On Counting and Naming | |
In previous years, written summaries had wrong answers and it was not clear whether they
were mistakes of grammar or mistakes of understanding. Consider a sentence such as
"The statistical unit is the 120 patients." The mistake of grammar is a mismatch of
number between a verb and a noun: the singular "is" must go with a singular "patient."
The mistake of understanding is confusing the statistical unit with the sample size.
Statistical Unit. "Unit" is another word for "one." So "the patient" can be the statistical unit for a case report with one subject or for a multicenter clinical trial with thousands of patients. Do not confuse the statistical unit with the sample size. The key idea of the statistical unit is to see what is being counted to lead to the sample size. (Investigators who do surveys and epidemiology prefer the term "sampling unit" to statistical unit or experimental unit. Any of these three are acceptable here.) Independent Variable. An independent variable is used to organize the statistical units into groups. In a pre-experimental design the independent variable is the same as the inclusion criterion and leads to one group. For the other designs, one independent variable will lead to two or more groups.     Some examples follow. First example: three groups are formed by giving three different drugs. So we have one independent variable--the type of drug. Second example: six groups are formed by giving three drugs to men and the same three drugs to women. Now we have two independent variables: type of drug and gender.     In the statistics course you will learn that the second independent variable more than doubles what you learn from the experiment. From the first independent variable -- drug -- you learn if all three drugs are equally efficacious. From the second independent variable -- gender -- you learn if males and females react equally on the average. Finally, you also learn if a gender and a drug interact to give a result unexpected from each alone. The statistician uses a slightly different naming system. What is called the independent variable here is called in statistics a "factor" and sometimes a "main effect." The subdivisions of the factor or the independent variable such as the particular drugs or the genders are called the "levels" of the factor. The epidemiologists have their own jargon. At this point I see I need a table. |
Table 1. Comparison of Terms | ||
Research Design | Statistics | Epidemiology |
Experimental unit | Statistical unit | Sampling unit |
Pre-experimental |   | Case report |
Quasi-experimental | Statistics focuses on the number of groups, whether the data are independent or not, and the type of data used for the DV but not on the way the groups were formed. | Case-control |
True experimental | Randomized clinical trial | |
Independent variable | Factor |   |
Components of IV | Levels of factor |   |
In the table that follows are three abstracts. See if you can identify the design features before you look at my opinions below the table.   |
Table 2. Typical Research Abstracts |
M.G. Hans, L. Scaletta, & J.C. Occhino. The effects of antirat nasal septum cartilage antisera on facial growth in the rat. Amer. J. Orthod. Dentofac. Orthop. 109: 607-615, 1996. |
Antirat nasal septum cartilage antisera (RNS-IgG) produced in rabbits by injection of crude
antigens derived from rat nasal septum cartilage was cytotoxic for rat chondrocytes in vitro.
The effect of this antisera on rat facial growth was tested by injecting three groups of
growing rats at 4-day intervals from birth to 30 days. The treatment group (n = 19) received
injections of RNS-IgG, one control group (n = 11) received injections of the IgG fraction of
preimmune rabbit sera (PI-IgG) and a second control group (n = 16) received injections of
normal saline. All animals were killed at the conclusion of the experiment, and lateral and
dorsoventral cephalometric radiographs were taken. Statistical difference between treatment
and control groups were found for 15 cephalometric measurements. Specifically, snout length
(as measured from the intersphenoidal synchondrosis to the upper incisors (is-i) was reduced
in animals treated with RNS-IgG compared with both PI-IgG and saline injected controls (p <
0.06, p < 0.005, respectively). In addition, premaxillary length, premaxillary displacement, and bimaxillary width were significantly reduced (p < 0.05) in RNS-IgG treated animals compared with saline injected controls. Bimolar width was reduced (p < 0.05) between RNS-IgG and PI-IgG groups. These results demonstrate that injection of antinasal septum antisera reduces midfacial dimensions in experimental rats and that nonimmune rabbit antisera may have an effect on the growth process. In summary, the results of this pilot study suggest the possibility for using more specific antinasal cartilage antibodies to effect dose-dependent, tissue specific, modulation of facial growth. |
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J.Y.M. Chau, J.W. Hunter, T.O. Mork, & B.K. Nicoll, An in vitro study of furcation performation repair using calcium phospohate cement. J. Endodont. 23: 588-592, 1997. |
Furcation perforations created in the pulpal floors of 30 extracted human molars were repaired with either light-cured glass ionomer cement (GI), calcium phosphate cement (CPC), or light-cured glass ionomer cement placed over a CPC matrix (M). After the cement was set, the teeth were immersed in India Ink for 48 h, dried, and sectioned longitudinally. Dye penetration into the furcation repair was independently evaluated by three board-certified endodontists. There was no significant difference in the mean extent of dye leakage among the three experimental groups. The use of CPC, with its enhanced biocompatibility, potential for osteoconduction, and sealing ability, may improve the prognosis of teeth with furcation perforations. |
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E. Singer and R. Dionne, A controlled evaluation of ibuprofen and diazepam for chronic orofacial muscle pain. J. Orofacial Pain 11: 139-146, 1997 |
The clinical efficacy, side effect liability, and hormonal effects of two prototypic
pharmacologic agents were evaluated for the management of chronic myogenous facial pain in
a double-blind, randomized, controlled clinical trial. Thirty-nine subjects (35 women,. 4 men)
with daily or near-daily orofacial pain of at least 3 months' duration and tenderness to
palpation of masticatory muscles participated. Patients were randomly allocated to one of
four treatments: placebo, diazepam, ibuprofen, or the combination of diazepam and ibuprofen.
Pain, mood, muscle tenderness, maximal interincisal opening, and plasma levels of beta-endorphin were measured following 2-week baseline and 4-week treatment periods. Pain, as
measured by a visual analog scale, was significantly decreased in the diazepam and diazepam
plus ibuprofen groups but not for the ibuprofen or placebo groups. Analysis of variance
showed a significant drug effect for diazepam but not for ibuprofen, indicating that pain relief
was attributable to diazepam. No significant changes were noted in muscle tenderness,
interincisal opening, or plasma beta-endorphin level. This study supports the efficacy of
diazepam in the short-term management of chronic orofacial muscle pain. The lack of effect
following administration of an anti-inflammatory analgesic suggests that inflammation is not
the basis for chronic muscle pain in the orofacial region, and that the analgesic effect of such
medications is not sufficient for pain relief in this condition. |
Independent Variable. Hans, et al., have three groups of rats but one independent variable: injected substance. Chau, et al., have three groups of molars but one independent variable: cement type. Notice that one group received both cement types but there was not a group with no cement at all. Singer and Dionne have four groups, but the organization of the groups differs from Chau et al. Singer and Dionne have one group with neither treatment and one group with both treatments. So one independent variable is ibuprofen (with and without), and the second independent variable is diazepam (with and without). In the group where both IVs are "without" the patients get "none" and in the group where both IVs are "with" the patients get "both." If the "both" group does better than you would expect from the dose of each drug alone, then there was an interaction between the two drugs. (You don't have to grasp the interaction concept for the Research Design course, and if you do grasp it for the Statistics course you will be way ahead of your colleagues.) Statistical Unit. The statistical unit for Hans, et al., was the rat; for Chau, et al., the molar; and for Singer and Dionne, the patient. |