Threshold effect

A threshold effect is a specific type of effect in which an effect on an outcome variable (dependent) occurs only after the value of a related variable reaches a specific quantitative limit, or critical value, called the threshold. All effects of every type are simply relationships between variables, so when "threshold effect" is defined as a specific type of effect, what is meant is that it is a specific type of relationship between variables. In threshold effects, the variables have one relationship across a given range of values for one of the variables, but as soon as the value of the variable exceeds that range (exceeds a critical value), it crosses a threshold that fundamentally changes the relationship between the variables. To illustrate the concept, lets take three examples of relationships between independent and dependent variables from economics, psychology, and medicine.
The relationship between sensory stimuli (IV) and response (DV) depends on a threshold. At the lowest values subjects can't even detect the stimuli (the touch is too light to feel, the sound is too quiet to hear, etc.) so in that low range there is never any response at all and thus there is no relationship at all between stimuli and response. However, on passing the threshold for detection, a relationship between the two variables becomes obvious. The harder a subject gets pinched by an experimenter (Stimuli-IV), the larger the subjects pain response (DV). Below the threshold for detection, no relationship, but above the detection threshold, a positive relationship, a "threshold effect".
The relationship between toxin exposure (IV) and tissue damage (DV) depends on a threshold. The relationship is measured by the dose-response curve which is usually a sigmoid function above a threshold and zero below. At the lowest values most toxic substances cause no harm at all so there is no relationship at all between exposure amount and tissue damage. However, on passing the threshold for response, a sigmoid (flat-steep-flat) relationship between the two variables becomes obvious. Below the threshold for dose toxicity, no relationship, but above the threshold, a positive relationship, a "threshold effect".
The relationship between inflation rate (IV) and economic growth (DV) depends on a threshold. At the lowest values (below 3%) inflation doesn't slow growth at all all. However, on passing that threshold there is a negative relationship between the two variables and higher inflation (IV) results in slower economic growth (DV), another "threshold effect".
SPECIFIC INSTANCES OF THRESHOLD EFFECTS:
* Renormalization group effect, a particle physics calculation
* , a trait in genetics

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