sft (version 0.0-5)

micTest: Test of the Mean Interaction Contrast

Description

Performs either an Adjusted Rank Transform or ANOVA test for an interaction at the mean level.

Usage

micTest(HH, HL, LH, LL, ART=TRUE)

Arguments

HH

Response times from the High--High condition.

HL

Response times from the High--Low condition.

LH

Response times from the Low--High condition.

LL

Response times from the Low--Low condition.

ART

If TRUE, use the adjusted rank transform test. If FALSE use ANOVA.

Value

• statistic
  The value of the test statistic from an ART or ANOVA.
• p.val
  The p.value of the test statistic.

Details

The mean interaction contrast (MIC) indicates the architecture of a process. Serial processes result in MIC equal to zero. Parallel-OR and Coactive process have a positive MIC. Parallel-AND process have a negative MIC. A test for a significant MIC can be done with a nonparametric adjusted rank transform test (described below) or an ANOVA.

The Adjusted Rank Transform is a nonparametric test for an interaction between two discrete variables. The test is carried out by first subtracting the mean effect of the salience level on each channel. Suppose, $m_{H,\cdot} =$ E[RT; Level of Channel 1 is Fast], $m_{L,\cdot} =$ E[RT; Level of Channel 1 is Slow], $m_{\cdot, H} =$ E[RT; Level of Channel 2 is Fast], $m_{\cdot, L} =$ E[RT; Level of Channel 2 is Slow]. Then for each response time from the fast--fast condition, $m_{H, \cdot}$ and $m_{\cdot,H}$ are subtracted. Likewise, for each of the other conditions, the appropriate $m$ is subtracted. Next, each mean subtracted response time is replaced with its rank across all conditions (e.g., the fastest time of all conditions would be replaced with a 1). In this implementation, tied response times are assigned using the average rank. Finally, a standard ANOVA on the ranks is done on the ranks and the $p$-value of that test is returned. This test was recommended by Sawilowsky (1990) based on a survey of a number of nonparametric tests for interactions. He credits Reinach (1965) for first developing the test.

References

Reinach, S.G. (1965). A nonparametric analysis for a multiway classification with one element per cell. South African Journal of Agricultural Science, 8, 941--960.

Sawilowsky, S.S. (1990). Nonparametric tests of interaction in experimental design. Review of Educational Research, 60, 91--126.

Houpt, J.W. & Townsend, J.T. (2010). The statistical properties of the survivor interaction contrast. Journal of Mathematical Psychology, 54, 446-453.

Examples

T1.h <- rexp(50, .2)
T1.l <- rexp(50, .1)
T2.h <- rexp(50, .21)
T2.l <- rexp(50, .11)

Serial.hh <- T1.h + T2.h
Serial.hl <- T1.h + T2.l
Serial.lh <- T1.l + T2.h
Serial.ll <- T1.l + T2.l
micTest(HH=Serial.hh, HL=Serial.hl, LH=Serial.lh, LL=Serial.ll)

Parallel.hh <- pmax(T1.h, T2.h)
Parallel.hl <- pmax(T1.h, T2.l)
Parallel.lh <- pmax(T1.l, T2.h)
Parallel.ll <- pmax(T1.l, T2.l)
micTest(HH=Parallel.hh, HL=Parallel.hl, LH=Parallel.lh, LL=Parallel.ll, ART=TRUE)