Is the Correlation Between Hypertrophy and Strength Gains Stronger Than We Realized? • Stronger by Science

That is going to be a reasonably technical article, discussing a recent(ish) study by Marques and colleagues. I’ve beforehand written fairly a bit in regards to the relationship between muscle progress and power beneficial properties, and I’m not going to recap all of that earlier content material on this article. If that is your first time giving a lot thought to the topic, it’s possible you’ll get pleasure from studying a few of these prior articles:

For our functions right here, crucial factor to notice is that, till lately, analysis investigating the connection between hypertrophy and power beneficial properties painted a reasonably constant image. In research on untrained topics, we see a reasonably weak relationship between hypertrophy and power beneficial properties. Nonetheless, as coaching standing will increase, this relationship will get progressively stronger. 

The graph under roughly depicts our earlier understanding in regards to the explanatory energy of hypertrophy for predicting adjustments in power.

And, for what it’s price, I believe one of these relationship makes intuitive sense. If hypertrophy is causally associated to power beneficial properties (and I believe it is), we must always anticipate the connection between hypertrophy and power beneficial properties to get stronger as different elements influencing power beneficial properties develop into increasingly more normalized/equated between topics. Specifically, early power beneficial properties are primarily attributable to enhancements in method, motor studying, and many others. In studies on untrained lifters, the common beneficial properties noticed are a 5% enhance in muscle dimension and a 22% enhance in power. Even when hypertrophy has a causal affect on power beneficial properties in untrained lifters, it could solely clarify, at most, a bit lower than 1 / 4 of the power beneficial properties noticed in that inhabitants (in most circumstances). Nonetheless, as coaching standing will increase, there are merely fewer beneficial properties available from additional marginal enhancements in method and motor studying. Because of this, hypertrophy explains increasingly more of the variance in power beneficial properties as coaching standing (and mastery of the lifts used to evaluate power) will increase.

Nonetheless, a latest research appeared to flip this understanding on its head. The research by Marques and colleagues is titled Muscle Growth Is Very Strongly Correlated with Strength Gains after Lower Body Resistance Training: New Insight from Within-Participant Associations. This research proposes that prior analysis on this subject might have underestimated the power of the connection between hypertrophy and power beneficial properties through the use of suboptimal statistical strategies. From the research’s introduction:

“Importantly, the statistical evaluation might additionally have an effect on our understanding of the connection between power beneficial properties and putative underpinning variables. Earlier analysis has closely relied on the usage of between-participant analyses, resembling easy regression or Pearson’s correlation, to research the relationships between adjustments in muscle dimension or activation with adjustments in power. These strategies assess interindividual associations however might lack sensitivity in capturing within-participant adjustments over time. For instance, the most typical strategy has been to think about the share change (i.e., pre-training to post-training) in power and dimension/activation over a coaching interval, utilizing one knowledge level per topic, which can obscure the affiliation because of the aggregation of the 2 dependent time factors. In different phrases, comparatively fastened particular person elements (e.g., second arm, contractile particular stress) could also be substantial, such that particular person pre and submit values are dependent and higher thought-about collectively. Thus, when two or extra measurement factors are obtained from the identical particular person, the within-participant (or repeated-measures) correlation is the popular statistical methodology for analyzing the frequent intraindividual affiliation. As a result of repeated-measures correlation accounts for the non-independence of every paired knowledge, it tends to yield a lot higher energy than knowledge which can be averaged or derived from the adjustments between time factors.”

That will sound summary, however it is a pretty straightforward idea to understand. Think about two individuals who at the moment have biceps of the identical dimension. Nonetheless, particular person A’s biceps have favorable insertions (lengthy inner second arms on the elbow) and really high specific tension (the quantity of linear contractile pressure a muscle can produce per unit of CSA), and particular person B’s biceps have unfavorable insertions and really low particular stress. Because of this, if each of those people expertise the identical enhance in biceps dimension, particular person A will probably expertise a bigger acquire in power than particular person B. So, in case you plotted the relative enhance in dimension and power for these two people, you may see a 5% enhance in biceps dimension for each, however a power enhance of 20% in particular person A versus 10% for particular person B. Repeat this for a gaggle of 20-30 topics, and it could seem that there’s a weak relationship between hypertrophy and power beneficial properties to your cohort, even when hypertrophy is definitely having a robust, direct impact on power beneficial properties inside every particular person within the cohort.

Repeated measures correlation may be a legitimate statistical device to account for a few of these inter-individual variations. For instance, under you’ll discover a determine from a paper cited by the authors illustrating how impactful the usage of repeated measures correlations can be. On this theoretical instance, the connection between the 2 variables for every topic (denoted by completely different colours) has a distinct intercept, however the slope of the connection is identical for all topics. Because of this, within-subject associations (on the left) reveal a really sturdy relationship, whereas between-subject associations (on the appropriate) would fail to determine the connection.

Usually, I actually, actually like the thought of specializing in within-subject associations for a similar causes supplied by the authors. Moreover, prior research has proven that statistical strategies that account for within-subject associations can clarify a bigger proportion of the variance within the power/hypertrophy relationship than strategies that solely think about associations between topics.

Within the prior study by Vigotsky and colleagues, associations between topics have been in step with what we sometimes observe in untrained topics: adjustments in muscle dimension defined <5% of the variance in power beneficial properties. Nonetheless, a hierarchical linear mannequin (HLM), was capable of clarify 7.4-24.1% of the variance (equating to a r-value within the vary of ~0.25-0.50). It was capable of clarify a lot extra of the variance as a result of it allowed every topic’s power/hypertrophy relationship to have its personal intercept and slope, that means it accounted for variations between topics at baseline, and variations in how hypertrophy or atrophy may affect power adjustments between people.

So, with that context, let’s briefly focus on this new research by Marques and colleagues.

On this research, 39 untrained males accomplished 15 weeks of resistance coaching centered on the quads. Power (knee extension 1RM and most isometric torque) and dimension (quadriceps quantity, assessed by way of MRI) have been assessed earlier than and after this coaching interval. On common, isometric knee extension power elevated by 21.6 ± 9.2%, knee extension 1RM elevated by 28.6 ± 12.9%, and quadriceps quantity elevated by 12.7 ± 7.1%.

Moreover, the r-value for the repeated measures correlation between hypertrophy and power was 0.92 for isometric knee extension power, and 0.89 for knee extension 1RM. In distinction, the between-subjects associations have been within the vary of r = 0.35-0.60. So, utilizing repeated measures correlations, hypertrophy appeared to clarify ~80-85% of the variance in power beneficial properties, whereas extra conventional between-subject correlations steered that hypertrophy solely defined ~12-35% of the variance.

At first, this seems to be a really placing end result. This discovering doesn’t simply battle with earlier analysis on the subject – it’s in a completely completely different universe. If we take these outcomes at face worth, it will recommend that prior researchers didn’t detect an nearly excellent relationship between hypertrophy and power beneficial properties in untrained topics on account of insufficient statistical strategies, and have been as an alternative solely capable of detect a really weak correlation.

So, is that what truly occurred right here?

Not precisely.

The primary trace that one thing is amiss arises after we distinction the outcomes of this research with the outcomes of the prior research by Vigotsky and colleagues. If the shortcomings of prior analysis simply boiled right down to the usage of between-subjects analyses slightly than within-subjects analyses, the Vigotsky research ought to have recognized the identical sky-high correlations noticed by Marques and colleagues, because it additionally used a statistical strategy designed to evaluate within-subject associations. In actual fact, the statistical fashions within the Vigostky research ought to have been capable of account for much more of the variance than the repeated measures correlation utilized by Marques and colleagues. Repeated measures correlation, as employed by Marques and colleagues, is tantamount to a hierarchical linear mannequin that enables intercepts to differ between topics whereas assuming that the slope of the scale/power relationship is identical for all topics. Against this, the HLM within the Vigotsky research allowed for slopes and intercepts to differ between topics.

Until a given enhance in dimension yielded actually the very same enhance in power in all topics, permitting each intercepts and slopes to differ between topics would essentially mean you can clarify extra of the variance than solely permitting intercepts to differ. In different phrases, if hypertrophy really explains >80% of the variance in power beneficial properties in untrained topics, we must always have seen associations of an analogous (and even higher) power within the Vigotsky research. And, to make certain, within-subject analyses did clarify extra of the variance than between-subject analyses within the Vigotsky research, however even the within-subject analyses (with assorted intercepts and slopes) discovered that hypertrophy defined lower than 25% of the variance in power beneficial properties.

So, what may clarify this distinction?

Let’s begin by asking a easy query: how sturdy of an affiliation would we’ve got seen within the Marques paper with repeated measures correlation if hypertrophy and power beneficial properties weren’t truly associated?

You’d assume that two issues that aren’t associated would have a correlation coefficient of r = 0. Nonetheless, that’s truly not the case right here.

To try it out, I randomly generated 5000 “topics” matching the abstract statistics within the Marques paper (with the identical group-level means, normal deviations, change scores, and alter rating SDs for knee extension 1RM, knee extension isometric torque, and quadriceps quantity). Nonetheless, by design, adjustments in quadriceps quantity have been totally unrelated to adjustments in power in these “topics.” This simulation exists in a universe the place hypertrophy has zero affect on power beneficial properties. Every “topic’s” 1RM, isometric knee extension power, and quadriceps quantity modified by a random quantity in keeping with the means and normal deviations of the reported change scores, however every change was completely impartial of all different adjustments.

Subsequent, I calculated the repeated measures correlation for these topics. The correlation coefficient is calculated utilizing this method:

To calculate “SS_Measure,” you simply have to subtract the pre-training and post-training power measures from the common power measure for every topic, and sq. the outcomes. So, for example, if somebody had a 1RM of 30kg pre-training and 40kg post-training, their particular person “SSmeasure” can be (30-35)^2+(40-35)^2 = 50. To calculate “SS_Measure” for the complete pattern, you simply repeat this course of for the entire topics, and sum the outcomes.

For “SS_Error”, you’d first calculate how a lot of the topic’s power can be anticipated to alter, given their change in quadriceps quantity. For the complete pattern, quadriceps quantity elevated by a mean of 237.5cm³, and 1RM knee extension power elevated by a mean of 14.6kg. So, you’d anticipate every topic’s knee extension 1RM to extend by 14.5/237.5 = 0.0615kg per cm³ enhance in quadriceps quantity. So, for example, if somebody’s quadriceps quantity elevated by 300cm³, you’d anticipate their 1RM knee extension to extend by 300 * .0615 = 18.45kg.

From there, you match a regression line with a slope of 0.0615kg per cm³ that passes by means of the purpose comparable to the common of the topic’s pre- and post-training quadriceps quantity (x-coordinate) and the common of their pre- and post-training knee extension 1RM (y-coordinate), and remedy for his or her anticipated pre- and post-training knee extension 1RMs at x-coordinates comparable to their pre- and post-training quadriceps volumes. Then, subtract the anticipated knee extension 1RM values from the precise values, sq. each outcomes, sum them collectively, and repeat the method for all different topics.

When you’ve calculated your sums of squares, you simply plug these values into the method above.

So, let’s circle again to our query: If hypertrophy had no affect on power on this research by Marques and colleagues, how sturdy would the repeated measures correlation nonetheless seem like?

Even when hypertrophy and power beneficial properties have been totally unrelated, and hypertrophy had no affect on power beneficial properties, the repeated measures correlation carried out within the Marques research would have returned r-values within the vary of 0.81-0.83. In different phrases, repeated measures correlation would make it seem that hypertrophy defined ~65-70% of the variance in power beneficial properties on this research, even when hypertrophy truly had 0 affect on power beneficial properties, and no relationship to power beneficial properties in any way.

With that context, the reported r-values of 0.89-0.92 look significantly much less spectacular. To be clear, these values are meaningfully larger than the r-values we’d anticipate to see within the null case outlined above, a minimum of nominally. However, they roughly suggest that hypertrophy solely explains about 12-17% extra variance (additively) than can be defined by random noise matching the topics’ abstract statistics. Although, to be charitable, that additive distinction of 12-17% accounts for about 35-55% of the unexplained variance. In different phrases, in case you’d anticipate to see a r² worth of roughly 0.67 when the precise correlation is 0, we are able to simply deal with an r² worth of 0.67 as our efficient r² of 0, and scale from there. If the distinction between “no correlation” and “excellent, causal relationship” is (a bit lower than) 33 factors as an alternative of 100, an extra 12 factors will get us about 37% of the best way from our efficient 0 to 100, and an extra 17 factors will get us about 53% of the best way from our efficient 0 to 100.

My basic take is that the values on the backside of those tables probably present the fairest and most correct description of the research’s outcomes (and so they roughly suggest that hypertrophy might clarify about ~20-25% extra of the variance in power beneficial properties than between-subjects correlations on change scores would recommend – 37% as an alternative of 12% for hypertrophy and 1RM power, and 53% as an alternative of 36% for hypertrophy and isometric torque). I do assume normal between-subjects correlations underestimate the precise power of the connection between hypertrophy and power beneficial properties, nevertheless it’s fairly clear that repeated measures correlation (when interpreted uncritically) overshoots the power of the connection to a hilarious diploma. Simply to hammer this level house, the correlation coefficient for the connection between hypertrophy and 1RM power within the Marques research (r = 0.89) doesn’t even differ considerably (statistical significance; i.e., p > 0.05) from the null case (r = 0.82), for the reason that reported confidence interval prolonged from r = 0.81-0.94.

For emphasis: Repeated measures correlations produce such inflated r-values that we are able to’t be assured that r = 0.89 truly implies the existence of an affiliation meaningfully stronger than what we’d anticipate to see purely by likelihood.

I’ve a number of extra notes about repeated measures correlations, however first, I’d similar to to make it clear that I’ve no main criticisms of the research itself, and even the selection of statistical strategy. I do assume the best way the outcomes have been offered and mentioned is a bit off the mark, however not in any manner that’s suggestive of dishonesty or an try to deceive. I don’t assume it will have harm to do some simulations earlier than working the research, and I believe some simulations would have made it clear to the authors that correlation coefficients of ~0.9 with repeated measures correlations require a extra cautious interpretation than correlation coefficients of an analogous power from between-subjects analyses – however I additionally applaud them for attempting one thing new for the reason that typical strategy (Pearson correlations on p.c adjustments) has loads of its personal shortcomings.

Additionally, it’s price noting that even their “old skool” between-subjects Pearson regression evaluation discovered stronger correlations than we sometimes see in untrained lifters (r = 0.35 for the connection between hypertrophy and adjustments in 1RM, and r = 0.60 for the connection between hypertrophy and adjustments in isometric power). As discussed in a recent article, we sometimes see weaker correlations between hypertrophy and power beneficial properties within the analysis than most individuals would anticipate, and I strongly suspect that among the elements explaining these comparatively weak correlations are simply boring statistical issues. There’ll all the time be some extent of measurement error, but when there’s an extended period between measurements, and (relatedly) if bigger precise beneficial properties in power and muscle dimension can happen, your measurements will essentially replicate comparatively extra sign and comparatively much less noise.

This research by Marques ran for longer than most research on untrained lifters (15 weeks), leading to fairly a bit extra hypertrophy and barely bigger power beneficial properties than we sometimes see. Moreover, one among their power measurements required minimal ability (maximal isometric knee extension torque), which helps cut back the affect of a significant confounder – completely different charges and levels of ability acquisition influencing power diversifications. So, though the Pearson correlations on this research have been fairly a bit stronger than we sometimes see in research on untrained topics, additionally they don’t shock me an excessive amount of, and I applaud the researchers for the general methodological high quality of the research.

With that stated, I simply wish to shut with a last phrase of warning about repeated measures correlations, as a result of I strongly suspect they’ll begin cropping up extra ceaselessly within the train science literature. As talked about above, my main curiosity was in poking round on the “null case” – the varieties of obvious associations we must always anticipate to see when no relationship truly exists. What I discovered was that repeated measures correlations are solely minimally affected by imply change scores and variability between topics at baseline, however they’re very delicate to alter rating SDs (i.e., change rating coefficients of variation).

Power and hypertrophy outcomes have a tendency to have coefficients of variation within the neighborhood of 1.0 (that means that the usual deviations of the adjustments we observe are usually similar to the imply adjustments. In different phrases, if the common power enhance in a research is 10kg, the usual deviation tends to be someplace between 5 and 15kg). See Figure 8C and D here. When power and hypertrophy outcomes are each constructive and each have CVs between 0.5-1.5, repeated measures correlations within the vary of 0.65-0.85 could also be values which can be truly suggestive of little-to-no affiliation (the smaller the CVs, the upper the repeated measures correlation will probably be, even when there’s no causal affiliation between variables).

Trying again on the method above, to get an r-value under 0.5, SS_Error should exceed SS_Measure threefold, which is fairly unlikely to happen, for the reason that fastened slope for every particular person corresponds to the common slope to your complete cohort. To get anyplace close to r = 0.5, you’d have to have a number of very massive outliers the place the precise change is minimal, however the predicted change may be very massive (or vice versa – very small predicted adjustments, however a handful of very massive precise adjustments). However, more often than not, repeated measures correlation will spit out a fairly large correlation coefficient any time two imply adjustments are transferring in the identical route. For instance, right here’s a plot I whipped up in actually 2 minutes. The “baseline” measures for each variables are simply 0 ± 1. Dummy 1 will increase by 1 ± 1 unit, and Dummy 2 will increase by 3 ± 1 models fully at random – there’s no interplay between Dummy 1 and Dummy 2 in any way. And but, r_rm = 0.83. 

And, for the file, Pearson regression nails the (lack of) correlation:

Once more, I’m not saying there’s something improper with repeated measures correlation. Nonetheless, if repeated measures correlations begin exhibiting up in publications extra ceaselessly, I believe that appropriately decoding them goes to take fairly a bit extra work than most individuals are accustomed to when encountering a correlation coefficient. I’m totally braced for a load of obvious r = 0.7-0.9s that find yourself being full mirages, and I’m writing this text to ship to people each time I would like to clarify that r = 0.7-0.9 doesn’t all the time imply what you assume it means. Actually talking, r = 0.8 with repeated measures correlations means the identical factor as r = 0.8 with Pearson correlation (i.e., they only talk the diploma of variance defined by your statistical mannequin), however they will suggest very various things about how strongly adjustments in a single variable are predicted by adjustments in one other variable.

On the very least, in case you’re utilizing repeated measures correlations in a research you’re conducting, then please run some simulations to estimate the r and r² values you must anticipate with null outcomes. Whip up a simulated dataset matching the descriptive statistics of your outcomes (or the outcomes you anticipate to see) the place the outcomes you’re working correlations on are, by design, fully impartial and unrelated to one another. See what repeated measures r-value functionally equates to r = 0 to your dataset, and preserve that in thoughts when decoding your outcomes. I believe that specializing in the additive or relative enhance in r or r² values past what you’d anticipate to see within the null case is in all probability extra consultant of the power of your findings than simply presenting the r-value as-is, and decoding it the identical manner you’d interpret a fundamental Pearson correlation.

And, the identical applies in case you’re a shopper of scientific info encountering repeated measures correlation. Don’t simply take the reported outcomes at face worth, or interpret the r-values the identical manner you’d interpret another correlation coefficient. Fortunately, there’s a shiny app (made and maintained by the authors of the paper about repeated measures correlation cited above) that makes the evaluation a lot simpler – you simply want to have the ability to whip up some dummy knowledge in Excel, and also you’re off to the races. That shiny app was invaluable for me whereas I used to be engaged on this text, to verify my understanding of repeated measures correlations was right.

So, simply to wrap issues up:

1. Hypertrophy does in all probability contribute extra to power beneficial properties in new lifters than prior research steered … however the relationship is nowhere close to as sturdy as (what is usually implied by) r = 0.9.
2. Be cautious when decoding repeated measures correlations. That prime r-value in all probability isn’t fairly as spectacular because it seems at first look.