theoretical concepts, or assist in identifying possible causal relationships, which can then be tested by causal analyses. All of the data for the analysis need to be from a single population from which values were available on all variables to be examined in a correlational analysis.

Data measured at the interval level provide the best information on the nature of the relationship. However, analysis procedures are available for most levels of measurement. Data for a correlational analysis also need to span the full range of possible values on each variable used in the analysis. For example, if values for a particular variable can range from a low of 1 to a high of 9, each of the values from 1 to 9 will probably be found in subjects in the data set. If all or most of the values are in the middle of that scoring range (4, 5, and 6) and few or none have extreme values, a full understanding of the

relationship cannot be obtained from the analysis. Thus, large samples with diverse scores are desirable for correlational analyses. (Burns, 2011). Variables within work, personal, and educational interactions can be different for a variety of reasons. The way each person acts in certain location and/or different communities can be compared to black and white. The way we interact with each other as class room peers is different than the way we practice being a nurse at work and also different than the way we are on a personal/family level.

Burns, Grove. Understanding Nursing Research, 5th Edition. W. B. Saunders Company, 2011. WEEK SEVEN DQ1 Describe the error in the conclusion. Given: There is a linear correlation between the number of cigarettes smoked and the pulse rate. As the number of cigarettes increases the pulse rate increases. Conclusion: Cigarettes cause the pulse rate to increase. DQ2 Now that you are familiar with the basic concepts of statistics, what are some examples of when you have seen or heard statistics used inappropriately?