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# Comparisons

Papers typically have many comparison statements (e.g., those comparing the proposed method to existing methods). The most common problems I have seen are:

This section shows you how to avoid these problems and gives you common patterns that you can use throughout your paper.

## Common comparisons

For two like quantities A and B (i.e., quantities A and B are of the same type; see Comparison of like quantities), the following comparisons can be made.

Table 1. Common comparisons between quantities A and B (e.g., A = Dx, B = Dy).
Case Comparison statement

A = B

A is equal to B.
Dx is equal to Dy.

A != B

A is not equal to B.
Dx is not equal to Dy.

A > B

A is higher than B.
Dx is higher than Dy.

A < B

A is lower than B.
Dx is lower than Dy.

A ≥ B

A is higher than or equal to B.
Dx is higher than or equal to Dy.

A ≤ B

A is lower than or equal to B.
Dx is lower than or equal to Dy.

Table 2. Common comparisons between property P of item A (PA) and property P of item B (PB) (e.g., P = velocity, A = model A, B = model B).
Case Comparison statement

PA = PB

A has the same P as that of B.
Model A has the same velocity as that of model B.

PA != PB

A has a different P from that of B.
Model A has a different velocity from that of model B.

PA > PB

A has a higher P than that of B.
Model A has a higher velocity than that of model B.

PA < PB

A has a lower P than that of B.
Model A has a lower velocity than that of model B.

PA ≥ PB

A has the same or higher P compared with that of B.
Model A has the same or higher velocity compared with that of model B.

PA ≤ PB

A has the same or lower P compared with that of B.
Model A has the same or lower velocity compared with that of model B.

"higher"/"lower" should be replaced by "stronger"/"weaker", "lighter"/"heavier", etc. where necessary. Note that for "PA ≥ PB" and "PA ≤ PB", "compared with" is used because "the same" requires "as" ("the same as") whereas "higher/lower" requires "than" ("higher/lower than").

## Similarity

"similar to" is used to express similarity. Three common patterns are listed below.

 Pattern 1 Item 1 has X similar to that of item 2. Model A has a velocity similar to that of model B. Pattern 2 Item 1 has similar X to that of item 2. Model A has a similar velocity to that of model B. Pattern 3 X of item 2 is similar to that of item 2. The velocity of model A is similar to that of model B.

## Degrees of difference

The difference between A and B can be small or large.

Table 3. Degrees of difference.
Case Comparison (A first) Comparison (B first)

A = 30, B = 50

A is lower than B.

B is higher than A.

A = 30, B = 35

A is slighly lower than B.

B is slightly higher than A.

A = 30, B = 90

A is much lower than B.

B is much higher than A.

A = 30, B = 31

A is almost equal to B.

B is almost equal to A.

## Comparison is relative

A comparison requires at least two quantities or items.

Example 1. Comparison of two quantities or items A is higher than B. C outperforms D.

"A is higher" is sufficient if the preceding text makes it clear what is being compared. This is often not the case. Do not rely on implied comparisons. The reader should not have to guess the two quantities or items being compared.

Mistake
• The author uses a comparison word ("higher", "lower", "more efficient", etc.) but makes no actual comparison.

Remedy
• Make a comparison when using a comparison word.

Example 2. Common mistake. The accuracy of our method was higher. The accuracy of our method was higher than that of the conventional method.

## Comparison of like quantities

A comparison must compare like quantities (i.e., quantities that are of the same type). For example, temperature must be compared with temperature and velocity must be compared with velocity.

Incorrect comparisons are probably the most common mistake that I correct.

Mistake
• The author compares a quantity of type A to a quantity of type B.

Remedy
• Compare like quantities.

Example 3. Incorrect comparisons (unlike quantities) The length of segment A is equal to segment B. A length is compared with a segment. The length of segment A is equal to that of segment B. "that" = "the length", so now a length is compared with a length. The proposed method has a higher accuracy than the conventional method and Chen’s method. An accuracy is compared with methods. The proposed method has a higher accuracy than those of the conventional method and Chen’s method. "those" = "the accuracies", so now an accuracy is compared with accuracies.
Mistake
• The author incorrectly uses "that of" or "those of".

Remedy
• Carefully check what "that" or "those" refers to.

Example 4. "that of" and "those of" The cells doped with Al nanoparticles have lower Rct values than those of Au nanoparticles. Here, "those" = "Rct values", so the sentence compares Rct values of cells with Rct values of nanoparticles. The cells doped with Al nanoparticles have lower Rct values than those of cells doped with Au nanoparticles.

## Comparison of performance

Proposed methods are commonly compared with existing methods.

A useful structure for such comparisons is shown in Figure 1. Figure 1. Common pattern used for comparisons.
Example 5. Comparison of performance using "outperform" Our method outperforms state-of-the-art methods. Our method outperforms state-of-the-art methods in terms of accuracy. Our method outperforms state-of-the-art methods in terms of accuracy, but not computation time.