## 2 Materials and Methods
### Data Analysis  
To separate sections of data corresponding to the time volunteers were performing the walking task of the protocol, recorded videos were used. Labeling of data according to video sections was performed manually for each individual and each sock ply condition. Raw FSR signals were filtered using a second order Butterworth low pass filter to remove noise. The cut-off frequency for the Butterworth filter was determined based on the Welch's power spectral density estimate of the signal being filtered. Peaks of filtered signals were extracted. Each peak corresponded to one step as pressure/force at the distal end of the socket peaks once in every step taken by the monitored foot, the leg with amputation in this case, at the time when the maximum amount of user's weight is loaded on the foot during the mid-stance phase of a gait cycle. Peak values of FSR signals were averaged to obtain a single value per sensor for each participant and each condition. This averaging step was required because peak values were dependent and treating them as separate measurements would have caused pseudoreplication [24]. Moreover, averaging multiple steps for each participant and each test provides a more realistic measure of the force by taking into account the variability of gait in different steps.  
The average peak values of FSR readings were converted to force. To convert FSR readings to force, a calibration method was used in which the sensors' readings in response to known values of varying applied force were measured for multiple FSR sensors. In this experiment, the value of force was measured using an ATI Mini 45 six-axis load cell as the force was increased up to approximately 280 N and decreased in cycles of approximately 25 s. Using measurements obtained in this experiment, an exponential curve was fitted to map the sensors' responses to force values (\(R^{2}=0.944\), \(RMSE\%=1.85\%\) ). Exponential fitting was chosen for this calibration based on the documentation of FSR sensors used in this study.  
In order to generalize the results, average peaks of force values were normalized with respect to the values obtained in the normal piles condition for each participant. Normalized means of peaks of force were final measures compared in different conditions of sock piles. The process of data analysis is shown in Figure 2.  
It is worth noting that at the beginning of each test, after donning the socket, there was a transient period when the user's residual limb and the prosthetic socket were adjusting to the test conditions. The length of this time in each test depended on the socket fit, the shape of the residual limb, the number of sock piles, and other variables such as the user's weight. For the purpose of this study, this transient section, which was four steps on average, was removed from the beginning of the protocol in each test condition since it appeared only at the beginning of the tests and did not represent normal operations of the socket.  
For statistical analysis, a randomized complete block experimental design with mixed-model analysis was used where volunteers were considered random effects. This was done to remove the effect of variations of data due to individual-specific factors [25]. In this repeated measures design, normalized means of peaks of force obtained from different participants for each sock ply condition and for each phase were considered as repeated measures. All statistical analyses performed for this study were done using JMP statistical analysis software from the Statistical Analysis System (SAS) institute (Cary, NC, USA).  
Statistical analysis was performed based on the assumption of normality of residuals. Shapiro-Wilk test, which is recommended for small sample sizes [26], was used to assure normality of residuals before statistical tests were carried out in this study.