Precalculus with Limits
More product info
From Ron Larson
Refresh the report to view the most up-to-date data available:
Report Card
Most Trusted Reviews
TRUST
- Unverified Purchaser
- Overlapping Review History: reviewed 1 of 9 top products
- Easy Grader (avg. rating: 4.9)
Least Trusted Reviews
TRUST
- Verified Purchaser
- Created on a high volume day
- Contains repetitive phrases (show)
- One-Hit Wonder
- Overrepresented Participation (posted 1 Review)
- Easy Grader (avg. rating: 5.0)
Analysis Details
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- 11%
- Created over 13 days
We counted 228 reviews for this product over the span of 7,340 days, an average of 0.0 reviews per day. If these reviews were created randomly, there would be a 99.9% chance that we would see 1 or fewer reviews on any given day.
However, we see the following 13 days exceeding this threshold:In total, we found that 26 reviews were created on just 13 days. The reviews on these high volume days have rated this product an average of 4.6 while reviews from other days have rated this product an average of 4.1. Based on our statistical modeling, the discrepancy in average rating between these two groups is significant enough to believe that the difference is not due to random chance, and may indicate that there are unnatural reviews.
17 of the 228 total reviews for this product use substantial repetitive phrases between them. These reviewers have rated this product an average of 4.9 while reviews without substantial repetitive phrases rated this product an average of 4.1. Based on our statistical modeling, the discrepancy in average rating between these two groups is significant enough to believe that the difference is not due to random chance, and may indicate that there are unnatural reviews.
We discovered a total of 5 deleted Reviews for this product, with an average rating of 4.8. Even though deleted reviews don't affect the average rating, the fact that action was taken to delete reviews raises some red flags about the integrity of the reviews for the product as whole.
There are a few limitations to keep in mind regarding the Deleted Reviews test:
- We don't have a magic ability to collect every single deleted review; we can only identify reviews as deleted if we collect them on one date and then notice they are no longer visible on a subsequent date.
- We have no information on reviews that were never published in the first place.
- We also don't know why these reviews were removed. It could be action from the platform, personal decision by the review author, part of an entire account closure, even some data error on our part, etc.
One-Hit Wonders
34 of the 228 reviewers have only reviewed this product. While this is more One-Hit Wonders than we'd expect to see, it does not appear to have a significant impact on the overall rating.
Take-Back Reviewers
9 of the 228 reviewers have had at least one of their past reviews for another product deleted. While this is more Take-Back Reviewers than we'd expect to see, it does not appear to have a significant impact on the overall rating.
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- 77%
- From reviewers with an overrepresented participation
We see the following 2 participation groups with a statistically significant greater concentration than what we'd expect to see:In total, we found that 176 reviewers (or 78%) are within an overrepresented participation group. This is an excessively high number of reviewers in overrepresented participation groups.
42 of the 228 total reviews for this product are unverified purchases. This is within an acceptable range and it does not appear to be significantly affecting the overall rating for this product.
Unverified purchases may be the result of Kindle Unlimited readers, buyers who didn't pay full price, or reviewers who did not purchase the product at Amazon. Read more about our Unverified Purchases test.
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- 21%
- Have an overrepresented word count
In the graph above, we can see the distribution of review word counts for this product and the expected distribution for this category. We see the following 1 group with a statistically significant greater concentration than what we'd expect to see:In total, we found that 47 reviews (or 21%) are within an overrepresented word count group. This is within an acceptable range and it does not appear to be significantly affecting the overall rating for this product.
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from the same brand
16 of the 228 reviewers have substantial overlapping product review history. This is within an acceptable range and it does not appear to be significantly affecting the overall rating for this product.
4.3 Product's Average Ease Score
4.3 Category's Average Ease Score
Read more about our Reviewer Ease test.
Brand Repeaters
12 of the 228 reviewers have reviewed other products for this brand. This is within an acceptable range and it does not appear to be significantly affecting the overall rating for this product.
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- 0%
- Admitted to receiving an incentive
Read more about our Incentivized Reviews test. Check out our study showing that Incentivized Reviewers are much more likely to leave a positive review.