[From Rick Marken (2006.12.16.2050)]
Martin Taylor (2006.12.16.15.53) --
Bill Powers (2006.12.16.0555 MST)]
In the traditional approach, the null hypothesis is simply that there is NO RELATIONSHIP between the manipulated environmental variable (IV) and the action of the organism (DV). So rejecting the null hypothesis does not support any particular relationship -- it simply says there is some kind of relationship, without saying what kind it is.
I don't intend here to quarrel with the IV-DV-CV set of issues under discussion, but some of the comments on "traditional statistics" are, I think, a bit unfair.
As one who has just finished teaching "traditional statistics" to a class of 230 undergrads at Ucla (to a standing -- well, sitting -- ovation) I would say that Bill's statement is not only fair but precisely accurate. This is because in most psychological research the IV is qualitative. So the null hypothesis is simply that the population averages of the DV in each condition (level of the IV) will be the same: mu1=mu2 =...muN. TIn other words, the null hypothesis is that there is no relationship between the IV and DV. The alternative hypothesis is that there is _some_ relationship between IV and DV, in the sense that the population averages of the DVs in each condition are not the same. Neither the null nor the alternative hypothesis says anything about the _functional_ relationship between IV and DV (whether it is linear, quadratic, logarithmic, etc) because of the qualitative nature of the IV.
I Hold no brief for "traditional" statistics, meaning statistics based on "significant" deviations from "null hypotheses", but I do think soem of your criticism is unwarranted.
I don't think Bill was criticizing traditional statistics; he was just stating succinctly how statistics are used in psychological research.
The above is an example. The "null hypothesis" can be anything at all, and very typically asserts that "if there is a relationship between X and Y, it is non-negative". Another null hypothesis possibility is "The effect of X on Y is exatly Z (or 'at least Z')".
Yes, you can do this kind of hypothesis testing, but it is rarely used in psychological research because, in order to do it, both the IV and DV must be measured quantitatively and, as I said above, the IV in most psychological research is qualitative. Doing the sort of tests you discuss here requires non-linear regression analysis, which is certainly not part of the basic statistics course.
Note that the sign of the correlation is not considered in the traditional analysis.
The sign is as likely as not to be considered. Whether it is or not will depend on the experimenter's theoretical predeliction. If the theory being tested says that the effect must be in one direction, and absence of effect or an effect in the other direction would be counter-evidence, then the analysis will use one-sided tests.
Yes. You can measure the correlation (r) between IV and DV when both IV and DV are measured quantitatively. In that case, you can do a one or two tailed test of the significance of r. A one tailed test in the negative tail would allow you to reject the null hypothesis (population r = o) only if the observed r were negative. I think Bill's "mistake" here was using the term "correlation", which can refer to a relationship (of any kind) between IV and DV or to the statistical measure r that represents the degree of linear relationship between two variables. In most "traditional" analysis (t test, ANOVA) the IV is qualitative so all that is tested is whether there is a relationship in the first sense (a relationship of any kind) between IV and DV. It's probably better to say that traditional analysis looks only for an _effect_ of the IV on the DV (the value of the DV differs at different levels of the IV), in which case the sign of the "correlation" between IV and DV is not only _not_ considered; it _can't_ even be determined because it is impossible to measure a correlation (in the second sense of correlation as a measure of the degree of linear relationship between two variables) between a qualitative IV and a quantitative DV.
Because of changes of units between input and output, there is no "natural" interpretation of the signs: is a bar-pressing response in the same direction as the sound of food rattling in the dish? Is jerking the arm away opposed to the direction of the pain caused by a needle jab?
If the experimenter theorizes that the rat will press the bar less when it hears the food rattle, then that imposes a directionality on the interpretation, and on the statistical analysis. The "null hypothesis" will be that the rat does not increase the bar pressing when the food rattles, and the analysis will use one-sided significance tests.
I think you missed Bill's point. Saying there is no "natural" interpretation of the sign of a relationship between variables (which you can measure when both IV and DV are quantitative) doesn't mean that you can't do directional tests of a hypotheses about relationships. It means that the sign of the observed relationship between IV and DV, as measured, depends on the way you happened to measure the IV and DV; the sign of the relationship, therefore, doesn't say whether the DV is opposed to the IV or not.
In Bill's examples, the relationship between the variables might come out positive even though the DV is actually opposed to the IV. For example, as the size of the needle increases the distance the arm is jerked from the needle increases: there is a positive relationship between these variables but, in fact, the jerking is actually done in opposition to the size of the needle. This would show up as a negative relationship if, for example, the jump were measured as distance from a point behind the arm rather than as distance from the needle. Then the arm jump numbers would decrease as the needle size numbers increased, making the observed sign of the relationship between IV and DV (needle size and jump) correspond to the "true" negative relationship that exists in order to control for pain (the CV).
Bill's point was not related to traditional statistics. It was really related to the problems of trying to use observed IV-DV relationships as a test of control. The problem is ignoring possible CVs.
Best
Rick
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