Statistical Analysis for your Dissertation and Thesis

What types of statistical analysis are appropriate for a dissertation or thesis?

Multivariate statistics are usually appropriate but not exclusively used. I help graduate students everyday with dissertations and theses that utilize simple linear regressions, correlations, and t-tests, however, most institutions and committees want to see multivariate statistics used by their graduate students. That said, here is a very short list of the common ones.

Multiple Regression

Multiple regression for your dissertation or thesis will simply include more than one predictor. The advantage to using this statistical test for your dissertation or thesis is that you include multiple variables in your model predicting your variable of interest. Very rarely – if ever – is it the case that only one variable is responsible for values of another variable. I like an example using the Super Bowl. I may be able to predict a good percentage of Super Bowl victories with salaries, but we all know there are many more factors involved in predicting Super Bowl victories, such as injuries, weather, experience, and strength of schedule. Including multiple predictors makes for a more accurate model. Get help with using multiple regressions for your Master's thesis, Master's dissertation, Ph.D. thesis, or Ph.D. dissertation.

Logistic Regression

The logic behind the multiple regression applies to the logistic regression, except that the logistic regression utilizes an odds ratio to predict the occurrence of a dichotomous variable. Get help with using logistic regressions for your Master's thesis, Master's dissertation, Ph.D. thesis, or Ph.D. dissertation.

n – way ANOVA (Analysis of Variance) or Factorial ANOVA(Analysis of Variance)

The n in this case is simply referring to the virtually limitless number of independent variables that can be used in an ANOVA. A two-way ANOVA is the equivalent of conducting two ANOVAs or t-tests in one test and is simply a factorial ANOVA. A factorial ANOVA is just an ANOVA with two or more independent variables. An n-way ANOVA or factorial ANOVA could have three, four, five, or more independent variables. This method also allows for not just testing of differences between the groups but also testing of interactions between the independent variables. Get help with n-way ANOVA factorial ANOVA for your Master's thesis, Master's dissertation, Ph.D. thesis, or Ph.D. dissertation.

Mixed ANOVA(Analysis of Variance)

Again, the logic behind this test is the same as the n-way ANOVA or factorial ANOVA, but is the equivalent of conducting:

• a dependent samples t-test or paired samples t-test and an independent samples t-test or two sample t-test at the same time.

• a repeated measures ANOVA and simple ANOVA at the same time. 
  

The complexity of the test depends completely on the number of variables involved in the statistical analysis. The effect of conducting a mixed ANOVA is the increase in power from conducting multiple statistical tests in one test, while protecting your alpha in the process. Get help with using mixed ANOVA for your Master's thesis, Master's dissertation, Ph.D. thesis, or Ph.D. dissertation.

MANOVA (Multivariate Analysis of Variance)

The same logic again, except this time we are analyzing multiple dependent variables. For example, we may want to test for significant differences in GPA, SAT scores, and ACT scores, by religious affiliation. We can do all of these comparisons at the same time in the same test with the MANOVA or multivariate analysis of variance. This is a favorite of many a professional researcher and committee. Get help with using MANOVA or multivariate analysis of variance for your Master's thesis, Master's dissertation, Ph.D. thesis, or Ph.D. dissertation.

ANCOVA (Analysis of Covariance) MANCOVA (Multivariate Analysis of Covariance

These have the same benefits and accomplish the same thing as their siblings without the "C" or "Co" but add that capability of excluding variables that could somehow invalidate your results. To do this, the ANCOVA and the MANCOVA utilize a control variable. For example, if I wanted to know if there is a significant difference in GPA between college students, there could be any number of factors that could cause the difference. But by isolating the effect those factors have on my test, I am able to test for real differences. In this case I might control for socioeconomic status and the number of extracurricular activities. Utilizing the control variable will do a great deal to silence the critics of your research that may attribute the differences you found to the existence of some extraneous, unidentified, and unaccounted for variable. Get help with using ANCOVAs (analysis of covariance) or MANCOVAs (multivariate analysis of covariance) for your Master's thesis, Master's dissertation, Ph.D. thesis, or Ph.D. dissertation.

Doubly Multivariate Analysis of Covariance

I just thought I would throw this in here to get you thinking a little about what's possible. If your head's spinning at this point, click here and I will be more than happy to help you with your statistics for your dissertation or thesis.

Bivariate Correlations Continued

To this point I have been writing about what I thought people might be interested in reading, but I thought I would start taking requests… Debussy's Clair de Lune, 50 Cent, Michael Bolton, Britney Spears… okay maybe not Michael Bolton. Post what you would like to see a blog entry about and I will do my best to comply.

It seems a great number of you are interested in bivariate correlation, so here is another entry on this favorite of statistical tests. I also think I could be a bit more comprehensive on the assumptions of ANOVA, so look for that in the very near future. I also plan on covering the assumptions of bivariate correlation. In the meantime…

What is bivariate correlation?

A bivariate correlation is a statistical test that measures the association or relationship between two continuous/interval/ordinal level variables. This test will use probability and tell the researcher the nature of the relationship between the two variables, but not the direction of the relationship in the sense of describing causality…but I digress.

How to interpret bivariate correlation

To understand how to interpret a bivariate correlation, we have to first understand what the possible results are. If the correlation is significant, our correlation coefficient will be either positive or negative.  

Positive Correlation Coefficients

A positive correlation coefficient means that the relationship between the two variables is positive and that the variables move in the same direction. It also means that an increase in say… height, corresponds with an increase in weight. Stated another way, "As height increases, weight also increases, or as weight increases, height also increases."  

Negative Correlation Coefficients

A negative correlation coefficient means that the relationship between the two variables is negative and means that the variables move in opposite directions. Using the same example, we would say, "As height increases, weight decreases, or as weight increases, height decreases." 

The sign of the correlation coefficient tells us the nature of the relationship, as in one variable decreasing as one variable is increasing, or both variables increasing or decreasing together, but does not tell us how one variable affects another variable.  

Note that the sign of the correlation – negative or positive – can be interpreted two ways. With a positive correlation, as height increases, weight also increases, or as weight increases, height also increases. Both are correct. For a negative correlation, as weight increases, height decreases, or as height increases, weight decreases. I hope this isn't confusing. If any of you are having trouble, just post a comment and let me know. Better yet, let me do the correlations for you. Get help with how to interpret bivariate correlation coefficients for your Master's thesis, Master's dissertation, Ph.D. thesis, or Ph.D. dissertation. 

What does the bivariate correlation coefficient mean?

Correlation coefficients range from -1 to +1. If the bivariate correlation coefficient is -1, the relationship between the two variables is perfectly negative, and if the bivariate correlation coefficient is +1, the relationship between the two variables is perfectly positive. The closer the correlation coefficient is to -1 or +1, the stronger the relationship. The closer the correlation coefficient is to 0, the weaker the relationship.  

What is r²?

Often the correlation is interpreted in terms of the amount of variance explained in one variable by another variable – just remember, though, that the correlation is bidirectional and can be interpreted either way. If you are conducting a Pearson correlation, in your output, you will get a Pearson correlation coefficient or a product-moment correlation coefficient. Squaring this gives you…r². If I have a correlation coefficient of 0.4, then r² = 0.16 and would be interpreted as, "…16% of the variance in height is explained by weight," and vice versa. Get help with interpreting r² for your Master's thesis, Master's dissertation, Ph.D. thesis, or Ph.D. dissertation. 

How to report a Pearson correlation or a Pearson product-moment correlation?

Here is the gem of the entire post and free of charge.  

There was a significant, positive relationship between height and weight, r(98) = 0.40, p < 0.01, indicating that as height increases, weight also increases. Height accounted for 16% of the variance in weight.  

Of course there is more to it than this, such as determining which variable is going to be your dependent variable and which variable is going to be your independent variable, as well as how the appropriateness of the test and how it relates to the rest of your thesis or dissertation. Click here for help with writing bivariate correlations for your Master's thesis, Master's dissertation, Ph.D. thesis, or Ph.D. dissertation.  

What are the degrees of freedom for a bivariate correlation?

The degrees of freedom for a bivariate correlation are n – 2, where n is the sample size. This is also the number in the parenthesis above. The number in parenthesis is not the sample size.

How do I use the bivariate correlation?

If you were interested merely in the relationship of two variables, you would use the bivariate correlation. If you are interested in the effect of one variable on another variable, you would use a regression. The regression is the same as the correlation, but will tell you the specific impact one variable has on another variable in terms of the unstandardized beta coefficient and the standardized beta coefficient. It will also tell you the equation for the best fit line. We'll cover regressions very soon. Sometimes knowing the relationship of the two variables is enough, however, and if this is the case then bivariate correlation is the statistical test for you. Get help with how to use bivariate correlation for your Master's thesis, Master's dissertation, Ph.D. thesis, or Ph.D. dissertation. We even provide customized videos of your bivariate correlations being conducted.

 

The Dependent Samples t-test or the Paired Samples t-test

What is a dependent samples t-test or a paired samples t-test?

One of the most common statistical test, a dependent samples t-test, or a paired samples t-test, is used to find significant mean differences between two groups on a particular measure like SAT scores, ACT scores, GPA, height, or weight. In the case of the dependent samples t-test or a paired samples t-test, the groups of interest are related somehow as siblings or in the environment of a pretreatment vs. posttreatment setting. Either way, the two groups being compared are related somehow. Get help with dependent samples t-test

What is the difference between a dependent samples t-test or a paired samples t-test and an independent samples t-test?

Both tests are used to find significant differences between groups, but the independent samples t-test assumes the groups are not related to each other, while the dependent samples t-test or paired samples t-test assumes the groups are related to each other.

If you're familiar with the tests, a dependent samples t-test or paired samples t-test would be used to find differences within groups, while the independent samples t-test would be used to find differences between groups. Get help with dependent samples t-tests or independent samples t-tests

In a dependent samples t-test or a paired samples t-test, what is the independent variable and what is the dependent variable?

The independent variable and the dependent variable is the same in both the dependent samples t-test and the independent samples t-test. The variable of measure of the variable of interest is the dependent variable and the grouping variable is the independent variable. Get help with dependent samples t-test

Example of dependent samples t-test or a paired samples t-test

The most common use of the dependent samples t-test is in a pretreatment vs. posttreatment scenario where the researcher wants to test the effectiveness of a treatment.

1. The participants are tested pretreatment, to establish some kind of a baseline measure
   
2. The participants are then exposed to some kind of treatment
   
3. The participants are then tested posttreatment, for the purposes of comparison with the pretreatment scores
   

Having both pretreatment scores and the posttreatment scores for the same participants allows us to measure the effectiveness of the treatment, ceteris paribus. Get help with dependent samples t-test

Analysis of Variance (ANOVA)

An analysis of variance (ANOVA) is a statistical test conducted to examine difference in a continuous variable by a categorical variable. Let’s talk about:

1. The variables in ANOVA,
   
2. The assumptions of ANOVA,
   
3. The logic of ANOVA, and
   
4. What the ANOVA results indicate.
   

I am going to limit the conversation to a one-way ANOVA (i.e., an ANOVA with just 1 independent variable).

Variables in ANOVA

The variables in ANOVA: there are two variables in an ANOVA—a dependent variable and an independent variable. For example, let’s imagine we want to examine differences in SAT scores by gender. SAT scores are the ANOVA dependent variable (i.e., the scores depend on the participants), and it’s a continuous variable because the scores range from 200 to 800. Gender is the ANOVA independent variable (i.e., the designation of male and female are independent of the participant). Further, the independent variable is categorical—you are either male or female. (For more on variables, look here.)

The Assumptions of ANOVA

The assumptions of ANOVA: when an ANOVA is conducted, there are three assumptions. The first ANOVA assumption is that of independence—in this example, males’ scores are unrelated or unaffected with the females’ scores. This ANOVA assumption cannot be violated; if it is, then a different test needs to be conducted. The second ANOVA assumption is normality—that is, the distribution of females’ scores are not dissimilar from a normal bell curve.

The third ANOVA assumption is homogeneity of variance. This ANOVA assumption essentially assesses whether the standard deviation of males and females scores are similar (or homogeneous); that is that the males’118.15 standard deviation is not dissimilar from females standard deviation of 101.03 (Table 1). The ANOVA assumption is homogeneity of variance can be assessed with the Levene test. Table 2 shows the resulting Levene test statistic, where a non-significant difference (i.e., sig > .05) indicates no difference between the standard deviations and the assumption is met.

Table 1.

Descriptives
sat
	N	Mean	Std. Deviation
male	13	608.5385	118.15288
female	13	506.7692	101.03148
Total	26	557.6538	119.55415

Table 2.

Test of Homogeneity of Variances
sat
Levene Statistic	df1	df2	Sig.
.062	1	24	.806

The Logic of ANOVA

The logic of ANOVA: the logic of ANOVA is to test whether the males mean score (M=608.53) differs from females mean score (M=506.76).

What the ANOVA Results Indicate

What the ANOVA results indicate: the ANOVA (Table 3) shows the resulting F-value (F=5.571) with a significance level of .027, indicating that the F-value would occur by chance less than 3 times in 100. We can than say there is a statistically significant difference between the male and female scores, with male achieving a higher average scores compared to females.

Table 3.

	df	F	Sig.
Between Groups	1	5.571	.027
Within Groups	24
Total	25

For a customized, confidential help with ANOVA and/or conducting your statistical analysis, please email us at James@StatisticsSolutions.com or call Statistics Solutions Inc. at (877) 437-8622 for a free 30-minute consultation.

Statistical Analysis using Independent Samples t-test

This very common method of statistical analysis allows us to test the difference between two independent means. In layman’s terms, this means we are looking for differences between two groups of participants that are not related. In statistical terms, this means that the scores of the two groups are not correlated.

How is the independent samples t­-test used?

The independent samples t-test can be used when looking for differences between any two groups on a single measure, e.g. differences on SAT scores by gender, differences on GPA by gender, or differences on ACT scores by ethnicity (African American vs. Caucasian).

What types of variables can be used in an independent samples t-test?

There are two variables in an independent samples t-test, an independent variable and a dependent variable. The independent variable is the grouping variable and must be dichotomous or two groups. The dependent variable must be continuous/interval, however, sometimes it’s okay to use ordinal variables, but that is a whole other topic.

What are typical uses of the independent samples t-test?

Often, independent samples t-test are used to look for differences between control and experimental groups. Some research designs employ both an experimental group and a control group with measures before a treatment and after a treatment for both groups. While the statistical test for examining differences within the control group before and after the treatment and within the experimental group before and after the treatment is a dependent samples t-test, the statistical test for examining differences between the control group and the experimental before the treatment and then again after the treatment is an independent samples t-test.

If I am a researcher hoping that my additional math class as a treatment is effective, I am hoping to find that the control and experimental groups are the same pre-treatment, but different post-treatment. Hopefully, my experimental group would have higher math scores post treatment, than my control group. For information on conducting the independent samples t-test in SPSS, please see the information on www.

Statistical Analysis

How do I know what type of statistical analysis to conduct?

Researchers working on studies, theses, and dissertations, often ask this question. Ideally this is a question to ask at the beginning of the research project, rather than the end. It is at this point that research needs should be assessed and hypotheses determined. During the initial stages of planning is the time to involve a statistics consulting firm to help you formulate the basis of your study. There are many things that can influence the type of statistical analysis to use but here are a few important ones:

1. Empirical information (statistical analysis) related to your study

If you are at the point in your study or dissertation that you have begun to consider the type of statistical analysis you need to conduct, then hopefully you have considered the statistical analysis of other researchers in similar studies. It is wise to do this, if only for comparison purposes. However, utilizing the same statistical analysis that has been utilized by other researchers and experts in your field will lend credence to your findings and avoid the difficult, if not embarrassing, task of defending why you chose a different type of statistical analysis.

2. University/College requirements

While I don’t believe it appropriate, many colleges and universities stipulate the type of statistical analysis their dissertation candidates can use. Often, the statistical analysis requirement is the use of multivariate analysis. Make sure you are aware of any of these requirements prior to formulating your research questions and hypothesis.

3. Formulation of the research questions and hypothesis

It is very important to have an idea of the statistical analysis to be used before formulating your research questions, hypothesis, and methodology. The wording of your research questions and hypothesis will determine the type of statistical analysis to be conducted.

· Words like relationship and correlation, tend to correspond with correlational statistical analysis. Sometimes these words also represent regression statistical analysis, but usually correlational statistical analysis.

· Words like predict, affect, and impact tend to correspond with regression statistical analysis, both linear regression and logistic regression.

· Research questions using the difference tend to correspond with t-­tests, both dependent and independent and ANOVAs.

This means you should have an idea of the statistical analysis to be used before crafting your research questions and hypothesis. It is much easier to do this before the proposal is approved than after.

4. Ability of the researcher

While every researcher aspires to change the world, the statistical analysis should fit within the comfort and abilities of the researcher. If you are having difficulty formulating your methodology around statistical analysis with which you are comfortable, it may be wise to consult a statistics consulting firm to help you with the data analysis and statistical analysis. If you have had two or three statistics classes three years ago, you may not want to choose a complex statistical analysis utilizing structural equation modeling or even multivariate analysis. Though a statistics consulting firm will help tremendously in explaining and using complex analysis, you are ultimately the one that will be defending it and explaining it to your committee. Just a reminder, a wise person knows their limitations.

For a customized, confidential help formulating your research questions and hypothesis, and/or conducting your statistical analysis, please call Statistics Solutions Inc. (877) 437-8622 for a free 30 minute consultation .

Where can I find Dissertation Assistance?

Most students secure dissertation assistance in the dissertation process. Let’s face it, the dissertation is new terrain. Statistics Solutions are professional researchers and statisticians providing dissertation assistance in this new terrain. Most students need dissertation assistance with their method section—refining their research questions, selecting the correct data analysis plan, and justifying the sample size.

When you write your research questions, make sure each of the variables in your research questions can be measured, and use language in your questions that relates to the heart of what you want to know. For example, are you looking to examine differences on SAT scores by gender? If so, a t-test is the appropriate statistic to examine differences. Or are you seeking to predict SAT scores from gender? Here a linear regression would be the correct statistical test. You can see that the phrasing of the research question drives the type of analysis: this is the type of dissertation assistance that Statistics Solutions provides.

Frequently, justifying the sample size is dissertation assistance that students look for. Just like the phrasing of the research question drives the statistical test, the statistical test drives how many participants are necessary. Statistics Solutions frequently assists dissertation students daily with sample calculations and sample size equations.

When you get dissertation assistance, get assistance from individuals that have actually completed a dissertation! It only makes sense to get dissertation assistance from those who have personally traveled the dissertation path themselves.

If you have questions and need dissertation assistance, feel free to contact Statistics Solutions for a free 30-min consult. Our phone number is (877) 437-8622, or email us at: www.StatisticsSolutions.com.

Get the dissertation assistance that you need and the very best in finishing your dissertation!

Dissertation Writing

Where do I start with writing my dissertation?

My name is Dr. James Lani, and in this short blog, I hope to demystify aspects of the dissertation writing process, overcome dissertation writing barriers, have you feel confident that you can write your dissertation, and move on with your life.

What is the first step in the dissertation writing process?
The very first step to dissertation writing is overcoming your fear. Yes, the idea of writing a dissertation can be ominous. But here’s a key: your attitude is going to make the difference! For example, have you ever thought something was going to be hard—and then it was? The same principle applies in writing your dissertation writing. When something is new, we can get afraid—and writing a dissertation is no different. First, acknowledge that you made it this far, your almost there, and you can complete this too. I’m suggesting you acknowledge, and then overcome your fear (Yes, thank your fear and move on). Now let’s spend your time thinking and writing!

OK, we’re a bit more empowered, now what?
Obviously, dissertation writing implies you have something to write about—you need a dissertation topic! You don’t need a world changing dissertation topic, just a topic. I don’t agree that it has to be a “large project.” It’s a paper with components—that’s all.

Dissertation topic, dissertation writing, and time management books
Forget all of these dissertation writing books and time management books (heck, if we had enough time to read a book, we’d have already completed method section). Dissertation writing is a task to completed to be sure, but dissertation writing process need not be associated with a study in itself.

How do I write my dissertation?
I’m going to make this very easy. Start with the method section. I’ll tell you, if you can settle on a few research questions and find some survey instruments that can test those research questions, you are almost home. From there we can write the data analysis section (we can help: James@StatisticsSolutions.com; 877-437-8622), and get information on the reliability and validity of the instruments, almost always available from the instruments’ authors. You can then focus on the rationale for doing your study, then focus the lit review on the research variables of interest. This will get you through the proposal.

Dissertation Writing Help
Seek out help to write your dissertation. A company like ours (James@StatisticsSolutions.com; www.statisticssolutions.com) can help you organize your topic and research questions, and help with the dissertation writing process. I hate to confess that our company can organize a method section in one day! How can that be? Because we don’t have the baggage of “it’s tough,” and we’ve been doing it for 16 years. So get the help to move forward with your dissertation writing.

Final thoughts on the dissertation writing process and completing your dissertation
Life is not without bumps on the road, and writing a dissertation is no different. As an old friend once said, let the bumps on the road be your stepping stones rather than stumbling blocks. Get help, get support, get sleep, and if you’re depressed and anxious, get a therapist. Never get defeated, never give up. You can and will complete the dissertation writing process. I sincerely wish you well!
James Lani completed his dissertation in 2003 from Miami University in Oxford Ohio, an APA-approved Ph.D. program in Clinical Psychology. He was blessed with a chair that was tough on his dissertation writing. That toughness has now inspired James to assist literally thousands of students smooth the dissertation writing road, and help students move on with their best lives. His company, StatisticsSolutions.com is based in Clearwater, FL with office opening in New York City, Los Angeles, Atlanta, Austin, Phoenix, and Chicago. He can be reached at James@StatisticsSolutions.com or at 877-437-8622.

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.