In Search Engine Optimisation (SEO), you often want to know how strong a website is. Two different metrics that attempt to measure this are Domain Authority (DA) from Moz and Trust Flow (TF) from Majestic.

Both Trust flow and Domain Authority help SEO professionals make judgements about the usefulness of backlinks from a site in order to ensure their website ranks higher in Google (and other search engines).

What I’ve been wondering is: do they measure the same thing? That’s what we will find out in this report.

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## Why should we analyse these two metrics?

If the two metrics measure the same thing (they correlate), it would suggest two things:

First, you can translate one into other. This can be useful in practice when for example when you want to compare sites but don’t have all the data.

Second, if two metrics correlate, this suggests the are probably both pretty good metrics . Because what are the odds that two companies independently both get it wrong in the same way?

However, if the metrics are not similar (when there is little correlation between them), it would seem that at least one of them must must be wrong.

Last year, we already concluded that Trust Flow is a good predictor of organic search engine traffic to a domain. This is an indication that it is a good metric for estimating the strength of a domain from a search engine perspective.

## How do we compare Trust Flow and Domain Authority?

To analyse the similarity I first collected the Domain Authority and Trust flow for a sample of 2309 domains. The sample was created from domains that that rank on Google.co.uk for keywords related to celebrity gossip and showbiz news.

Note that the topic of the domains is not relevant to the conclusion of the study. It is expected generalise to all websites, regardless of their category.

To analyse the data, I used linear regression. This statistical method enables me to estimate the relationship between Domain Authority and Trust Flow. It also lets me determine correlation bewteen the metrics, which is a meassure of the strength of this relationship.

## The Data

Before we start, I want to get to know the data a bit better. Below are two charts, one for Trust Flow and one for Domain Authority, that shows the 2309 domains and how they are distributed over the values of the respective metrics. Each x axis is divided it bars of 10. On the Y axis is the count of domains in that group.

We can see that metrics have more low quality than high quality domains. However where Majestic has most of its sites under Trust Flow 30. Domain authority has most between 10 and 40.

Trust flow’s higher value domains gradually reduce in quantity as the Trust Flow increases. Domain Counts for Domain Authority’s higher values stay constant up to DA 100.

## Regression analysis

We want to understand how Trust Flow and Domain Authority are related, and how strong the relationship is. Both goals are achieved through regression analysis. This means that we let the computer draw the best fitting line through the points in the charts below. How well this line fits the points determines the strength of the relationship (correlation). This can be expressed as the correlation coefficient .

### Regression 1

In the chart below, every black dot represents one of the 2309 domains analysed, with their Trust Flow value on the Y axis, and Domain Authority on the X axis. The thin blue line is the average Trust Flow at the corresponding level of Domain Authority. The red line is the best fit for the first order relationship between Trust Flow and Domain Authority. A first order relationship means that it is a formula in the form:

Were *a* and *b* are the coefficients to be found by the regression analysis.

The analysis shows that the relationship between TF and DA is:

The correlation for this formula is:

This is a very high number that suggests that Trust Flow and Domain Authority can are related. Specifically, more than 80% of the value of Trust Flow can be explained when you know the Domain Authority of a website and the other way round.

### Residuals 1

We can learn more about the relationship between TF and DA by analysis the residuals of the regression model. The residuals are the difference between the real values, and the values predicted by the formula calculated in the regression analysis. The residuals (difference) of Trust Flow are plotted on the y axis against the predicted Trust Flow on the x axis. The blue line is the smoothed average at the corresponding Trust Flow value

.

In a well-fitting model the residuals are equally distributed above and below the y = 0 line for all values of the x axis. In this chart that is mostly true. However, in the low and high values of the prediction, the line goes up. This means it that appears the model underestimates the actual Trust Flow when we know the Domain Authority. Maybe the model can be improved.

### Regression 2

When we look at the first scatter plot, it seems that the dots follow a slightly curved trajectory. Therefore it may be appropriate to try a second order polynomial regression. This means we try to find a formula in the form:

The plot below shows the same dots as in the first chart, but now the red line represents this second order relationship.

In this case, the relationship can be expressed as follows:

The correlation for this formula is

The correlation for this formula is slightly higher than the first order equation. Thus, this formula is better than the previous. We can also see this in the residuals plot below.

### Residuals 2

This plot shows that in the lower levels of predicted Trust Flow, the relation is much better. In the higher values it’s still skewed upwards, though less than in the first order relationship.

## Confidence intervals

Thus as analysed above, it appears that we can use the formula

To calculate Trust Flow from Domain Authority. A correlation of over 82% means that it is mostly correct, but as the residuals chart shows, in many cases the actual value is higher or lower than the predicted one. To get a better understanding of the relationship, we can calculate a confidence interval where 95% of the time, the actual Trust Flow value will fall inside.

The formulas for the upper and lower limits of the confidence intervals are as follows:

Lower confidence limit

Lower confidence limit

## Conclusion: The Correlation between Majestic Trust Flow & Moz Domain Authority

In this post I showed how we can translate the Moz Domain Authority into MajesticSEO Trust Flow. The relationship has a correlation coefficient of 0.82. This suggests that the two metrics are mostly measuring the same thing, and can thus be substituted for each other. We use the quadratic equation to map the DA to TF.

Because there is a spread in the results, it may be better to express the relationship as confidence intervals. The formulas for the 95% confidence interval have specified.

The practical meaning of this analysis has been to show that MajesticSEO and Moz mostly agree on their way of classifying authority of website. Moz is more generous than Majestic giving higher values, but this in itself doesn’t tell you which metric is better.

That’s because this analysis cannot tell us which of the metrics are more closely related to SEO performance. It does however instil confidence because two companies independently create proxies for PageRank that agree with each other. Hopefully this means they also agree with Google.

**Appendix**

For your convenience, I provided below a table that you can use to translate a Domain Authority of a site into the corresponding Trust Flow, and vice versa. The 95% confidence interval column gives the amount that you need to add or subtract to stay within the interval. Note that all values are rounded to the nearest integer. For example, a Domain Authority of 10 is 95% of the times equal to Trust Flow between 8 and 12.

Domain authority | Trustflow | Trustflow 95% confidence (up or down) |
---|---|---|

1 | 3 | 2 |

2 | 4 | 2 |

3 | 4 | 2 |

4 | 4 | 2 |

5 | 4 | 2 |

6 | 5 | 2 |

7 | 5 | 2 |

8 | 5 | 2 |

9 | 6 | 2 |

10 | 6 | 2 |

11 | 6 | 2 |

12 | 6 | 2 |

13 | 7 | 2 |

14 | 7 | 2 |

15 | 8 | 3 |

16 | 8 | 3 |

17 | 8 | 3 |

18 | 9 | 3 |

19 | 9 | 3 |

20 | 10 | 3 |

21 | 10 | 3 |

22 | 10 | 3 |

23 | 11 | 3 |

24 | 11 | 3 |

25 | 12 | 3 |

26 | 12 | 4 |

27 | 13 | 4 |

28 | 13 | 4 |

29 | 14 | 4 |

30 | 14 | 4 |

31 | 15 | 4 |

32 | 16 | 4 |

33 | 16 | 4 |

34 | 17 | 4 |

35 | 17 | 5 |

36 | 18 | 5 |

37 | 19 | 5 |

38 | 19 | 5 |

39 | 20 | 5 |

40 | 20 | 5 |

41 | 21 | 5 |

42 | 22 | 5 |

43 | 22 | 5 |

44 | 23 | 6 |

45 | 24 | 6 |

46 | 25 | 6 |

47 | 25 | 6 |

48 | 26 | 6 |

49 | 27 | 6 |

50 | 27 | 6 |

51 | 28 | 6 |

52 | 29 | 7 |

53 | 30 | 7 |

54 | 31 | 7 |

55 | 31 | 7 |

56 | 32 | 7 |

57 | 33 | 7 |

58 | 34 | 7 |

59 | 35 | 8 |

60 | 36 | 8 |

61 | 36 | 8 |

62 | 37 | 8 |

63 | 38 | 8 |

64 | 39 | 8 |

65 | 40 | 8 |

66 | 41 | 9 |

67 | 42 | 9 |

68 | 43 | 9 |

69 | 44 | 9 |

70 | 45 | 9 |

71 | 46 | 9 |

72 | 47 | 9 |

73 | 48 | 10 |

74 | 49 | 10 |

75 | 50 | 10 |

76 | 51 | 10 |

77 | 52 | 10 |

78 | 53 | 10 |

79 | 54 | 11 |

80 | 55 | 11 |

81 | 56 | 11 |

82 | 57 | 11 |

83 | 58 | 11 |

84 | 60 | 11 |

85 | 61 | 12 |

86 | 62 | 12 |

87 | 63 | 12 |

88 | 64 | 12 |

89 | 65 | 12 |

90 | 67 | 13 |

91 | 68 | 13 |

92 | 69 | 13 |

93 | 70 | 13 |

94 | 71 | 13 |

95 | 73 | 13 |

96 | 74 | 14 |

97 | 75 | 14 |

98 | 76 | 14 |

99 | 78 | 14 |

100 | 79 | 14 |

Gillis,

Thankyou for your work. I understand that Majestic & MOZ have their different metrics. It would be nice if we could have a single metric. Thanks for your attempt to bring some correlation between them. The SEO community definitely needs this. Nice report.

This is getting a little tough to understand. I am trying to report our link building activity and stuck between choosing Domain Authority or Moz Trust flow as a quality of link metric. What do most SEO’s recommend?

I have very little confidence in Moz metrics. there isnt enough correlation between their metrics and rankings, whereas majestic correlates far better

Thanks for the table…It helped me a lot. With the sea of data majestic provides, all I need to do now is figure out which is most important.

Great report!

Informative, Do-follow or No-follow links are matter to increase Domain Authority and Trust Flow metrics?

Moz , as of late, seems to have become a little less reliable than Majestic or Ahrefs. Simply look at the # of links the Ahrefs aggregator returns as compared to any other. No contest. Domain authority though still seems to be a pretty reliable metric. I prefer to see a 1to1 correlation between TF and CF if I can achieve it. That’s the magic for me.

Definitely, same here.

Hi,

Thanks for the detailed comparison. Seems now people and companies are more looking for the TF and CF rather than DA and PA. But again it seems of being time as earlier people used to look for PR and Alexa 🙂

Thanks for sharing.

Good Lord! That is so much math. Thank you for taking the time to do all of that. I hope you don’t mind, but I just skipped to the conclusion.

BUT….I’m really glad you did the math. Thanks!

This goes really in depth to the maths aspect. Thanks for taking the time to explain the differences Gillis!