Welcome back to the AI Bayeslab Statistics series. First, let's consider three hypothetical scenarios to introduce the core value of signal detection theory.
1.Differentiating Objective Sensitivity from Subjective Bias
Scenario 1:
Imagine Company A is experimenting with the number and placement of ads in a new app. While increased ad displays generally enhance commercial returns, too many ads might cause users to leave. Two groups, A and B, consisting of 1000 participants each, participate in A/B testing. Even though the ad frequency and content are the same for both groups, Group A experiences considerably lower churn than Group B. Theoretically, churn rates should be similar for both groups.
Question 1: What causes the same ad frequency and content to lead to notable differences in user churn across groups?
This involves the issue of "objective sensitivity (d prime) vs subjective response bias."
Objective Sensitivity: Refers to users' actual perception of ads. Ideally, identical ad frequency and content should have similar perceptual effects on both groups.
Subjective Response Bias: This involves different reaction standards that groups may use for the same ad stimulus. Differences in churn might reflect the groups' varying acceptance or tolerance levels towards ads.
First Core Value of Signal Detection Theory:
Distinguishes objective sensitivity from subjective response bias, influenced by factors like motivation and personal preference. Consequently, Company A can achieve a better balance between monetization and user loyalty by modifying the quantity of ads.
In other words, two individuals with identical sensitivity levels may yield varying results based on their distinct judgment criteria—one adopting a cautious approach with stringent standards, while the other possesses more relaxed standards. In the aforementioned scenario, "ad aversion" can similarly be interpreted as "user preferences and interests," resulting in different churn rates.
Other subjective factors that could affect churn rates include:
Ad Fatigue: Certain users are more sensitive to advertisements and can quickly become irritated by repetitive ones.
User Experience and Expectations: The varying expectations and experiences users have with an app can influence their tolerance for how often they see ads.
Cultural and Background Differences: Users' cultural backgrounds may shape their perceptions and responses to ad content and formats.
Previous Experiences or Lessons: Negative experiences with ads in the past can result in higher churn rates due to unfavorable views.
Personality Traits: Some users prefer avoiding interruptions from ads, while others might be more accepting of them.
App Usage Purpose: The main reason for using an app can impact how users react to ad interruptions. For example, casual users may be more accepting of ads than those seeking quick information. ons. For instance, casual users might be more tolerant of ads than those needing quick information.
By differentiating objective sensitivity from subjective response tendencies, Company A can enhance ad quantities to align commercialization objectives with user loyalty, thus prolonging the overall app lifecycle.
2.Accountability of Prior Probabilities and Criterion Shifts
Scenario 2:
Imagine Amy investigating whether a silent fan operates quietly. The study accounts for consistent background noise and other unrelated factors while ensuring that participants are blindfolded to eliminate any tactile feedback, helping to prevent the sensation of airflow from influencing their responses. Test subjects are left with two choices: "sound" or "no sound." The likelihood of stimulus occurrence, referred to as "prior probability," is indicated by P(S)=1, wherein S signifies the "stimulus" (when the fan activates, it produces a specific decibel level), corresponding to the actual sound levels generated when the fan is turned on. Obviously, different fan speeds will result in varying noise levels.
Question 2: If test subjects provide inaccurate reports, such as making random claims about whether the fan is on, how can we eliminate the interference or errors resulting from these false reports?
This issue pertains to the concept of "prior probability." If we adjust the prior probability and treat P(S) as an independent variable, P(S) can be interpreted as the frequency with which the fan is genuinely on in 100 inquiries posed to users about whether they can hear the fan. For instance, if the fan is actually on only 5 times in 100 inquiries, or if it’s on 88 times, this results in different prior probabilities for P(S).
This leads to the classic four types of responses we introduced in the previous article:
Hit (fan is on, response is yes)
Miss (fan is on, response is no)
False Alarm (fan is off, response is yes)
Correct Reject (fan is off, response is no)
Now, let y represent the user reporting sound. The probabilities of the two possible responses reporting sound are:
P(y) = P(H) + P(FA)
We find that varying fan activation frequencies, referred to as the absolute threshold of sensation, impact the relationship between P(y) and the intensity of the physical stimulus (the sound level when the fan engages), subsequently affecting the size of the 50% sensory threshold.
Additional research shows that as the likelihood of an event increases, users are more likely to respond with "yes." In contrast, when the probability is lower, they tend to reply with "no."
This introduces the second core value of signal detection theory:
It challenges the conventional psychophysics perspective that regards thresholds as stable sensory limits. In standard psychophysics, thresholds are defined as the minimal sensation limits that pertain solely to sensitivity. If the intensity of the physical stimulus remains constant (for instance, a steady fan speed), the psychological response from the same user should not exhibit significant fluctuations.
It is important to highlight a phenomenon known as "criterion shift," which results from very low prior probabilities and can lead to missed detections. For instance, someone tasked with monitoring earthquakes faces an extremely low likelihood of detecting earthquake signals. In this situation, because it is impossible to maintain full attention on the monitoring screen at all times, there will inevitably be a chance of missing reports.
3.Decision-Making Based on Potential Gains and Losses
Scenario 3:
Imagine receiving a call about a package left at your doorstep versus a neighbor alerting you that your house is on fire. While both involve phone calls, which situation would compel you to rush home immediately? Clearly, the fire is the more urgent matter.
Question 3: Why does your decision differ despite receiving a call in both scenarios?
This involves the impact of decision consequences on thresholds and the relationship between your judgments and the gains or losses from events. Not responding to a call about a package is an event with minimal loss, whereas failing to respond to a call about a fire involves significant potential loss.
This introduces the third core value of signal detection theory:
The rewards of a Hit or Correct Reject, and the costs associated with a Miss or False Alarm.
These three scenarios illustrate that an individual's response formation isn't solely based on physical stimuli; it also incorporates objective sensations and subjective decision-making processes. The final response results from the interplay between these two elements.
Stay tuned, subscribe to Bayeslab, and let everyone master the wisdom of statistics at a low cost with AI Agent Online tool.