dr.carroll@optonline.net

# Blog by Dr. Susan Carroll

## How statistics can empower you - really!

The nuts and bolts of dissertation research will be presented in a user friendly manner. Roadblocks will be overcome, anxiety minimized, and dissertations completed so that you can get on with life.

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Essentially there are three benefits of using statistics.

1. To summarize information and present it in a straightforward, compelling manner. Some statistics called “measures of central tendency” allow one number to indicate the central message of a group of data.  A singular number can tell us how subjects performed. This is of great value. The measures (means, medians and modes) are used often to make decisions.  Another type of statistic is used to qualify the message of central tendency.  It is called “variability” and it can show how much dispersion or spread there is in your data set.  Again, from a single number we can tell if subjects are performing similarly or disparately to each other.
2. To tell us whether something we did had an impact and was worthwhile, so that we can take action.  Statistics are used to provide empirical evidence upon which we can make sound decisions.  They tell us how seriously we should regard differences among groups. Did gains in job performance occur by chance or are they statistically significant?  What treatment regimen works best? Did the new medicine make a difference?  What impact did our policy have? Should we maintain the status quo or make a change?  Should this program be modified, and if so, in what way?  We  can make smart choices with just a few simple statistical techniques such as t-tests, One Way Analysis of Variance procedures and Chi Square Analyses.
3. To document relationships that are meaningful so that we can take action. Correlation statistics can tell us whether two events are related, and to what degree.  Similar to the previously stated purpose, we can use these data to make decisions and to take action. For example, what is the relationship between exercise and heart health? Do teens who are absent from school get suspended more often? Is having breakfast related to job performance? Is voter participation related to logistical support (childcare, transportation)?  What impact does our town's emergency program have on subsequent civil preparedness?

For all of us today, statistics have emerged as fundamental tools.   Data are relied upon more and more often. To correctly provide answers to questions, we must be comfortable in determining what data are needed and then collecting, ordering, sorting, categorizing, summarizing, manipulating and reporting what is compiled. Statistics can make the process smooth and ultimately make life easy for the most critical step – interpreting what you find out.

### Research Designs: Avoiding the Headaches

Students that I work with are oftentimes despondent, frustrated and ready to quit altogether - due to Chapter Three. The underlying culprit for this is the research design. Unfortunately, many doctoral students have research designs that are poorly constructed. Some include innumerable variables - everything but the kitchen sink. Others want to change the world and have a design that would take years and years to complete. Others have no alignment among the design, the variables, the measurement tool, the research questions and the statistical analysis. Don't let these scenarios happen to you! The purpose of the research design is simple. It is to guide the collection of data so that the results provided will be interpretable, defensible and generalizable. And hopefully it will be a satisfying experience for you so that you will have the confidence to do more research after the degree is completed.

### Research Designs: Avoiding the Headaches

Students that I work with are oftentimes despondent, frustrated and ready to quit altogether - due to Chapter Three. The underlying culprit for this is the research design. Unfortunately, many doctoral students have research designs that are poorly constructed. Some include innumerable variables - everything but the kitchen sink. Others want to change the world and have a design that would take years and years to complete. Others have no alignment among the design, the variables, the measurement tool, the research questions and the statistical analysis. Don't let these scenarios happen to you! The purpose of the research design is simple. It is to guide the collection of data so that the results provided will be interpretable, defensible and generalizable. And hopefully it will be a satisfying experience for you so that you will have the confidence to do more research after the degree is completed.

### Why We Need A Roadmap: Research Designs

Research designs are your roadmap. They guide you in the collection of data so that your results will be interpretable and generalizable.

Many things have to be considered in even the simplest of designs. The research questions, null and alternate hypotheses you are interested in; your key variables, how extraneous variance will be controlled; how subjects will be selected, how large the sample should be, and assignment to groups or treatments if appropriate; how your data will be collected in a protocol that can be replicated in the future.

Thinking all of this out in advance is required for a dissertation. It is a good process because if you don't know where you are going, any road can take you there. Give this design phase some time and strategic thought. You will be happy that you did.

### More Dissertation Sampling Strategies than just Random

Simple random sampling is the premier way to draw your sample. There are other sampling strategies that are very useful as well. Here is a summary of a few procedures that you can consider.

Systematic sampling is an often-used sampling strategy and cost effective. Determine both the size of the population and the size of the sample you want to work with. Then, divide the sample size (n) into the population (N) size to get your key number, symbolized as “k”. You might use systematic sampling to select a sample of households in your community for a community survey. The City Hall might have the listing already available, in random order and with ID numbers in sequence. This saves you time and labor. If the City Hall will give you a set of mailing labels, then it will be all the better.

Cluster sampling is exactly what its title implies. You randomly select clusters or groups in a population instead of individuals. This would work if a state wanted to sample all third graders on their writing skills. They would randomly select third grade classrooms from all third grade classrooms in the state. Each of those classrooms selected would have 100% of the students in that classroom in the sample. The sampling unit or cluster is the third grade classroom not the individual student

Stratified sampling is used when the population is heterogeneous and it is important to represent the different strata or sub-populations. There is a proportional representation of strata in the sample - proportional to the population strata. We divide the entire population into strata (groups) to obtain groups of people that are more or less equal in some respect. Then, select a random sample from each stratum. This insures that no group is missed and improves the precision of our estimates. This might be used with different racial/ethnic groups if we wanted to insure that our sample included a proportional representation of African Americans, Asians and Latinos in addition to the Caucasians that pre-dominated our demographic pool.

### Population and Samples for Your Dissertation: The Difference!

The population in statistics includes all members of a defined group that we are studying or collecting information on.The operative descriptor is “all” – all children under the age of 5, senior executives, first offenders, hospital patients, or the entire community of households in whatever geographic circle we are focused on. So the “population” in our statistical study is defined by the “who” (target group) and the “where” (the geographic boundary that this group exists in).

A part of the population is called a sample. Samples are studied to obtain valuable information about the larger group called the population. Once we define our population, we can take a sample of the population to conduct our statistics.A sample is a subset or subgroup of our population.It is a proportion of the population, a slice of it, a part of it and all its characteristics.

A sample is a scientifically drawn group that actually possesses the same characteristics as the population – if it is drawn randomly.This may be hard for you to believe, but it is true.