## 2 Methods
### Data Analysis  
By using a method proposed by [PERSON] et al., the ankle accelerometer and gyroscopic readings were used to estimate the gait parameters (stride length, cycle time, and gait speed) for evaluation and analysis [31]. Each trial was split into sections, as shown in Figure 4. The gait readings (stride length, cycle time, and speed) for each trial were split into these sections (Base, Before, After, and Post) and grouped by condition (SI, SD, PI,and PD). The sections represent the average of the values, as shown in Figure 4, and the descriptions are as follows:  
* Base refers to the average of the values in the first phase of the trial before the first turn and with no avatar showing. Ten strides at the start and end of the phase were omitted to eliminate acceleration and deceleration readings. This was used as the baseline and control value for comparison for the learning effect.
* Before refers to the average values of 10 strides after the first turn but before the gradual cue. The 10 strides immediately after the turn were omitted not to include the acceleration values.
* After refers to the average values of 10 strides before the second turn but after the gradual cue. The last 10 strides before the turn were omitted to eliminate the deceleration readings.
* Post refers to the average of the values in the final section of the trial after the second turn and with no avatar showing. The 10 strides at the start and end of the phase were omitted to eliminate the acceleration and deceleration readings.  
The gradual change lasting 12 s in either the distance or phase difference between the participant and the avatar occurred approximately 20 m after the first turn for each of the four conditions. The first 10 and last 10 strides in each trial were removed from analysis, as they featured unstable and high variability gait readings caused by the acceleration and deceleration at the start and end of the trial.  
Normalized values were applied to decrease the impact of participant height on the trends [32] and were calculated by using the following equation:  
\[Norm_{X}=X_{i}/(h_{i}/\hat{H}), \tag{7}\]  
where \(Norm_{X}\) represents the normalized value of \(X\), which represents cycle time, speed, or stride length. \(X_{i}\) represents the average value for participant \(i\), \(h_{i}\) represents the height of participant \(i\), and \(\hat{H}\) represents the average height of all participants. After the averages were calculated for each trial, they were grouped into the four conditions and averaged to provide their respective values for comparison. Comparison between the Before and After values were used to reveal the immediate effect of the cues. Additionally, the comparison between the Base and Post values shows the carry-over or learned effect of the cue.  
Change ratio values were used to observe the differences in changes between the conditions. Change ratio values were calculated by using the following equation:  
\[ChangeRatio=\frac{After\ Value-Before\ Value}{Before\ Value} \tag{8}\]  
The change ratios were used for comparisons between the Base and Post sections (Base-Post) and comparisons between the Before and After sections (Before-After).  
Repeated measures analyses of variance (ANOVAs) were conducted by using a significance factor of 0.05. Python and its statsmodels library were employed to analyze differences before and after the changes. Two independent factors were tested: conditions (SI, SD, PI, and PD) and sections (Base, Before, After, and Post). Multiple comparison analyses were conducted by using the Benjamini-Hochberg correction method with a significance level of 0.05.