#Excel for mac 2011 command e how to#
#Excel for mac 2011 command e full#

In particular, the regression process calculates the smallest grand sum of the squared residuals, which is why this process is termed least squares regression (for a thorough discussion on this topic, see Motulsky & Christopoulos, 2004). Specifically, a best fit line or curve is generated by estimating a free parameter (e.g., k) within the model until the vertical difference between each observed data point and the estimated point (called the residual value) on the line is minimized to the smallest possible value (see Figure 1). Next, a best fit line (or curve) is generated according to those initial values. First, the researcher is required to enter the numerical value of the dependent variable at each level of the independent variable (or the subjective value of the LLR or indifference point at each delay value in the case of delay discounting) into the quantitative model.

#Excel for mac 2011 command e full#

Although a full understanding of how nonlinear regression works requires mastery of matrix algebra, the basic method is relatively easy to follow. The researcher then uses least squares nonlinear regression to fit a curve to the data points.ĭescribing participant patterns of discounting presents numerous analytical challenges for researchers who are unfamiliar with advanced statistics because of reliance on nonlinear regression models. To determine k, the researcher must plot the subjective values against reward delays. Higher k values translate to higher degrees of discounting or impulsivity.

Parameter k is thus the dependent variable in quantitative studies of discounting. The parameter k is a free parameter that denotes the degree of discounting (or the discounting rate) observed in the data path (i.e., steepness of the curve or how fast the value drops as a function of delay). Nevertheless, numerous studies have demonstrated that values obtained from hypothetical choices correlate with values obtained from actual rewards (see Johnson & Bickel, 2002 Lagorio & Madden, 2005 Madden, Begotka, Raiff, & Kastern, 2003 Madden et al., 2004). As the reader may surmise, the employment of hypothetical choice, as well as the use of verbal self-report, is a substantial deviation from the direct measurement techniques usually used in behavior-analytic studies. This methodology then is replicated across numerous delay values (i.e., the delay until the receipt of the LLR) to arrive at an understanding of the individual's preference for reward over time (the reader is encouraged to consult Madden & Johnson, 2010, for a lengthier discussion on discounting assessment methodology). This indifference point serves as an estimation of the subjective value of the LLR after some delay. The point at which an individual switches from choosing the LLR to the SSR is commonly termed the indifference point. Typically, hypothetical monetary choice paradigms feature a titrating series of choices between smaller sooner rewards (SSRs) and a larger later reward (LLR). The commonly used procedure for studying discounting is the administration of a series of hypothetical monetary choice trials (see Critchfield & Kollins, 2001 Madden & Johnson, 2010). This behavioral interpretation of impulsivity has led to numerous advances in clinical issues such as increasing tolerance to reinforcement delay in individuals with acquired brain injury or autism ( Dixon & Cummings, 2001 Dixon & Falcomata, 2004), as well as in the general assessment of impulsivity in children with attention deficit hyperactivity disorder (ADHD Hoerger & Mace, 2006 Neef et al., 2005), serious emotional disturbance (e.g., Neef, Mace, & Shade, 1993), and severe problem behaviors (e.g., Vollmer, Borrero, Lalli, & Daniel, 1999). For instance, behavior analysts have come to define a form of impulsivity as preference for a smaller sooner reward, despite a larger delayed alternative being available (see Schweitzer & Sulzer-Azaroff, 1988). Specifically, this operationalization of decision making is translated easily to issues concerning impulsivity and self-control. Analyses of delay discounting (the process by which delayed rewards have lower subjective values than sooner rewards of the same magnitude) have become increasingly popular due to their ability to allow researchers to investigate the temporal properties of reward for socially important problems (see Critchfield & Kollins, 2001 Madden & Bickel, 2010).

#Excel for mac 2011 command e how to#

The goal of this technical article is to present researchers with a tutorial on how to conduct both nonlinear regression and area under the curve (AUC) estimations using Microsoft Office Excel 2010 and Excel for Mac 2011 (hereafter referred to simply as Excel) to analyze delay-discounting data.