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The phrase "a variable interval of" is correct and usable in written English.
It can be used when discussing time periods or measurements that can change or vary in length.
Example: "The experiment was conducted over a variable interval of time to observe the effects of the treatment."
Alternatives: "an adjustable duration of" or "a fluctuating period of".
Exact(7)
The collected samples at a variable interval of time were filtered using filter papers of 0.45 µM size (Make: Millipore) to remove the traces of solid particles.
To facilitate this imagination, after a variable interval of 1500 3500 ms after the cue a brief video sequence of an opening door (3000 ms) announced the number comparison task.
The cysteine sequence motif C...CXXXC...GXC...CXC is conserved in this group, where X is any amino acid and... is a variable interval of AA [ 72].
The attention task response was followed with a variable interval of 0, 1, or 2 s in which the fixation cross was presented, followed by a memory probe digit.
Reinforcement started on a fixed-ratio schedule (1 press earns 1 reward) and gradually shifted to the VI-30 schedule (after a variable interval of time elapsed that averaged 30 s, then 1 press earned 1 reward; Figure 2A, left).
For both the simple and four-choice reaction time trials there was a variable interval of between 1 and 3 seconds between the participant's response and onset of the next stimulus.
Similar(53)
Sample Phase 2, which followed after a variable interval, consisted of eight more trials of standard object recognition (1 min retention), using new sets of objects.
The children completed a computerized game-like task where mouse clicks on one of two squares on the screen resulted in delivery of a reinforcer according to a variable interval schedule of reinforcement.
The dot display was followed by a black screen with a variable interval (jitter of 1000 to 1400 ms, average 1200 ms), during which participants gave their response; and then by a visual feedback screen (1500 ms) consisting of a face (with either a smiling or angry expression) paired with a verbal indication of actual performance on the counting task (either "WON" or "LOST").
5-HT depletion in the amygdala impaired response choice on a probabilistic visual discrimination task by increasing the effectiveness of misleading, or false, punishment and reward, and decreased response suppression in a variable interval test of punishment sensitivity that employed the same reward and punisher.
To test our hypothesis, we used fast-scan cyclic voltammetry (FSCV) to measure real-time, phasic dopamine activity in the DLS, DMS, and NAcc of rats to determine how phasic dopamine release corresponds to reward-associated cues during alcohol and sucrose self-administration on a variable interval schedule of reinforcement.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com