Dissertation Statistics Helper

07/22/2020

Stockholm Syndrome in Dissertation Students?

Stockholm Syndrome is a condition in which those held hostage by their captors develop an alliance with those captors. The captors in these circumstances hold all the cards. They control behavior through their power to punish, but they are also the benevolent distributors of positive reinforcement—food, water, blankets, etc. Stockholm Syndrome was first noted in 1973 when four individuals were taken hostage in a bank robbery in Stockholm, Sweden. After being released, the hostages would not testify against their captors and even defended the robbers' actions.

But Stockholm Syndrome isn’t just a phenomenon seen in those who were taken hostage by bank robbers or terrorists. It is not uncommon to see it in doctoral students who are in the throes of the dissertation process. I have worked on the doctoral dissertations of about a dozen students who sought their doctoral degrees from one of the large American universities that specialize in online doctorates. That school’s process is soul crushing, consisting of multiple reviews, each performed by individuals who have absolute authority to stop the dissertation dead in its tracks if they aren’t pleased or feel that they haven't been sufficiently kowtowed to. Absolute power corrupts absolutely, and that principle is manifested clearly in the behavior of these reviewers. Many times these people are as thoroughly confident in their ability as they are, in reality, incompetent. But they can demand anything, no explanation or justification needed, and the student must deliver. Or else the dissertation process stops. And when the next reviewer in the endless series of reviews demands just the opposite (yes, I’ve seen that), the student must deliver. Or else. And this continues until the university has squeezed the student dry—financially and emotionally—and moves on to the next victim.

The remarkable thing is that I’ve seen students working through the dissertation process at this institution (and, to be fair, at some other schools as well) who sided with their captors, attempting to explain the wisdom of the process to me, and justifying the abuse they received by pointing out that it was balanced by the most benevolent encouragement from the same reviewers who created the need for that encouragement in the first place! Good cop. Bad cop. All the same cop.

When I have suggested to some of these students that they’re the victims of academic bullying and manipulation, a few reacted defensively or even angrily. One such client recently terminated our consulting relationship me when I suggested that some push back was called for against a committee member who was requiring multiple reviews when one would do, demanding that statistical results be moved to chapter 5 from chapter 4 where they belonged, insisting that one statistic be substituted for an equivalent statistic (no justification offered), and making multiple other whimsical demands--whatever ticked his fancy at the moment it seemed. Stockholm Syndrome? I think so.

Wouldn't this make an interesting dissertation?! Good luck finding a committee, though!

03/10/2020

A Data Transformation Should Not Be Used to Make Outliers Appear to Be More Valid Than They Are

When a distribution of scores, particularly scores on a dependent variable, are non-normal and contain outliers, it is sometimes the case that a data transformation that normalizes the distribution also makes the outliers less extreme, even to the point that they are no longer recognized as outliers. Does this mean that the transformed outliers can be “saved” and that they needn’t be deleted? I don’t think so. Outliers are not just mathematically inconvenient values that exert a disproportionate effect on statistical outcomes and contribute to non-normal distributions. They are scores of questionable validity. Changing their numerical values through transformation and making them less extreme in the process doesn’t make them any more valid. Raw scores that are identified as invalid due to their outlier status as just as invalid once transformed, even though they may no longer be as extreme as transformed scores. Identify raw score outliers, delete them, and then use a normalizing transform if the distribution is still strongly non-normal. A data transformation should not be used to make bad data appear to be well behaved.

I provide research design and statistical consulting services to dissertation, thesis, and DNP capstone students whose universities allow the use of such services. For more information, check my website: https://DissertationStatsHelper.com. I do not check FaceBook messages. Please use the Contact page on my website.

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04/06/2019

G*Power does not provide any direct application for estimating sample size requirements for partial or semipartial (“part”) correlation analysis. Various workarounds are suggested online, ranging from the impossibly complicated to simply ignoring the covariates and using the same app within G*Power that is used for the Pearson correlation.

The procedure I favor is to use the G*Power app for estimating sample size (in a priori power analysis) or power (in post hoc power analysis) for tests of the significance of the individual predictors in multiple linear regression. This approach is based on the fact that the tests of significance of the individual predictors in SPSS multiple regression analysis are also the tests of the significance of the related partial and semipartial correlations.

Here is the G*Power procedure:

Tests > Correlation and regression > Linear multiple regression: Fixed model, single regression coefficient

Type of power analysis: a priori

Tail(s): chose one-tail if you have predicted the sign of the partial or semipartial correlation; chose two-tail if you’ve not made a prediction or are interested in a correlation in either direction

Effect size f-squared: Use .02 if you want to detect a weak population correlation, .15 for a medium population correlation, and .35 for a strong population correlation

Alpha err prob: your chosen level of significance, typically .05

Power (1 – beta err prob): your chosen level of statistical power, typically .80 which will give you a Type II error probability of .20

Number of predictors: set equal to the total number of variables in your partial or semipartial correlation analysis (X and Y and all the covariates) minus one.

If you’d like to see some additional tips and techniques, I hope you’ll visit my website: www.DissertationStatsHelper.com

If you need statistical consulting work, email me at [email protected]. (Please note that I don’t check FaceBook for messages.)

A PhD author of two statistics textbooks will guide you to a successful dissertation. Contact me today for a free initial consultation!

06/09/2018

In the presence of skewed data distributions, one or another of the commonly used data transformations (square-root, log10, or reciprocal) can help to normalize the data. Any of the texts by Tabachnick & Fidell are a good source of information about score transformations. Of course the transformed scores take on different numerical values than the original scores, sometimes even resulting in score reflection--the lowest original scores become the highest transformed scores and the highest original scores become the lowest transformed scores. Reflected scores can be (and should be) re-reflected (again, see Tabachnick and Fidell, 2013) to solve that problem, but nothing will change the fact that the transformed scores will still take on different values than the original scores. This can be vexing in some applications. For instance, where the mean of a set of original IQ score might have a value of 100 and be perfectly interpretable ("average"), the transformed mean might be 10, not a directly meaningful value. One should not make too much of these changed values, though. Assuming that one has re-reflected reflected scores, high transformed scores still reflect greater amounts of the attribute and low transformed scores still reflect lessor amounts of the attribute. This is a point that is missed by some, who make far too much of the fact that transformed scores take on different numerical values than the original scores, to the point that they believe that the transformed scores no longer measure the same construct that was measured by the original scores. The quickest way to dispell this misimpression is to examine the correlation between original and transformed scores. That correlation typically runs in the upper 0.90's. It is axiomatic in statistics that, to the extent that two variables are correlated, they measure the same thing. Data transformations do not change the construct being measured; just the score values and the shape of the distribution of the scores.

If you need statistics or research design assistance with your thesis, dissertation, DNP capstone research, or other project, I hope you'll check my website: www.DissertationStatsHelper.com

A PhD author of two statistics textbooks will guide you to a successful dissertation. Contact me today for a free initial consultation!

05/22/2018

Why is it that a dichotomously-scored (two-category) nominal scale variable can be used as a predictor in statistical procedures like multiple regression and discriminant analysis? (Yes, discriminant analysis too, notwithstanding statements from lots of authors that this method requires continuous predictor variables, i.e., interval or ratio scale variables.) It's because a dichotomously-scored nominal scale variable (often called a binary variable, because the only two scores are 0 and 1) is actually a ratio scale variable. How can it be that what appears to be a 2-category nominal variable is actually a ratio scale variable? Here's your answer. A ratio variable is one in which a score of 0 = none of the attribute and each successive score point,--1, 2, 3, ...--represents one more fixed-sized unit of the attribute being measured. Now let's take the dichotomous variable, "Military Veteran," with two categories coded no = 0 and yes= 1. Someone with no military service is scored 0 because they possess none of the attribute being measured. Someone with military service is scored 1 because they possess one unit of military service. There don't happen to be any cases scored 2, 3, 4 or higher because we don't need those values. We just need 0 for none and 1 to represent those individuals with one "fixed size unit" of military service. But lack of need for scores above 1 doesn't somehow disqualify a binary variable from being ratio scale. Any dichotomous variable can therefore be treated as a nominal variable or as a ratio variable, whichever is more convenient at the moment.

If you are seeking assistance with your dissertation or other research, I hope that you will consider using my research design and statistical consulting services. Visit my webpage for complete information: www.DissertationStatsHelper.com or email me with a description of your project at [email protected]. (Please don't message me via FaceBook--I'm terrible about checking for those messages.)

A PhD author of two statistics textbooks will guide you to a successful dissertation. Contact me today for a free initial consultation!

05/26/2017

Should Multi-Item Inventories Contain Reverse-Worded Items?

One common practice used to control for one form of response bias when collecting rating scale data is to reverse-word some items. Survey respondents who are presented with a series of items that are all positively worded (e.g., "I think that statistics is fun." "I have a good time working with statistics." "I enjoy reading about statistics.") can lead some respondents to start checking all high (or all low) ratings without really thinking about what they're doing. By reverse-wording some of the items (e.g., "I do not think that statistics is fun." "I do not have a good time working with statistics." "I do not enjoy reading about statistics.") the idea is that respondents are forced to read the items more closely which should lead them to make more informed ratings. Of course reverse-worded items must be reverse-scored before total scores are calculated.

While this seems like a good idea in theory, in practice I've observed something else when inventories are constructed of a mixture of positively-worded and negatively-worded items. Factor analyses of these inventories frequently finds two factors--one on which positively-worded items load strongly, and one on which negatively-worded items load strongly. That means that the internal consistency of the inventory is challenged and that means the inventory totals (or averages) are invalid.

Perhaps a more desirable approach to breaking response bias is to mix together the items from two (or more) inventories measuring very different constructs. Word items in both inventories in a positive direction, but force respondents to slow down and read the items by ensuring that any two consecutive items deal with different issues.

If you are working on a dissertation, thesis, or DNP capstone research project and need a methodologist, I hope you'll check my website: www.DissertationStatsHelper.com

Statistical consulting for students working on doctoral dissertations and masters theses.

09/03/2016

Measuring Interrater Reliability When the Measure is Categorical: Cohen's Kappa and a Handy Kappa Calculator

When a construct is measured subjectively by a scorer, it is always wise to check the reliability of the scores. If the scores assigned are numbers along a continuum, inter-scorer and intra-scorer reliability are both typically measured by computing a Pearson correlation between the two sets of scores. Well trained and motivated scorers can be expected to produce inter- or intra-scorer reliability coefficients of .80 or higher. If the reliability correlations run lower than this, the quality of the data (or the scorers) is doubtful.

But what about the situation in which the “scores” aren’t numbers, but rather, categories? For instance, suppose a scorer is asked to read the autobiographical data of 20 individuals and then categorize those individuals according to whether they are oriented predominantly toward achievement, power, or affiliation. Regardless of whether the evaluations were completed once by two different scorers (inter-rater reliability) or twice by the same scorer (intra-rater reliability), agreement between the two sets of categorical scores could not be evaluated using the Pearson correlation. However, Cohen’s kappa statistic is perfect for use in evaluating the reliability of categorical scores of this sort.

Calculating kappa by hand is a tedious task, but there on online calculators that can help. One in particular is unusually easy to use and complete. Written by Richard Lowry at Vassar, the kappa calculator can be found at http://vassarstats/kappa.html. The input to the calculator is a cross tabulation showing how many times each scorer assigned each case (e.q., autobiography in the example in the preceding paragraph) to each category (e.g., achievement, power, and affiliation in the example in the preceding paragraph).

But where is one to get these cross tabulations? SPSS provides a simple solution: Analyze > Descriptive Statistics > Crosstabs. In the dialog box, move the scores from Scorer 1 to “Rows” and the scores from Scorer 2 to “columns.” Click the Statistics button, check the kappa selection, and click Continue. Finally, click OK. The output will include the cross tabulations table which is easily typed into the kappa calculator.

The SPSS calculator will also include an “unweighted” kappa value which is fine if the categories your scorers are using are truly nominal scale with absolutely no ordinal properties. However, if the categories have some ordinal qualities (like letter grades A, B, C, D, F or the categories mild, moderate, severe) then you probably need to use the linearly weighted kappa value which is available from the Vassar statistics calculator, but not from SPSS.

Issues of scoring reliability are part of the larger specialty within statistics called psychometrics. I can help you with the psychometric evaluations associated with your dissertation or other research. Please visit my website, www.DissertationStatsHelper.com.

03/10/2016

The "causal-comparative" design so popular in education DOES NOT ESTABLISH CAUSE-AND-EFFECT!

I was called upon the other day to write an argument to convince a dissertation committee chair of something I’d always assumed everyone knew: One can’t claim that a non-manipulated Independent Variable exerts a causal impact on a Dependent Variable. Only when the researcher randomly assigns cases to the Experimental and Control groups can one draw causal conclusions.

The causal-comparative design looks on its face very much like a simple experiment. To use Campbell and Stanley’s (1963) method of designation:

Treatment Group: X O
Comparison Group: O

What makes it a quasi-experimental design rather than a true experiment, is the absence of random assignment of cases to groups.

Suppose that one wished to evaluate the effectiveness of meditation in reducing trait anxiety. Using the causal-comparative approach, you’d identify a group of people who practiced meditation (the treatment X being evaluated) and a group of people who don’t practice meditation and then see if their scores on a trait anxiety measure O differ significantly.

Suppose that meditators are found to be significantly less anxious than nonmeditators. Would this indicate that it was their practice of meditation that caused this lowered anxiety? NO! It’s just as likely that people are already low in anxiety are drawn to meditation and that people who are high in anxiety are too jittery to sit still long enough to meditate! In other words, it is just as likely that people’s preexisting stress levels caused them to choose or shun meditation as it is that meditation caused lower levels of anxiety.

If the causal-comparative design does not establish that the IV and DV are causally related, what does it establish? Only that the IV and DV are correlated. Only a true experiment, with experimenter-controlled random assignment of cases to the meditation and control groups would provide a logical basis for drawing causal conclusions about meditation (or any other treatment whose effects are being evaluated.)

I'm happy to work with students at any stage of their research, whether it's at the proposal stage in selecting a design that really addresses the intended research questions, or later in the analysis of data. Please visit my website, http://www.DissertationStatsHelper.com for more details.

Statistical consulting for students working on doctoral dissertations and masters theses.

02/18/2016

Every so often changes are made in SPSS syntax that can catch one by surprise. For instance, a couple versions back, one could write a couple simple lines of syntax to specify that analyses beyond that point would run on only a select group of cases.

For instance, if you wanted to run an analysis on only cases whose age was less than 30, you could type these two lines in a syntax file and run them:

SELECT IF (AGE LT 30).
EXECUTE.

Those two lines of syntax would simply tag unselected cases (i.e., cases who were 30 and older) and not include them in the analysis, but the cases still remained in the data file.

At some point in the recent past, however, the rules changed! Running those same two lines now doesn't just exclude the cases from the analysis, but DELETES THEM FROM THE DATA FILE!!

The syntax required to select a subset of cases for analysis but still leave the other cases in the data file is a lot more complex. For the example begun above, where you wanted to select cases for subsequent analysis who were less than 30 years old:

USE ALL.
COMPUTE filter_$=(age lt 30).
VARIABLE LABELS filter_$ 'age lt 30 (FILTER)'.
VALUE LABELS filter_$ 0 'Not Selected' 1 'Selected'.
FORMATS filter_$ (f1.0).
FILTER BY filter_$.
EXECUTE.

Yikes! I recommend that you use the menu system to generate the necessary syntax and then paste it into your syntax file in the appropriate location:

Data > Select Cases > Check "If condition is satisfied" > Click the "If..." button > type in "age lt 30" (without the quotes) > Click the "Continue" button > Click the "OK" button.

If you are looking for assistance with research design or statistical analysis on your dissertation or thesis research, I'd invite you to visit my website, www.DissertationStatsHelper.com Perhaps I can help.

04/24/2015

Have you ever needed a measure of variability for a nominal scale variable? I did recently, as a way of measuring the diversity of corporate boards of directors. (I’ll give examples later.) Statistics texts focus on measuring variability of continuous variables (e.g., range, inter-quartile range, variance, standard deviation), but are remarkably silent on the matter of measuring variability in categorical variables. Kader, G. D. and Perry, M. (2007) Variability for categorical variables. Journal of Statistics Education, 15(2), 1-16, www.amstat.org/publications/jse/v15n2/kader.html provide one measure, however, with the unlikely name “coefficient of unalikability,” abbreviated with the symbol, u2. The logic behind the unalikeability statistic takes them 16 pages to explain, but we can cut to the computational formula and see how it works with some examples.

Here are some data to illustrate the unalikeability statistic. The variable is Religious Preference, with four categories: Christian, Jewish, Muslim, Hindu. Shown next are frequency distributions for two samples, one with no variability on the variable, and the second with maximum possible variability.
Sample 1: shows very little variability or diversity in religious preference
freq proportion
Christian 8 1.0
Jewish 0 0.0
Muslim 0 0.0
Hindu 0 0.0
N = 8

Sample 2: shows maximum possible variability or diversity as cases are evenly distributed across categories of the variable

freq proportion
Christian 2 0.25
Jewish 2 0.25
Muslim 2 0.25
Hindu 2 0.25
N = 8

Next, here’s the formula for the unalikeability statistic:

u2 = 1 - Sum of the squared proportions

In words: (1) square the proportions associated with each category of the variable; (2) add these squared proportions; (3) subtract that sum from 1.

For the first distribution: u2 = 1 – (1^2 + 0^2 + 0^2 + 0^2) = 0

For the second distribution: u2 = 1 – (.25^2 + .25^2 + .25^2 + .25^2) = .75

You can see that where there is no variability or diversity, u2 takes on a value of 0. With a more variable or diverse distribution, the value of u2 increases appropriately to reflect that greater variability.

The only thing that’s annoying about the unalikeability statistic is that the maximum value of u2 is different depending on the number of categories. For a two-category variable (like s*x, for instance), the highest possible value is u2 = 0.50. For a three-category variable, maximum u2 = 0.67. For a four-category variable, maximum u2 = .75. What this means is that one can’t use u2 to compare levels of variability in categorical variables that contain different numbers of categories. However, u2 does at least allow us to measure differences from one group to the next on the same categorical variable.

I suppose that this limitation of the unalikeability statistic really isn’t that limiting. After all, we can’t compare the variances or standard deviations of two different variables either because those measures of variability are influenced not only by actual data variability but also by score magnitude.

If you need statistical or research design assistance with a dissertation, thesis, or other project, I invite you to visit my website, www.DissertationStatsHelper.com to learn more about the services I offer.