This page contains the information pre-registering a series of experiments designed to test the theory that egocentric information can be used in Bayesian ways, showing three classic Bayesian effects, while allocentric information does not show the same effects in closely matched conditions. The first deals with priors, the second with cue integration, and the third with loss functions. Priors ------ **Narrative Overview** This experiment will test the hypothesis that participants take advantage of an egocentric prior, but not an allocentric prior, by biasing their responses towards the prior mode. In every condition, the task is to see a target relative to a red line and then indicate where it lands after a rotation under a cover. In the baseline condition, the target’s final position is uniformly distributed in both the egocentric frame (position on the screen) and the allocentric frame (position relative to the red line). In the allocentric condition, there is a normal prior distribution in the allocentric frame. In the egocentric condition, there is a normal prior distribution in the egocentric frame. All conditions share 8 key trials that are exactly the same across conditions. These key trials are the only ones used in the analysis. The difference between conditions is the context of the other 88 trials that induce either the normal (informative) or uniform (uninformative) prior distributions in the relevant frames. Any difference in performance on the key trials can therefore only be explained by the presence of the different prior distributions; the only trials that are used in the analysis are exactly the same in every respect. **Participants** 25 adult participants per condition will be recruited primarily from the LJMU Sona system. **Apparatus** The experiments are programmed through Pavlovia. Inside a grey void there is a large circle. In the center is a black dot. Around the edges there are 4 squares that are attached to the circle. There is also a red line that touches the center dot and the edge of the circle. There is also a target, a small blue triangle. Finally there is a black disc that can cover all of this except for the squares. **Stimulus** ***General*** There are 96 trials split into two blocks of 48. Each block uses the same stimuli in a random order. The distance from the target to the center dot is evenly distributed from 5% to 95% of the radius of the large circle. Of these 48 trials, 8 are designated as key trials and shared between all three conditions. These key trials all result in the red line being at 0 radians (straight right) and the target being in the upper left corner of the circle. Specifically, the program first generates an even distribution of rotations around the circle. The key trials are the 8 trials that are nearest to .75xpi (but not exactly equal to it). Trials also have a total rotation, a total amount that the target/line/disc/squares spin after the target is shown. This is generated as an even distribution from 0.25xpi to 1.75xpi. Added to this is a whole multiple of 2xpi, with a minimum multiple of 5 and a maximum of 10. ***Specific to Allocentric Condition*** The remaining 40 trials are allocentrically normally distributed. This means that the rotation from the line to the target is an approximate normal distribution. Specifically it is a linear spacing from .025 to .975 fed into an inverse normal CDF with a mean of 0.75xpi and a standard deviation of 0.1xpi, with the 8 points nearest the key trials removed. The remaining 40 trials are egocentrically uniformly distributed. This means that the final target’s position on the screen is evenly spaced around the disc. ***Specific to Baseline Condition*** The remaining 40 trials are allocentrically uniformly distributed and egocentrically uniformly distributed. ***Specific to Egocentric Condition*** The remaining 40 trials are allocentrically uniformly distributed and egocentrically normally distributed (same mean and standard deviation as the allocentric condition). **Procedure** Instructions are given to click on the target after the spin. The disc, squares, and red line are shown. The target pulses for 3 seconds. At this point, the target’s distance to the center is equal to its final parameter. However, its rotation value is determined by subtracting the total rotation from the final egocentric rotation value. The rotation value of the red line is calculated by subtracting the allocentric rotation from the target’s rotation value. The target pulses for 3 seconds and then is no longer visible. The black disc covers the large circle and red line. Over 2s, the line/target/squares/circle all spin for the total rotation amount. This places the line and target in the intended ego/allo position. The black disc fades away. The participant tries to click on the new position of the target. They are shown the correct target location for 3s. The next trial begins. Nothing marks the transition between blocks. **Planned Analysis** Participants will be removed as outliers if the circular correlation between target and response is not at least 0.4. Trials will be removed as outliers if the absolute theta error is more than 90 degrees. For each participant, we will examine the key trials in the second block. We will calculate the bias towards 0.75xpi. This is the absolute deviation from 0.75xpi to the target minus the absolute deviation from 0.75xpi to the response. The hypothesis is that the bias will be greater in the egocentric condition than the baseline condition, while the bias will not be greater in the allocentric condition than the baseline condition. This will be tested with a trio of one-tailed t-tests. We should see ego > baseline, see ego > allo, and not see allo > baseline if the hypothesis is correct. Cues ---- **Narrative Overview** This experiment will test the hypothesis that participants integrate egocentric cues, but not allocentric cues, to gain precision. Both conditions are otherwise matched as closely as possible. On a given trial, the participant is given a near cue, a far cue, or both cues to a target location. If cue combination is occurring, we should see better precision with both cues than the near cue. For the egocentric condition, the cues are two moving squares that come out of two landmarks. For the allocentric condition, the cues are seeing the target relative to the two landmarks before the scene spins. **Participants** 25 adult participants per condition will be recruited primarily from the LJMU Sona system. **Apparatus** On a white background, there are two small triangles (light grey and black) that serve as landmarks. Each landmark has a small black dot attached that can be moved towards the target for the egocentric condition. There is also a target, a small blue triangle. **Stimulus** ***General*** The targets are on a 6x6 grid, omitting corners (32 targets). These are 5/16, 3/16, 1/16, and so on from the center in each axis. Each target has an assigned total rotation with two components. The first is evenly distributed from .25xpi to 1.75xpi in 8 steps (each used 4x). The second is an even multiple of 2xpi, with a random whole multiple between 10 and 20. To make test trials, this is repeated with either the black triangle, the grey triangle, or both (96 trials). Added to this are 3 warmup trials to begin. The test trials are delivered in a random order. All that varies across trial types is the cues presented. ***Specific to Egocentric Condition*** To indicate an egocentric position, the square(s) attached to the landmark(s) move half-way to the target position over a period of 1s, moving faster at the beginning and slowing their velocity linearly to a stop. When stopped, they disappear. ***Specific to Allocentric Condition*** To indicate an allocentric position, the target pulses in place relative to the landmarks for 3s. This then disappears before the landmarks spin. **Procedure** Participants are instructed to find the target after the spin. Instructions explain how the relevant cue functions. On each trial, the black landmark begins at the top of the screen (.5xpi) and the grey begins at the bottom of the screen (1.5xpi). Depending on the trial type, they can be either visible or not (and their black square). In the allocentric condition, the target pulses for 3s. In either condition, the landmarks spin for 3s and come to a stop. In the egocentric condition, the squares move towards the target location. In either condition, the participant then clicks where they think the target is. The correct location is shown for 3s. **Planned Analysis** For each participant, six measures will be extracted: variable error with the near cue, the far cue, and both cues – each repeated along the x axis and the y axis. Variable error is the noise in responses, separate from the systematic biases present (often called the constant error). First, outlier participants will be removed by screening for any participant who does not have a correlation between target and response of at least 0.4. Second, outlier data points will be removed by removing any responses that are more than 2.5 standard deviations from the target (i.e. find the Pythagorean distance from target to location for all responses, find the root mean squared distance, and exclude anything more than 2.5x further). Variable error will be calculated by entering each participant’s data into a multiple regression. The response location on the relevant axis is the outcome. The target location, center point, and the position of the landmarks will be entered as predictors. From this we will extract the residuals and find their standard deviation. This standard deviation is then divided by a correction factor to remove the variance-reducing effects of certain biases (Aston et al., 2021). This factor is the beta value for the target location, capped at one. We will then do a paired one-tailed t-test for each condition, testing the hypothesis that near variable error (averaged over the two axes) is greater than both-cues variable error (again averaging). The hypothesis is that this effect will be present for the egocentric condition, but not the allocentric condition. A t-test is preferred here over an ANOVA main effect because it can be one-tailed. If this occurs, we will also check for a difference between conditions with a one-tailed t-test. The outcome will be variable error gain. This will be calculated by finding the difference, on a log scale, between the near variable error and the both-cues variable error (again averaged over the two axes). The hypothesis is that the gain is larger for the egocentric condition than the allocentric condition. The log scale is preferable here because there may be a meaningful difference in the base precision with the near cue. Gains ----- **Narrative Overview** This experiment will test the hypothesis that participants will use an asymmetric egocentric loss function to their advantage, biasing responses in the less-penalizing direction, but not an otherwise equivalent allocentric loss function. Participants will be given a simple but difficult spatial task, seeing a target relative to a red line and then indicating where it lands after a spin under a cover. Their score will be base 100 per trial, with points removed for errors in the rho dimension and theta dimension (i.e. polar dimensions). The conditions will either penalize theta errors symmetrically (baseline), penalize theta errors towards the top of the screen less (egocentric), or penalize theta errors towards the line less (allocentric). **Participants** 25 adult participants per condition will be recruited primarily from the LJMU Sona system. **Apparatus** Inside a grey void there is a large circle. In the center is a black dot. Around the edges there are 4 squares that are attached to the circle. There is also a red line that touches the center dot and the edge of the circle. There is also a target, a small blue triangle. Finally there is a black disc that can cover all of this except for the squares. **Stimuli** There are a total of 45 trials. The initial theta value of the red line is evenly spaced from 0 to 2xpi, as is the initial target theta value. The initial rho value of the target is evenly spaced from 10% to 90% of the way from the center dot to the large circle’s edge. The total rotation has two components. The first is evenly spaced from .25xpi to 1.75xpi. The second is an even multiple of 2xpi, with a whole number multiple between 5 and 15. Each of these were randomly ordered once (independently) and used in the same order for all participants. **Procedure** Instructions are given to click on the target after the spin. The disc, squares, and red line are shown. The target pulses for 3 seconds. Over 2s, the line/target/squares/circle all spin for the total rotation amount. The black disc fades away. The participant tries to click on the new position of the target. They are shown the correct target location for 3s. Alongside this, a short animation gives them their score. It marks out the rho error first, then the theta error. If the theta error is in a less-penalized direction (i.e. closer to the line/top than the target), the animation is green and the theta penalty is halved. If it is in a more-penalized direction, the animation is red and the theta penalty is doubled. **Planned Analysis** Participants will be removed as outliers if the circular correlation between target and response is not at least 0.4. Trials will be removed as outliers if the absolute theta error is more than 90 degrees. From each participant, we will extract the bias towards the top and bias towards the line. This is the average distance from top/line to target minus the average distance from top/line to response. We hypothesize that the bias to top will be higher in the egocentric condition than the baseline condition, whereas the bias to line will not be higher in the allocentric condition than the baseline condition. This will be tested with two one-tailed t-tests. If confirmed, a third one-tailed test will see if the relevant bias is larger in the egocentric than the allocentric condition.