Transfer of learning: Analysis of dose-response functions from a large-scale, online, cognitive training dataset

Fundamental to the efficacy of cognitive training (CT) is its dose. Here we used the power and breadth afforded by a large dataset to measure precisely dose-response (D-R) functions for CT and to examine the generality of their magnitude and form. The present observational study involved 107,000 users of Lumosity, a commercial program comprising computer games designed to provide CT over the internet. In addition to training with Lumosity games, these users took an online battery of cognitive assessments (NeuroCognitive Performance Test, NCPT) on two or more occasions separated by at least 10 weeks. Changes in performance on the NCPT between the first and second assessments were examined as a function of the amount of intervening gameplay. The resulting D-R functions were obtained both for overall performance on the NCPT and performance on its eight subtests. Also examined were differences between D-R functions from demographic groups defined by age, gender, and education. Monotonically increasing D-R functions, well fit by an exponential approach to an asymptote, were found consistently for overall performance on the NCPT, performance on seven of the eight subtests, and at each level of age, education, and gender. By examining how individual parameters of the D-R functions varied across subtests and groups, it was possible to measure separately changes in the effects on NCPT performance of 1) transfer from CT and 2) direct practice due to repeated testing. The impact of both transfer and direct practice varied across subtests. In contrast, while the effects of direct practice diminished with age, those of transfer remained constant. Besides its implications for CT by older adults, this latter finding suggests that direct practice and transfer do not involve identical learning processes, with transfer being limited to learning processes that remain constant across the adult lifespan.

A legend with numbers 1 to 9 and corresponding abstract symbols is presented across the top of the screen. The height of the numbers is equal to 1/24 the height of the screen, and symbols fill a space with height and width equal to 1/12 the height of the screen. The symbols are randomly selected from a pool of 18 possible symbols. In the middle of the screen a large, two-section box (top and bottom sections each having a height equal to ¼ of the screen height) is presented with the symbol in the top section. The participant is required to use the number keyboard to type the number that corresponds to the symbol. Once a number is pressed, it moves on to the next trial. Participants can see the next symbol grayed out, but they cannot go back to a previous trial. The assessment is timed for 90 seconds and the dependent measure is the total number of correct trials minus incorrect trials.

Forward and Reverse Visual Memory Span
Memory span is a common measure of visual short-term memory and functionally appears to measure the number of discrete units over which an individual can successively distribute attention and still organize into a working unit. To generalize, forward memory span refers to the ability of an individual to reproduce immediately, after one presentation, a series of discrete stimuli in their original order whereas reverse memory span requires reproducing the order in reverse.
The Visual Memory Span tasks are derived from the Corsi block-tapping test, which is a psychological test that assesses visuospatial short term working memory. The Corsi block-tapping task involves mimicking a researcher as he/she taps a sequence of up to nine identical spatially separated blocks. The backward Corsi block-tapping task is a slightly altered version of the original Corsi block-tapping task, and is considered a measure of working memory. In the backward task, the subjects are asked to watch the sequence and instead of mimicking the researcher's pattern, they are asked to repeat the sequence in reverse order. In computerized versions of the Visual Memory Span tasks, instead of cubes to be tapped on a board, the tests consist of circles that flash on a computer screen and participants reproduce the sequences by using a mouse to click on the circles [3,4].
Blue circles with radii equal to 1/20 of the window height are placed at randomized, non-overlapping spatial locations and individually highlighted in orange following a particular sequence. Circles are highlighted for 500 msec with a 100 msec inter-stimulus interval. The participant is asked to recall the sequence by clicking on each circle in same order as originally presented. The length of the sequence increases by one every three trials. The session ends when the participant gives three incorrect answers at the same span level. The total number of correct responses is the dependent measure.

Forward Memory Span
Reverse Memory Span

Trail Making A and B
The Trail Making Test (TMT) is one of the most popular neuropsychological tests and is included in most test batteries [5,6]. The TMT provides information on attention and speed of processing. Originally, it was part of the Army Individual Test Battery [7] and subsequently was incorporated into the Halstead-Reitan Battery [8].
In Trail Making A, blue circles numbered from 1 to 24 are arranged in 6 possible layouts with nonoverlapping spatial locations. Layouts are normalized for completion time with total path length equal to 5 1/3 times the screen height, as well as equivalent circle-to-circle distance and angle distributions and circle density distributions. The circles have radii equal to 1/25 of the screen height and the number height is equal to 1/24 of the screen height. The participant is required to click on the circles sequentially connecting the encircled numbers. When clicked the blue circles change color to orange and a straight line appears connecting the circles. Task requirements are similar for Trail Making B except the circles now include numbers (1 to 12) and capital letters (A to L) and the participant must alternate between numbers and letters (e.g., 1, A, 2, B, 3, C, etc.). The timer begins when the participant clicks number 1. If the participant clicks on an incorrect circle, an X appears and they must go back to the previous circle. The amount of time required to complete the task is the dependent measure.

Grammatical Reasoning
The grammatical reasoning test is a test of the ability to carry out mental operations involving chains of logical reasoning. The test is derived from Baddeley's Grammatical Reasoning Test [9] and measures the participant's facility to rapidly and accurately evaluate a potentially confusing grammatical statement.
A blue square and a blue equilateral triangle, each with height equal to 1/5 of the window height are shown side by side, with a logical statement written below. For example, the square may be positioned to the left of the triangle on a particular trial. The participant could be prompted with a statement of the form, "The square is not to the left of the triangle." In this case, the answer would be "false." The participant responds whether the statement is true or false by pressing a key on the keyboard that is indicated as corresponding to true or false. The probability that the statement includes a negative ("not") is 50%. The net number of correct responses (number correctnumber incorrect) in 45 seconds is the dependent measure, with a floor of zero. This test is a measure of cognitive flexibility and logical reasoning.

Progressive Matrices
The Progressive Matrices test was inspired by Raven's Progressive Matrices [10], with the exception that the NCPT version has dynamically generated problems. Matrix reasoning assessments require the participant to determine which stimulus most logically completes a multi-dimensional pattern. In this version of matrix reasoning, the participant is shown a 3x3 grid (each grid slot has width and height equal to 1/5 the window height) with abstract stimuli in the 8 upper-left slots. The task is to choose which of six possible answer choices best completes the pattern in the grid. The assessment is made up of 17 problems of increasing difficulty that are algorithmically generated from a set of parameters. The 17 problems are divided into three broad problem types: progression matrix, orbital/lateral movement, and Boolean logic. The first 12 trials involve progression matrix rules of increasing complexity.
Characteristics of the stimuli that may change include shape, number, color, rotation angle, and size. These patterns may progress across the matrix horizontally, vertically, from upper-left to lower-right diagonal, or from lower-left to upper-right diagonal. Trials 13-15 involve orbital or lateral movement in which square grids or circular orbits are partially filled with elements that progress according to a lateral or rotational movement rule. Trials 16-17 involve Boolean logic in which spatial patterns are combined using Boolean operators such as AND, OR, and XOR. For each problem type, the correct answer is indicated regardless of whether the participant answers correctly. The assessment ends once the participant completes 17 trials or answers three consecutive trials incorrectly. The total number correct is the dependent measure. Matrix reasoning is considered a measure of problem solving and fluid reasoning (often referred to as fluid intelligence).