The most baffling thing to me about the Terri Schiavo situation is how difficult people make it to be in the face of such simplicity.
1. The government is executing a citizen that has not been accused of a capital offense.
2. This is not permitted by the US Constitution
Alright, I have corresponded with many people about this. The responses tend to fall along the lines:
i. She is not a person
ii. She is not being executed
iii. Florida law says she can be executed
iv. You are a right wing theocrat
v. It all depends on the meaning of the word 'is'.
Frankly, no response above is both true and sufficient to refute the simple two point argument. If you are able to do this, I would be greatly obliged.
UPDATE: The closest consideration of this fundamental issue that I have read to date comes from Alec Rawls at Error Theory and a discussion of the Supreme Court's role in breaching individual sovereignty by Matthew Franck.
UPDATE: This summary by William Anderson is also well worth reading. My sole disagreement is over the rectitude of withholding fluids from those in an "irreversible deep coma". Anderson is a neurologist, so I understand that there may be some meaning to the phrase that escapes me. However, I would draw the line only at "brain death" as the irreversibility and true nature of a "deep" coma is not knowable at this time.
Thursday, March 31, 2005
Monday, February 21, 2005
Deductions from Minimal Information: Terri Schiavo
I have deduced the following in respect to the Terri Schiavo affair:
1. It is unlikely that the husband is responsible for the initial injury.
(Why would he call Terri's father to assist while she was still alive?)
2. The Schindlers and Schiavo are mutually antagonistic.
(More or less a simple observation)
3. Terri is now being used as a pawn by both the pro-life and the euthanasia movements.
4. It is impossible to know what are Terri's wishes here. It is irresponsible to assume that she would wish to starve to death.
5. The Florida Courts are hopelessly dysfunctional. In particular, Judge Greer is acting outside the law.
6. Under present conditions, it is unlikely that Gov. Bush will provoke a Constitutional crisis.
7. It is possible that Terri's condition may improve in the future. In the next ten years, we may have the means to radically improve her condition.
Conclusion:
The best strategy for a happy resolution is to have a 3rd party benefactor intervene and offer a mutually satisfactory solution. The husband deserves some compensation to this effect. He should relinquish custody to the parents.
Everyone is invited to challenge these deductions and conclusion. Please be prepared to support your contentions.
1. It is unlikely that the husband is responsible for the initial injury.
(Why would he call Terri's father to assist while she was still alive?)
2. The Schindlers and Schiavo are mutually antagonistic.
(More or less a simple observation)
3. Terri is now being used as a pawn by both the pro-life and the euthanasia movements.
4. It is impossible to know what are Terri's wishes here. It is irresponsible to assume that she would wish to starve to death.
5. The Florida Courts are hopelessly dysfunctional. In particular, Judge Greer is acting outside the law.
6. Under present conditions, it is unlikely that Gov. Bush will provoke a Constitutional crisis.
7. It is possible that Terri's condition may improve in the future. In the next ten years, we may have the means to radically improve her condition.
Conclusion:
The best strategy for a happy resolution is to have a 3rd party benefactor intervene and offer a mutually satisfactory solution. The husband deserves some compensation to this effect. He should relinquish custody to the parents.
Everyone is invited to challenge these deductions and conclusion. Please be prepared to support your contentions.
Friday, January 21, 2005
Understanding Mutual Information
The mutual information between random variables, I(X,Y) is a measure of information overlap, i.e. I(X,Y) = H(X) - H(X|Y) = H(Y) - H(Y|X) where H() is a measure of entropy/information. Information is a nebulous concept so we define information here to be equivalent to entropy -- a functional of the probability density function of the random variable. Mutual information between random variables is then a probabilistic measure. It is a measure of the probability of relating the two variables regardless of the form of the relationship that might be applied. If the pdf of a random variable is not known, then the entropy must be estimated from an estimate of the pdf. A consistent and straightforward method of estimating the entropy functional is by substitution of the pdf estimate for the pdf in the entropy function. In this case, the estimation of the probability of relating variables is dependent directly on the statistical properties of the joint pdf estimate of the r.v.s.
If we are without any knowledge of the random variables that might be used to form the estimate of their pdf, the frequentist method of estimation is all that is available. The relative number of occurrences of an observation of the variables is the estimate of the probability of that event over those measurement values. The grouping of occurrences can be done several ways typically either by kernels or by histograms. Again, without a priori knowledge of the r.v.s, we favor uniform histograms for their computationally efficiency. The drawback of histograms is that they enforce a discrete partition on the observations regardless of whether the underlying process that generated the r.v.s is discrete or not. However, when the dimensionality of the data is even moderately great and the number of observations is fixed, any benefit in the use of smooth kernels in approximating the pdf of a continuous process is negligible. Since we envision a locally smooth method of reconstruction of the process relationship based on the local estimates of MI, the discreteness of histograms is not a primary concern.
The partitioning of the variable space by bins gives us a basis for making local relations between the variables (assuming a causal relation we will label these as 'input' and 'output'). Ideally, a local bijection exists between each input and output bin. A necessary and sufficient condition for this existence is that the joint probability of the input/output bin in the input/output space is equal to its marginal probability in both the input and output spaces. Of course, a bijection may not exist between the events that fall into the bin, only the bins themselves.
Entropy is the (negative of the) expectation of the logarithm of the pdf of a r.v. Unlike linear measures of concentration, the logarithm used in the entropy functional has the effect of disproportionately weighting the differences in a distribution between bins so that the closer to equivalency the distribution of probability mass between bins, the lesser the change in entropy. Conversely, small deviations from concentrations of probability mass lead to disproportionately greater differences in entropy.
Note that the linear distributive probability relation demonstrated here is unique to the logarithm among other functions with the property previously mentioned.
For continuous processes, the relation between joint and marginal partitions will tend to be symmetric in the joint space. In general, the mutual information between two random variables can be visualized as the degree to which the probability masses of the partitions in of one marginal space can be traced through the joint space to the marginal distribution of the other variable. The more certain this can be done, the stronger and more accurate will be the mapping between the divisions of the variables. This is then the basis for a global mapping between the variables that is statistically robust and measurably accurate.
If we are without any knowledge of the random variables that might be used to form the estimate of their pdf, the frequentist method of estimation is all that is available. The relative number of occurrences of an observation of the variables is the estimate of the probability of that event over those measurement values. The grouping of occurrences can be done several ways typically either by kernels or by histograms. Again, without a priori knowledge of the r.v.s, we favor uniform histograms for their computationally efficiency. The drawback of histograms is that they enforce a discrete partition on the observations regardless of whether the underlying process that generated the r.v.s is discrete or not. However, when the dimensionality of the data is even moderately great and the number of observations is fixed, any benefit in the use of smooth kernels in approximating the pdf of a continuous process is negligible. Since we envision a locally smooth method of reconstruction of the process relationship based on the local estimates of MI, the discreteness of histograms is not a primary concern.
The partitioning of the variable space by bins gives us a basis for making local relations between the variables (assuming a causal relation we will label these as 'input' and 'output'). Ideally, a local bijection exists between each input and output bin. A necessary and sufficient condition for this existence is that the joint probability of the input/output bin in the input/output space is equal to its marginal probability in both the input and output spaces. Of course, a bijection may not exist between the events that fall into the bin, only the bins themselves.
Entropy is the (negative of the) expectation of the logarithm of the pdf of a r.v. Unlike linear measures of concentration, the logarithm used in the entropy functional has the effect of disproportionately weighting the differences in a distribution between bins so that the closer to equivalency the distribution of probability mass between bins, the lesser the change in entropy. Conversely, small deviations from concentrations of probability mass lead to disproportionately greater differences in entropy.
Note that the linear distributive probability relation demonstrated here is unique to the logarithm among other functions with the property previously mentioned.
For continuous processes, the relation between joint and marginal partitions will tend to be symmetric in the joint space. In general, the mutual information between two random variables can be visualized as the degree to which the probability masses of the partitions in of one marginal space can be traced through the joint space to the marginal distribution of the other variable. The more certain this can be done, the stronger and more accurate will be the mapping between the divisions of the variables. This is then the basis for a global mapping between the variables that is statistically robust and measurably accurate.
Tuesday, December 28, 2004
Connections and Consistency
One obvious question that arises from the TNL post is “Why should the progressive player seek an interior solution?” For that matter, “Why should the conservative player seek an exterior solution?” Neither of these questions was directly addressed in the post. However, the personality-political affiliation study does give a hint to the answer to these questions. Remember, it is a remarkable fact that there is a measurable personality difference between liberals and conservatives.
We found that the primary intrinsic information-processing distinction between self-described progressives/liberals and conservatives was that liberals “feel” while conservatives “think”. Both terms should be understood in the context of the study. They tell us how about the mode of decision-making of the individual based on information presented by the environment. The distinction is not a product of the moral status of the decision maker, but the mode of decision does have moral implications. Since the vast majority of individuals consider themselves to be “good” in a moral sense irregardless of political affiliation, the distinction must be a function of how we judge the imperatives of good action in relation to the environment.
The conservative makes decision based on discrete, measurable actions on his environment. Rationalism is a method of organizing the environment in a logically consistent method such that the environmental entropy is reduced. That entropy which cannot be reduced is treated in such a way that it does not enter the moral calculus. Thus, the misfortunes of Job were a test of fidelity while other randomness is ascribed to either the unavoidable byproduct of physical laws of creation or the consequences of other’s actions for which a collective moral consequence is assumed. There is moral order in the environment of the conservative because the conservative believes that he acts on the environment for a moral purpose. Internal feelings of happiness or guilt are a consequence of this measurable action. Feeling follows thinking.
The moral viewpoint of the progressive is not primarily a function of his perceived action on the environment. His judgement of good and bad action is more directly a result of his internal harmony, i.e. "feeling". The conflict which arises from discordant forces is to be minimized for the maximization of the good of the liberal -- conflict is inherently bad. Thus progressives do not seek to interact at odds with the environment; they seek consensus. This is by definition the search for an interior solution as the social/economic model is defined. The external environment is rationalized to come into agreement with internal needs and desires. Thinking follows feeling.
We found that the primary intrinsic information-processing distinction between self-described progressives/liberals and conservatives was that liberals “feel” while conservatives “think”. Both terms should be understood in the context of the study. They tell us how about the mode of decision-making of the individual based on information presented by the environment. The distinction is not a product of the moral status of the decision maker, but the mode of decision does have moral implications. Since the vast majority of individuals consider themselves to be “good” in a moral sense irregardless of political affiliation, the distinction must be a function of how we judge the imperatives of good action in relation to the environment.
The conservative makes decision based on discrete, measurable actions on his environment. Rationalism is a method of organizing the environment in a logically consistent method such that the environmental entropy is reduced. That entropy which cannot be reduced is treated in such a way that it does not enter the moral calculus. Thus, the misfortunes of Job were a test of fidelity while other randomness is ascribed to either the unavoidable byproduct of physical laws of creation or the consequences of other’s actions for which a collective moral consequence is assumed. There is moral order in the environment of the conservative because the conservative believes that he acts on the environment for a moral purpose. Internal feelings of happiness or guilt are a consequence of this measurable action. Feeling follows thinking.
The moral viewpoint of the progressive is not primarily a function of his perceived action on the environment. His judgement of good and bad action is more directly a result of his internal harmony, i.e. "feeling". The conflict which arises from discordant forces is to be minimized for the maximization of the good of the liberal -- conflict is inherently bad. Thus progressives do not seek to interact at odds with the environment; they seek consensus. This is by definition the search for an interior solution as the social/economic model is defined. The external environment is rationalized to come into agreement with internal needs and desires. Thinking follows feeling.
Saturday, December 18, 2004
Human Transactions
We transact with others on a continuum of trust and power. On one end of the spectrum, what we receive from the transaction cannot be differentiated from a gift. On the other end, it is a product of force and power applied to another. One relationship relies on human intuition to be profitable; the other is a product of brute calculation. As individuals in a generic situation we chose to transact on that basis that we expect to yield the more favorable result. That decision is a product of our personality and experience. When transacting with other humans with whom we have no prior experience, we proceed according to a characteristic bias. This same bias is also projected on anthropomorphized institutions such as government and corporations.
The continuum of interaction is directly correspondent to the feeling/thinking axis of decision making that differentiates liberals and conservatives. Conservatives tend to view government as best suited to taking a limited, contractual relationship with the governed. Meanwhile, liberals seek a paternalistic government that “feels their pain”. So, our approach to politics is again an extension of our personalities. We should be aware of the bias that we bring to our deliberations of problems that we wish to objectify; the best solution applies uniformly to the mass of society and not to ourselves alone.
The continuum of interaction is directly correspondent to the feeling/thinking axis of decision making that differentiates liberals and conservatives. Conservatives tend to view government as best suited to taking a limited, contractual relationship with the governed. Meanwhile, liberals seek a paternalistic government that “feels their pain”. So, our approach to politics is again an extension of our personalities. We should be aware of the bias that we bring to our deliberations of problems that we wish to objectify; the best solution applies uniformly to the mass of society and not to ourselves alone.
Saturday, November 13, 2004
Information-Theoretic Dependency Analysis
If there were only one criterion in one dimension with which to differentiate the conservatives and liberals out of the four Myers-Briggs factors, then the summary results would be sufficient to answer the question. However, people are not so single dimensional; we expect that the political affiliation decision to be a more complex function of personality.
Let’s first loosen the condition that the differentiation must be a single boundary in one dimension. Let’s allow that along this dimension there could be clusters of liberal and clusters of conservative respondents separated by multiple boundaries. So instead of a measure of central tendency such as the mean or correlation, we need a more general metric of dependency to determine which dimensions of personality tend to separate respondents according to their political affiliation. The measure of choice is the mutual information (MI) between the distributions of the respondents' political affiliation and the respondents' Myers-Briggs scores in each dimension. These totals are shown below where the number of bins is chosen to equally resolve all Myers-Briggs totals for our sample down to the individual question level:
The objective is to be able to assign each of the uniformly distributed bins to a certain political affiliation of the four different possibilities (weak/strong and conservative/liberal). To do this we want to use that information that has the closest one-to-one relationship with the distribution of the respondent’s political affiliation. This is the dimension with the highest MI value. The total information to be covered in the output dimension of political affiliation is 1.14 nats (natural units). So, while the decision making dimension is still the most potentialy descriptive of political affiliation, it is by no means comprehensive. It is possible that there is complementary information in another dimension that will yield a better discriminant.
Let's now expand the investigation into two dimensions while reducing the number of bins in each dimension to nine (gender is included with two bins) in order that the proportion of total bins to data records remain above three. The first 6 of the 15 combinations in rank order are:
For a more direct comparison with the single dimension results let's limit the grid to 4x4 for a total of 16 bins:
It is clear that a better differentiation in general can be had with certain combinations of two dimensions rather than just one. In this case the dimensions of processing and decision making should provide us with significant information by which to distinguish many conservatives from liberals. The plot below demonstrates this fact (red diamonds = conservatives; blue squares = liberals):
Compare the simplicity and efficiency of that discriminant to the dual case:
Let’s first loosen the condition that the differentiation must be a single boundary in one dimension. Let’s allow that along this dimension there could be clusters of liberal and clusters of conservative respondents separated by multiple boundaries. So instead of a measure of central tendency such as the mean or correlation, we need a more general metric of dependency to determine which dimensions of personality tend to separate respondents according to their political affiliation. The measure of choice is the mutual information (MI) between the distributions of the respondents' political affiliation and the respondents' Myers-Briggs scores in each dimension. These totals are shown below where the number of bins is chosen to equally resolve all Myers-Briggs totals for our sample down to the individual question level:
| Dimension | Bins | MI (nats) |
| Focus | 18 | 0.096 |
| Processing | 16 | 0.142 |
| Decision Making | 18 | 0.176 |
| Organizing | 19 | 0.143 |
| Age | 19 | 0.106 |
| Gender | 2 | 0.074 |
The objective is to be able to assign each of the uniformly distributed bins to a certain political affiliation of the four different possibilities (weak/strong and conservative/liberal). To do this we want to use that information that has the closest one-to-one relationship with the distribution of the respondent’s political affiliation. This is the dimension with the highest MI value. The total information to be covered in the output dimension of political affiliation is 1.14 nats (natural units). So, while the decision making dimension is still the most potentialy descriptive of political affiliation, it is by no means comprehensive. It is possible that there is complementary information in another dimension that will yield a better discriminant.
Let's now expand the investigation into two dimensions while reducing the number of bins in each dimension to nine (gender is included with two bins) in order that the proportion of total bins to data records remain above three. The first 6 of the 15 combinations in rank order are:
| Dimensions | MI (nats) |
| (Processing; Decision Making) | 0.391 |
| (Decision Making; Age) | 0.379 |
| (Focus; Decision Making) | 0.376 |
| (Decision Making; Organizing) | 0.363 |
| (Focus; Processing) | 0.363 |
| (Focus; Organizing) | 0.357 |
For a more direct comparison with the single dimension results let's limit the grid to 4x4 for a total of 16 bins:
| Dimensions | MI (nats) |
| (Processing; Decision Making) | 0.196 |
| (Processing; Gender) | 0.180 |
| (Decision Making; Organizing) | 0.173 |
| (Decision Making; Age) | 0.157 |
| (Decision Making; Gender) | 0.150 |
| (Focus; Decision Making) | 0.144 |
| (Organizing; Gender) | 0.136 |
| (Focus; Organizing) | 0.120 |
| (Focus; Processing) | 0.117 |
It is clear that a better differentiation in general can be had with certain combinations of two dimensions rather than just one. In this case the dimensions of processing and decision making should provide us with significant information by which to distinguish many conservatives from liberals. The plot below demonstrates this fact (red diamonds = conservatives; blue squares = liberals):
Compare the simplicity and efficiency of that discriminant to the dual case:
Saturday, November 06, 2004
Information Divergence in Political Affiliation
The way that we process the information around us leads ultimately to the decisions we make. One such decision is our choice of political affiliation. Is our choice of political party the result of the characteristic way in which we have learned to process information, i.e. our personality, or is it the result of our calculation of a number of issues? It turns out that our personality plays a statistically significant role in our political outlook. This fact is a major result of a study of blog readers conducted over the month of October. The preliminary results of this study also tells us something of how we differ.
The vast majority of respondents to the personality-political affiliation study were solicited from the political discussion websites PoliPundit and DailyKos. Both sites are dominant attractors of those interested in political discussion and news from the right and left, respectively. Both allow the posting of user comments in regard to topics of interest. The DailyKos is somewhat less restrictive as it also allows the posting of user created threads of discussion while Polipundit threads are topic driven (here a link to the study was provided by the site administrators). It is expected that these two sites would generate respondents representative of the political core of the two US political parties.
The study used the Myers-Briggs test to measure personality. The Myers-Briggs dimensions are translated here as values between 100 and −100 with the positive values corresponding to the INTJ personality type (negative values to ESFP). Each question has equal absolute value. The total value of the questions per respondent along a dimension is divided by the number of questions answered, scaled to the range, and rounded to the nearest integer. Zero is arbitrarily assigned a unit value for representation to the respondent by Humanmetrics. Here, the zero totals are reassigned to zero before data analysis. The basic statistics of the respondents are summarized below.
Single Factor Summary Statistics (mean / std)
The greatest difference between conservatives and liberals appears to arise along the decision making dimension. However, it is noted that there is also a gender distinction between the respondents in this same dimension. To investigate whether this gender gap is the reason for the political distinction, we need to separate by gender and look more closely. The double factor summary statistics are shown next.
Double Factor Summary Statistics (mean / std)
Under the assumption of normality, there is less than a 6% probability that female repondents are not differentiated by their decision making metrics while there is a statistically insignificant possiblitiy that the same is true in the case of the males by the two-sample t-test. As a result of the Lilliefors test of normality at a significance level of 0.05, we find that all samples except male conservatives can be assummed to satisfy the normality condition. This is likely due to the fact that the mean decision making index for male conservatives is much higher than the center of the finite index. Therefore, to satsify the hypothesis we will examine the statistical breakdown of male conservatives in the study a bit closer. The relevant triple factor statistical summary is shown below.
Selected Triple Factor Summary Statistics
Strong Political Affiliation (mean / std)
While the standard deviations of the male conservative (both strong and weak) and strong male conservative subsamples are very nearly equal as is likewise the case for the liberal males, the mean of the strongly partisan samples are even more greatly separated along the decision making dimension than the combined samples. Therefore the lack of normality of the strong conservative male sample is such that the distinction would be even greater than what one would expect had the subsample satisfied the Lilliefors test. We therefore conclude that there is a statistically significant difference between the way in which politically affiliated liberals and conservatives process information. Specifically, liberals are more feeling while conservatives are more thinking.
An explicit discrimination of the sample described by the model is shown here.
Data available by e-mail request.
The vast majority of respondents to the personality-political affiliation study were solicited from the political discussion websites PoliPundit and DailyKos. Both sites are dominant attractors of those interested in political discussion and news from the right and left, respectively. Both allow the posting of user comments in regard to topics of interest. The DailyKos is somewhat less restrictive as it also allows the posting of user created threads of discussion while Polipundit threads are topic driven (here a link to the study was provided by the site administrators). It is expected that these two sites would generate respondents representative of the political core of the two US political parties.
The study used the Myers-Briggs test to measure personality. The Myers-Briggs dimensions are translated here as values between 100 and −100 with the positive values corresponding to the INTJ personality type (negative values to ESFP). Each question has equal absolute value. The total value of the questions per respondent along a dimension is divided by the number of questions answered, scaled to the range, and rounded to the nearest integer. Zero is arbitrarily assigned a unit value for representation to the respondent by Humanmetrics. Here, the zero totals are reassigned to zero before data analysis. The basic statistics of the respondents are summarized below.
Single Factor Summary Statistics (mean / std)
| Group | Number | Focus | Processing | Decision | Organizing | Age |
| Weak | 45 | 31.98 / | 36.80 / | 22.80 / | 22.40 / | 38.00 / |
| Strong | 222 | 21.99 / | 42.21 / | 13.77 / | 18.92 / | 39.21 / |
Male | 166 | 23.30 / | 40.50 / 34.07 | 25.15 / | 20.83 / | 38.83 / |
Female | 101 | 24.29 / | 42.61 / | −0.90 | 17.33 / | 39.31 / |
| Conservative | 137 | 21.45 / | 33.60 / | 28.73 / | 30.57 / | 39.83 / |
Liberal | 130 | 26.02 / | 49.41 / | 1.13 / | 7.85 / | 38.14 / |
The greatest difference between conservatives and liberals appears to arise along the decision making dimension. However, it is noted that there is also a gender distinction between the respondents in this same dimension. To investigate whether this gender gap is the reason for the political distinction, we need to separate by gender and look more closely. The double factor summary statistics are shown next.
Double Factor Summary Statistics (mean / std)
| Group | Number | Focus | Processing | Decision | Organizing | Age |
| Weak Con | 29 | 27.97 / 43.47 | 40.66 / 27.33 | 30.10/ 34.55 | 28.00/ 39.08 | 38.83 / 10.07 |
| Strong | 108 | 19.70 / 42.44 | 31.70 / | 28.37 / 37.83 | 31.26 / 41.25 | 40.10 / |
| Weak Lib | 16 | 39.25 / 36.25 | 29.81 / 48.51 | 9.56 / 42.97 | 12.25 / 31.09 | 36.50 / 8.46 |
| Strong Lib | 114 | 24.16 / 46.97 | 52.17 / 31.39 | −0.05 | 7.22 / 42.79 | 38.37 / |
| Weak Male | 26 | 32.00 / 41.16 | 39.58 / 29.51 | 33.35 / 32.59 | 23.50 / 39.09 | 38.08 / 10.34 |
| Strong | 140 | 21.69 / 44.83 | 40.67 / | 23.63 / | 20.33 / | 38.96 / 11.62 |
| Weak | 19 | 31.95 / | 33.00 / | 8.37 / | 20.89 / | 37.89 / |
| Strong | 82 | 22.51 / | 44.84 / | −3.05 | 16.50 / | 39.63 / |
Male Con | 109 | 21.97 / | 35.58 / | 33.27 / | 29.52 / | 39.31 / |
| Male Lib | 57 | 25.84 / | 49.91 / | 9.63 / | 4.21 / | 37.89 / |
| Female Con | 28 | 19.43 / | 25.89 / | 11.11 / | 34.64 / | 41.86 / |
| Female Lib | 73 | 26.15 / | 49.03 / | −5.51 | 10.68 / | 38.33 / |
Under the assumption of normality, there is less than a 6% probability that female repondents are not differentiated by their decision making metrics while there is a statistically insignificant possiblitiy that the same is true in the case of the males by the two-sample t-test. As a result of the Lilliefors test of normality at a significance level of 0.05, we find that all samples except male conservatives can be assummed to satisfy the normality condition. This is likely due to the fact that the mean decision making index for male conservatives is much higher than the center of the finite index. Therefore, to satsify the hypothesis we will examine the statistical breakdown of male conservatives in the study a bit closer. The relevant triple factor statistical summary is shown below.
Selected Triple Factor Summary Statistics
Strong Political Affiliation (mean / std)
|
| Number | Focus | Processing | Decision | Organizing | Age |
| Male Con | 88 | 20.41 / | 33.63 / | 33.38 / | 31.15 / | 39.34 / |
Male Lib | 52 | 23.85 / | 52.60 / | 7.13 / | 2.04 / | 38.32 / |
Female Con | 20 | 16.60 / | 23.25 / 29.17 | 6.35 / | 31.75 / | 43.45 / |
Female Lib | 62 | 24.42 / | 51.81 / | −6.08 | 11.58 / | 38.40 / |
While the standard deviations of the male conservative (both strong and weak) and strong male conservative subsamples are very nearly equal as is likewise the case for the liberal males, the mean of the strongly partisan samples are even more greatly separated along the decision making dimension than the combined samples. Therefore the lack of normality of the strong conservative male sample is such that the distinction would be even greater than what one would expect had the subsample satisfied the Lilliefors test. We therefore conclude that there is a statistically significant difference between the way in which politically affiliated liberals and conservatives process information. Specifically, liberals are more feeling while conservatives are more thinking.
An explicit discrimination of the sample described by the model is shown here.
Data available by e-mail request.
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