What is included in the data analysis plan?

A critical component to theses' and dissertations' method section is the data analysis section or data analysis plan. The data analysis plan clearly identifies the specific statistical techniques (i.e., statistical tests) used to examine the research questions. Often, students get stuck in data analysis, or data analysis plan, because selecting the statistics can vary between parametric and non-parametric statistics. the data analysis plan describes not only the statistics, but the assumptions associated with these statistics. The data analysis plan can be a bit tricky: the specific statistics have to take into consideration the research questions and the type of data that the researcher is collecting(e.g., nominal data, interval data, etc.). A portion of the data analysis plan is to justify why these statistics selected are appropriate for a researcher's hypotheses and research questions. To give you an example for a data analysis plan, a researcher examining differences on an interval level variable (e.g., depression symptom) by gender, an independent sample t-test would be the appropriate statistical technique.

If you have any questions about the data analysis plan or justifying the appropriate statistics in the data analysis, feel free to visit us at www.StatisticsSolutions.com or call us at 877-437-8622. We are experts in writing data analysis and editing data analysis sections.

Chi Square

One of the most common statistical tests we are asked to run at Statistics Solutions is the chi-square, aka Pearson chi-square, cross-tabulation/cross-tab, ect... It seems like there is a lot of confusion about when to use this test and how to use this test. Let’s start out with the “when”.

Chi-square statistical analysis is used when we want to know if there is a relationship between 2 categorical or nominal variables. For example, say I want to know if there is a relationship between males and their level of education. Really, we are looking at a relationship between the variable gender, which is dichotomous (two levels or groups in the variable) with respondents or participants being either male or female, and the variable education, which we’ll say is also dichotomous (high school or below and above high school).

What is the relationship here? We might have hypothesized that there would be a significant relationship between males and education, the nature of which would be men tending to be less educated than women. If our chi-square test is significant - we’ll talk about what makes it significant later – we’ll see some pattern of relationship between these two groups.

Gender * Education Crosstabulation

Count

		Education		Total
		High School or Below	Above High School
Gender	Male	31	25	56
	Female	14	30	44
Total		45	55	100

This is the actual output table we would get if we ran this test. There is no real wrong way to look at the the numbers, since the chi-square is really telling us if the rows are significantly related to the columns.

You can see from the table that 31 participants were male and had an education level of High School or Below and looking at just that column we can see that far more males than females had an education level of High School or Below. There is another number that jumps out at me, and that is the Female row. Notice the 30. Within the Female row or group we could say, 30 had an education level Above High School compared to only 14 with an education level of High School or Below. This is fairly clear, but even more easily seen if we look at the percentages. Let’s look at percentages first within each of the education groups.

Again this is the exact table:

Gender * Education Crosstabulation

			Education		Total
			High School or Below	Above High School
Gender	Male	Count	31	25	56
		% within Education	68.9%	45.5%	56.0%
		% of Total	31.0%	25.0%	56.0%
	Female	Count	14	30	44
		% within Education	31.1%	54.5%	44.0%
		% of Total	14.0%	30.0%	44.0%
Total		Count	45	55	100
		% within Education	100.0%	100.0%	100.0%
		% of Total	45.0%	55.0%	100.0%

This table looks a little confusing, but look a closer look at the names and we can decipher what this means. The numbers of interest are bolded in red. The table shows that 68.9% of the participants/respondents are male and have an education level of High School or Below. You can see that the percentage of males in this education level is much higher than the percentage of females, which is 31.1%. In fact, there are more than twice as many males as females in the High School or Below education level.

What is exploratory factor analysis (EFA)?

Exploratory Factor Analysis is an item-reducing strategy intended to create factor scores. For example, if you have a 100 question survey, you probably don’t have 100 unique constructs/factors. Factor analysis would “boil-down” these 100 questions to perhaps 10 subscales or constructs.

Two important issues in Exploratory Factor Analysis is how many factors there are, and which questions load on (or relate) to that factor. There are several ways to determine the number of factors: scree plot, 70% or more of the variance accounted for, etc. After the number of factors is determined, the questions that go with each factor can be determined by taking your sample size, noting the critical value for a correlation given that sample, and doubling it. If you had 50 observations (participants), the critical value of the correlation at an alpha of .05 is .361; doubling this value equals .722. That is, questions that have a loading of .722 or more would go with that factor.

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What does a bivariate correlation indicate?

A correlation, or bivariate correlation, measures the relationship between two variables. The correlation measures the strength of the relationship.

The strength of a correlation ranges from the absolute value from 0 to 1; the closer the correlation is to 1, the stronger the relationship, the closer the correlation is to 0, the weaker the relationship. For example, the relationship between temperature and ice cream cones sold may be .80. This indicates a strong relationship. The direction can be positive or negative. For example, the positive correlation in the ice cream example is positive; as the temperature increase, ice cream cones sold increase. A negative correlation may be found between spending and saving in the bank; as spending increases, saving decrease.

There are other correlations, such as partial correlations, point-biserial correlations.

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What can a dissertation statistical consultant do for me?

A dissertation consultant should have been through the process of a dissertation because we know the challenges of committees and the importance of timely feedback.

Your consultant must be able to clarifying the research questions, assist with selecting the appropriate statistics, select the correct sample size given the statistical analyses selected, conducting the statistics while examining their assumptions and remedies of violations, write-up the results with APA tables, and clearly explain what the finding indicate. Further, you should get continued support!

If you have questions, feel free to contact Statistics Solutions for a free consult. Our phone number is (877) 437-8622 or email us at: www.StatisticsSolutions.com.

The best in finishing your dissertation!

How do I select a statistical consultant?

It only makes sense to hire a company where the consultant has dealt with dissertation committees (i.e., the consulting company have employees who have a doctorate degree) and has expertise in statistics (Ph.D. is preferred). Confirm their credentials—if they say they have a degree from Harvard Department of Statistics—call Harvard’s statistics department top confirm (I have a Ph.D. in Clinical Psychology from an APA-accredited program at Miami University in Oxford, Ohio).

Make sure the company is responsive, patient with answering your questions, and trust your experience with the potential company. Remember, you are the customer!

If you have questions, please feel free to call us at 877.437.8622 or visit our website at http://www.statisticssolutions.com/

How do I assess the assumptions of an independent sample t-test or ANOVA?

There are three main assumptions in these statistical techniques. The first, and most important, is independent of observations. That is, one participant does not influence the score of another participant. The second assumption is homogeneity of variance. ANOVA assumption can be tested by checking the SPSS box for “homogeneity tests.” For t-test, SPSS provides the Levene test as a default. The third assumption is normality assumption. This can be tested with a one-sample KS test. For more information you can email us at www.StatisticsSolutions.com or call 877-437-8622.

How do I calculate the sample size for my research?

Sample size is an elusive topic. While completing my master’s and doctorate degrees, the issue never arose! First, the sample size is determined in coordination with a preselected power (typically .80), alpha (typically .05), and an effect size (typically .50). Secondly, the sample size is different for different analyses (e.g., for multiple regression, t-tests, etc.) At www.StatisticsSolutions.com we use Cohen’s articles on statistical power and G-power (online) to calculate the required N. For more information you can email us at www.StatisticsSolutions.com or call us at 877-437-8622.