Error Rates

Another way of comparing whether reaction time data was confounded by errors on the lexical decision task involves explicitly examining error rates for each condition in which the task was administered. As can be seen from Table 5, p. 79, which summarizes descriptive statistics for error rates for the tasks, error rates were generally very low for all conditions.

 

Table: Error Rate Data for Each Condition

			Depressed			NonDepressed
Task	Duration	Valence	Mean	St Dev	N	Mean	St Dev	N
Lexical Decision	150	Positive	.04	.07	46	.07	.19	30
Lexical Decision	150	Negative	.02	.05	46	.07	.19	30
Lexical Decision	150	Neutral	.06	.07	46	.10	.20	30
Lexical Decision	150	Nonword	.07	.09	46	.10	.15	30
Lexical Decision	100	Positive	.05	.07	46	.08	.19	30
Lexical Decision	100	Negative	.04	.06	46	.06	.20	30
Lexical Decision	100	Neutral	.06	.07	46	.10	.19	30
Lexical Decision	100	Nonword	.09	.10	46	.13	.16	30
Lexical Decision	50	Positive	.06	.09	46	.09	.20	30
Lexical Decision	50	Negative	.04	.06	46	.09	.19	30
Lexical Decision	50	Neutral	.06	.09	46	.11	.19	30
Lexical Decision	50	Nonword	.17	.17	46	.18	.15	30

To examine differences in sensitivity to words of different valences in each condition, Dprime was calculated for each condition. As error rates for all tasks were very low, z-scores for error rates of zero were approximated to be 4 (i.e., a value for a probability less than 0.001), and z-scores for false-alarm rates of 0 were approximated to be -4. The resulting sensitivity indices are displayed in Table 6, p. 79. In general, sensitivity was excellent. As may be seen from the table, sensitivity went up slightly as the stimulus duration increased for both depressed and nondepressed people. This observation was confirmed by the presence of a linear trend in duration as revealed by a planned contrast using a 3 (Valence) x 3 (duration) repeated measures ANOVA, t(270)=-8.2, p<0.05. While nondepressed people appeared more sensitive than depressed people in every condition, this difference was not statistically significant in the context of a 2 (Depression) x 3 (Valence) x 3 (duration) multivariate split plot ANOVA which revealed no statistically significant main effects or interactions of depression on sensitivity.

 

Table: Dprime for Depressed and Nondepressed Groups

Duration (ms)	Valence	NonDepressed Dprime	Depressed Dprime
050	Negative	-5.17	-4.26
050	Neutral	-4.77	-3.92
050	Positive	-4.88	-4.34
100	Negative	-5.46	-5.53
100	Neutral	-5.03	-4.66
100	Positive	-5.34	-5.16
150	Negative	-6.20	-5.78
150	Neutral	-5.39	-5.35
150	Positive	-5.92	-5.85

To test the hypotheses that reaction time latencies on the valence identification and lexical decision tasks would be paralleled by increased error rates on these tasks, a 2 (Depression: Depressed, Nondepressed) x 2 (Gender: Male, Female) x 2 (Task: Lexical Decision Task, Valence-ID Task) x 3 (Valence: Positive, Negative, Neutral) x SD (50ms, 100ms, 150ms) multivariate split plot ANOVA with error rate was performed. Attribution of other than the normed valence for a word on the valence identification task was considered an error. The test revealed no statistically significant interactions or main effects involving depression or gender.

Another factor which might confound results involves confusion between valences on the valence identification task. If words of one valence are more easily identified than words of some other valence, this result might absorb variance in differential reaction times. As such, confusion matrices were generated for the task, in which each cell represents the average percent of responses to a stimulus of a given valence which were confused with a response of another valence. These confusion matrices are presented in Table 7. In the table, stimuli are presented vertically, and responses are presented horizontally.

 

Table: Confusion Matrices for the Valence Identification Task.

		50			100			150
	+	-	N	+	-	N	+	-	N
+		.02	.11		.02	.11		.01	.12
-	.05		.11	.03		.11	.03		.11
N	.16	.08		.15	.05		.14	.06

As may be seen from the table the confusion matrices are remarkably similar for each of the three stimulus durations, suggesting that the observed confusion coefficients have some generality. The confusion matrices are asymmetric suggesting either that an understanding of positive and negative words as being equidistant from neutral words in semantic space is inappropriate, or that people are biased towards responding to words of some valence. To investigate the latter hypothesis Luce's (1963) bias independent confusion coefficients ($\eta$) were calculated for each cell for the 150 ms condition as $\eta_{i,j}=\sqrt{\frac{p(\rho_i\vert w_j)p(\rho_j\vert w_j)}{p(\rho_i\vert w_i)p(\rho_j\vert w_j)}}$ to obtain the parameter estimates shown in Table 8, p. 81.

 

Table: Bias Independent Parameter Estimates for Valence Confusions

	+	-	N
+	1	.02	.15
-	.02	1	.09
N	.15	.09	1

It may be seen from this relatively bias-independent matrix that positivity and negativity are not equidistant from neutrality. Indeed, for most people, positivity was closer to neutrality than it was to negativity, and similarly negativity was closer to neutrality than it was to positivity. Yet, positivity was closer to neutrality than was negativity, suggesting that an understanding of positivity and negativity as equally far from neutrality may be flawed. This finding is congruous with results from task given in the third semester of the experiment which asked people to rate the relative positivity and negativity of stimuli to which they were exposed. In general people rated positive words as less intense (i.e., less far from neutrality) than the negative words used in the experiment. As put by one student ``You can't compare positive things like 'birthday' to really terrible things like 'bereavement'''. Potentially, though, this result is a function of the particular stimuli which were used in the experiment.