Performance-based correlates to vertical jump height and power values in women

Abstract

BACKGROUND AND OBJECTIVE:

Stark inter-gender differences in vertical jump performance exist. Performance-based correlates to the vertical jump are not well understood in women.

METHODS:

Women ( $n=$ 129) did countermovement vertical jumps as their data were collected concurrently by a Vertec and force plate; the latter provided performance-based correlates to their jumps. Multivariate regression examined the ability of the performance-based variable to serve as correlates of vertical jump height and power variances.

RESULTS:

Performance-based variables predicted moderate ( $r^{2}=$ 0.28) and large ( $r^{2}=$ 0.74) amounts of vertical jump height and power variance respectively. Per criterion measure, peak force did not have the highest univariate correlation.

CONCLUSIONS:

Peak force, typically the strongest correlate to vertical jump performance in men, was not as strong a predictor of the variance in women. Instead women rely on a variety of kinetic and temporal variables to maximize their vertical jump height and power values.

Keywords

Kinetic temporal countermovement

1. Introduction

Maximum vertical jump heights and power outputs occur when persons perform the task against their own body weight without added resistance [26]. Inter-gender differences in vertical jump performance include lower absolute jump height and power values attained by women [2, 24, 25]. Men, on average, have a vertical jump 20.3 cm higher as compared to maximum heights attained by women, with slightly greater inter-gender differences among college basketball players [25]. This performance outcome has been attributed to less absolute lower body strength and anatomical perturbations, such as valgus knee angles, more commonly seen in women [16]. As a result, women may attain lower vertical jump heights for fear of injury upon landing [17]. Since the vertical jump is crucial to athletic endeavors in which rapid vertical displacement of one’s own body is paramount, it is important to identify correlates to its performance [19, 26].

Prior research examined correlations between endogenous testosterone and vertical jump heights done by men ( $n=$ 48) and women ( $n=$ 22) [6]. Lower testosterone-vertical jump height correlations among women were attributed to gender differences in skeletal muscle sensitivity for the hormone [6]. Anthropometry was also assessed as a correlate to vertical jump heights [12, 14, 30]. While higher heights achieved by men may be attributed to greater lower body muscle mass, inter-gender differences were eliminated when performance was analyzed relative to thigh and calf cross-sectional areas [6, 34]. While many anthropometric variables correlated significantly to jump performance in male athletes, similar analyses done with female data correlated to a significant yet broad range ( $r^{2}=$ 0.14–0.70), of the variance seen in jump-based criterion measures [12, 14, 29, 30]. Though lower vertical jump heights in women were attributed to higher body fat percentages, correlations between female body fat and jump height values are not as high as those for men [1, 2, 24]. Since ability of female anthropometric indices to account for vertical jump performance is varied, perhaps identification of performance-based variables that act as stronger correlates to vertical jump prowess is warranted [2].

Vertical rate of force development (RFD, $\Delta$ force/ $\Delta$ time) produced during takeoff may impact jump heights [11, 20]. Women may produce smaller vertical impulses than men [2, 11, 24]. Such inter-gender differences appear to be due to the relatively lower peak forces exerted by women, which may have their origins relatively early in the lives of females, as girls see their ability to generate peak forces during takeoff decline as they go through puberty [24]. The interplay between force- and time-based variables may be crucial to achieve maximum vertical jump heights in women. Such indices are commonly categorized as kinetic- and temporal-based variables; it is of interest to identify which type best predicts the variance produced by countermovement vertical jumps done by women [11, 20]. However predictive indices that integrate each type of variable, whereby changes in force are quantified over time, may act as better correlates to jump performance [21]. They include variables such as the area under the curve [10]. Finally, since vertical jumps entail movement against gravity with one’s own body mass as resistance, variables expressed relative to body mass may help identify performance-based correlates [10].

Few studies have examined performance-based correlates when vertical jump height and power served as criterion measures [4]. To acquire an array of performance-based correlates, force plates are requ-ired [4, 11]. Force plates provide kinetic and temporal indices that were deemed valid and reliable [7, 33]. Furthermore, intra- and inter-session data from force plates are reproducible to values provided by a Vertec, a popular way to measure vertical jump heights [8, 23, 33]. Force plate data were examined as correlates to vertical jumps done by men, and showed performance-based variables accounted for moderate, but significant, amounts of vertical jump height and power variance [4]. Peak force (PF) was the best predictor of jump performance [4]. Since kinetic- and temporal-based data from women could help identify inter-gender differences in jump performance, and anthropometry’s impact on female vertical jump performance is mixed [2], this topic warrants inquiry. Our study’s purpose examines different performance-based variables (kinetic, temporal, force/time integrative, relative to body mass), derived from a force plate, as correlates to countermovement vertical jump height and jump power values obtained from women. We hypothesize the aforementioned types of variables will correlate with significant amounts of peak jump height and power variance data provided by women.

2. Method

2.1 Subjects

Before data collection, a university-based institutional review board approved our study protocol, and then subjects provided informed written consent. Moderately- to well-trained college-age women ( $n=$ 129) gave written informed consent to participate. All were in good health and had no injuries that would impair their participation. Each subject came to our laboratory three times, with their visits spaced 3–5 days apart, to fulfill their project involvement. They were instructed to come to the laboratory well rested, and to avoid consumption of stimulants such as caffeine prior to visits. Per subject, their data were collected at the same time of day in order to limit circadian influences on their vertical jump performance. Their general characteristics (mean $\pm$ sem) were as follows: age 20.1 $\pm$ 0.06 years, body mass 68.2 $\pm$ 1.0 kg.

2.2 Procedures

Our study’s force plate provides kinetic and temporal data that were previously deemed valid and reliable [7, 8, 33]. The force plate is shaped like an isosceles triangle; the length and depth to each of its sides equaled 98.5 and 11 cm respectively. To enhance surface contact stiffness and limit vibration, a 1.9 cm thick sheet of plywood covered the external surface of the platform. Polyurethane glue was applied to the plywood so that it adhered to the platform’s framework. Within the framework were two metal c-channel beams 6.4 cm apart that ran parallel to each other along each side of the platform. At each of the platform’s corners, between the beams, was a 114 kg capacity load cell (NTEP Grade III; Loadstar, Fremont CA, USA) that recorded force changes as jumps were performed. Force changes were converted to voltage signals and received by a 4-channel, 24-bit full bridge analog input module with internal excitation (model NI9237; National Instruments, Austin TX, USA). A CompactDAQ USB chassis (cDAQ-9172; National Instruments, Austin TX, USA) housed the bridge input module. Software (Labview 8.6; Austin TX, USA) collected data at 5000 Hz. Load cell calibration was routinely verified by an object of a known mass throughout data collection. Waveforms were captured within a 0–5 volt range per load cell and displayed on-line for visual recognition. Waveforms were divided into four phases. Countermovements (eccentric phase) are when considerable lower body series elastic element activity is created, while the takeoff (concentric phase) provides several performance-based variables that may correlate vertical jump height and power values [3, 15, 19, 22]. A representative force-time curve from a countermovement vertical jump appears in Fig. 1.

Figure 1.

On-line data collection of a representative force-time curve from a countermovement vertical jump from the current study’s instrumented portable force platform.

Subject’s first visits to our laboratory entailed collection of their anthropometric data, as well as familiarization and operation of our force plate. Their height and body mass were measured with a stadiometer and scale (Detecto Model 437; Webb City, MO, USA) as they stood upright. They next did a five minute warm-up on a stationary cycle ergometer (Ergotest; Stockholm, Sweden) at a rate of 75–90 watts. At the end of their first visits, they practiced countermovement vertical jumps on the force plate at a submaximal level of effort. The force plate was placed adjacent to a Vertec (Sports Imports; Columbus, OH, USA). As jumps occurred, data were collected from each device. Our criterion measures (peak height, power output) were derived from the Vertec; while the force plate provided variables that acted as correlates to our criterion measures’ variance. Jumps were done in the manner customary to subjects, with the caveat that countermovement knee flexion caused subjects thighs to descend below parallel to the force plate’s surface before ascenion. This was affirmed by visual inspection, as was done in a recent study [10]. As subjects ascended from the force plate they raised their dominant arm overhead and touched the highest Vertec slapstick they could reach. They were instructed to contact the force plate with both feet simultaneously as they landed. First visits allowed the capture of real time waveforms, as our software had only a three-second window to obtain data from each jump. Subjects usually did 3–5 vertical jumps; if technicians felt more practice was required additional jumps were performed.

Second and third visits used identical data collection procedures. They began with a warm-up identical to that of the first visit. Subjects then stood on the force plate and performed maximal-effort countermovement vertical jumps. Preceded by rapid ankle, knee, hip and vertebral flexion combined with concurrent glenohumeral hyperextension that characterizes the countermovement phase of jumps, subjects immediately applied contact forces to maximize vertical displacement and jump height values that characterizes the concentric portion of the movement. As they reached the jump’s apex, subjects made contact with the highest Vertec slapstick possible with their right hand. At the second and third visits they made 3–5 such jumps, each separated by 15–45 seconds of rest. Jumps not done in the described manner were excluded from analysis. For both the second and third visits, the highest jump per subject was used for statistical analysis.

Figure 2.

Some of our study’s performance-based variables. AUC is calculated from the hatched portion of the waveform.

Per subject, jumps that produced peak vertical height values from visits two and three were compared for their reproducibility with coefficients of variation (CV). As seen in Fig. 2, the following performance-based predictor variables, each obtained from the data provided by the force plate, were identified from the vertical jump takeoff: peak force (PF), area under the curve (AUC), time to peak force (TTPF), and time to peak force measured from the ascent (TTPFa). While TTPF is a temporal variable that includes both the concentric and eccentric phases, the other Fig. 2 predictor variables were derived solely from the concentric phase. The calculated AUC value (hatched region; Fig. 2) is an estimate of the force-time integral from the recorded force during the takeoff phase. It represents the impulse created during takeoff. The relationship between impulse and velocity change is given by: $\int$ Fdt $=$ $m\Delta v$ where $\int$ F dt is the force integral with respect to time and $m\Delta v$ equals momentum change. The force integral was estimated with a trapezoidal rule numerical integration scheme. PF, AUC, TTPF and TTPFa were also quantified as absolute values and relative to subjects’ body mass (BM). Each predictor variable underwent CV analysis. In similar fashion peak height and power values for the best jumps from the second and third visits also underwent CV analyses. Power was quantified with the Sargeant’s formula: 21.67 $\times$ BM(KG) $\times\surd$ D(M), whereby $\surd$ D(M) equalled subject’s vertical displacement in cm.

2.3 Data analysis

We used multivariate regression to identify the best correlates to peak height and power values. Our eight performance-based variables (PF, PF/BM, AUC, AUC/BM, TTPF, TTPF/BM, TTPFa, TTPFa/BM) were examined for their ability to predict the variance for our two criterion measures. Thus our predictor variables include kinetic-, temporal-, and force-time integrative-based indices of jump prowess expressed in absolute and relative terms. An alpha level of 0.05 denoted statistical significance for each multivariate analysis. With an effect size and power levels of 0.15 and 0.8 respectively, our sample exceeds the 108 subjects needed to perform multivariate regression analyses with eight predictor variables at a 0.05 alpha level [31].

3. Results

No subjects were injured through their project participation. Subjects verbally affirmed to the investigators that they achieved their maximum jump height at laboratory visits two and three. CV results (range 2–7%) for our eight predictor and two criterion variables were as follows: PF 6.6%, PF/BM 3.9%, AUC 6.1%, AUC/BM 5.4%, TTPF 6.8%, TTPF/BM 6.1%, TTPFa 5.1%, TTPFa/BM 3.1%, Jump height 2.0%, Jump power 2.7%. Each demonstrated high levels of reproducibility as well as less variability than that which is typical to biological systems [32]. Thus for each predictor and criterion variable, values from second and third visits were averaged per subject and then used for our multivariate regression analyses. For each predictor and criterion variable, Table 1 provides mean $\pm$ sem and range of current study values.

Table 1
Subject’s descriptive data for our eight predictor variables and two criterion measures

Variable (units)	Mean $\pm$ sem	Range
PF (newtons)	374.9 $\pm$ 6.7	218.4–560.1
PF/BM (newtons $\cdot$ kg ${}^{-1}$ )	5.14 $\pm$ 0.13	1.55–8.39
AUC	107.2 $\pm$ 2.5	29.7–174.9
AUC/BM	1.472 $\pm$ 0.038	0.17–2.02
TTPF (seconds)	1.09 $\pm$ 0.02	0.507–1.707
TTPF/BM (seconds $\cdot$ kg ${}^{-1}$ )	0.0151 $\pm$ 0.0004	0.003–0.027
TTPFa (seconds)	0.28 $\pm$ 0.01	0.006–1.407
TTPFa/BM (seconds $\cdot$ kg ${}^{-1}$ )	0.0039 $\pm$ 0.0002	0.000–0.009
Jump height (cm)	42.04 $\pm$ 0.48	30.48–53.34
Power (watts)	933.01 $\pm$ 16.45	546.7–1316.3

PF $=$ peak force; BM $=$ body mass; AUC $=$ area under the curve; TTPF $=$ time to peak force; TTPFa $=$ time to peak force ascent.

The multivariate regression results, with jump height as the criterion measure, appear in Table 2. The eight independent variables predicted a moderate ( $r^{2}=$ 0.28) yet significant ( $F=$ 5.82; $p<$ 0.05) amount of jump height variance. Table 2 univariate results show a broad range of collinearity among the predictor variables, yet PF ( $r=$ 0.248) and TTPF ( $r=$ $-$ 0.275), PF/BM ( $r=$ 0.317) and AUC/BM ( $r=$ 0.246) had the strongest correlations to jump height. The inverse relationship between TTPF and jump height implies lower values for the predictor variable produced better jump performances. The other four predictor variables each had negligible univariate correlations with jump height. Table 3 results, with power as the criterion measure, show the predictor variables correlated with a greater amount of variance. Multivariate regression showed the eight independent variables correlated with a significant ( $F=$ 43.63; $p<$ 0.05) and larger ( $r^{2}=$ 0.74) amount of power variance than when jump height served as the criterion. Table 3 univariate results also depict a wide range of collinearity among the predictor variables. PF ( $r=$ 0.527), AUC ( $r=$ 0.666) and TTPF/BM ( $r=$ $-$ 0.502) were the best univariate correlates to power. The Table 3 univariate matrix shows the other five predictor variables were each weakly correlated to power. Univariate matrices, $r$ , $r^{2}$ , prediction equations and standard error of multiple estimates (SEME) appear in Tables 2 and 3.

Table 2

Univariate correlations, $r$ , $r^{2}$ , SEME and prediction equation with jump height as the criterion measure

	PF	TTPF	TTPFa	AUC	PF/BM	TTPF/BM	TTPFa/BM	AUC/BM
PF	1
TTPF	$-$ 0.010	1
TTPFa	$-$ 0.030	0.068	1
AUC	0.375	0.014	0.687	1
PF/BM	0.440	$-$ 0.152	0.153	0.049	1
TTPF/BM	$-$ 0.280	0.435	0.231	$-$ 0.184	0.552	1
TTPFa/BM	$-$ 0.220	$-$ 0.091	0.845	0.364	0.384	0.482	1
AUC/BM	0.029	$-$ 0.142	0.735	0.563	0.628	0.506	0.820	1
Jump height	0.248	$-$ 0.275	$-$ 0.023	0.115	0.317	$-$ 0.033	0.062	0.246

$r=$ 0.53; $r^{2}=$ 0.2795; SEME $=$ 1.8114; jump height $=$ 12.928 $+$ 0.03 (PF) – 0.93 (TTPF) – 13.15 (TTPFa) – 0.054 (AUC) – 1.437 (PF/BM) – 32.66 (TTPF/BM) $+$ 136.3 (TTPFa/BM) $+$ 8.12 (AUC/BM). PF $=$ peak force; BM $=$ body mass; AUC $=$ area under the curve; TTPF $=$ time to peak force; TTPFa $=$ time to peak force ascent; SEME $=$ standard error of multiple estimates.

Table 3

Univariate correlations, $r$ , $r^{2}$ , SEME and prediction equation with jump power as the criterion measure

	PF	TTPF	TTPFa	AUC	PF/BM	TTPF/BM	TTPFa/BM	AUC/BM
PF	1
TTPF	$-$ 0.011	1
TTPFa	$-$ 0.025	0.068	1
AUC	0.375	0.014	0.687	1
PF/BM	0.440	$-$ 0.150	0.153	0.049	1
TTPF/BM	$-$ 0.276	0.435	0.231	$-$ 0.180	0.552	1
TTPFa/BM	$-$ 0.215	$-$ 0.090	0.845	0.364	0.384	0.482	1
AUC/BM	0.029	$-$ 0.140	0.735	0.563	0.628	0.506	0.820	1
Jump power	0.527	0.070	0.205	0.666	$-$ 0.204	$-$ 0.502	$-$ 0.018	0.008

$r=$ 0.863; $r^{2}=$ 0.7442; SEME $=$ 94.517; power $=$ 07.8 $+$ 2.31 (PF) $+$ 1.42 (TTPF) $+$ 51.43 (TTPFa) $-$ 0.41 (AUC) $-$ 139.3 (PF/BM) $+$ 1378.7 (TTPF/BM) $-$ 35765.6 (TTPFa/BM) $+$ 420.5 (AUC/BM); PF $=$ peak force; BM $=$ body mass; AUC $=$ area under the curve; TTPF $=$ time to peak force; TTPFa $=$ time to peak force ascent; SEME $=$ standard error of multiple estimates.

4. Discussion

Our hypothesis was affirmed. The current perform-ance-based variables generally explained more female vertical jump variance than prior studies that used predictive indices like anthropometry or testosterone [2, 6, 12, 14, 24, 30]. Performance-based variables were examined as correlates to vertical jump prowess in men [4]. Like the current study’s women, performance-based variables predicted significant yet moderate amounts of countermovement vertical jump height variance in men [4]. PF had the highest univariate correlation with vertical jump height [4]. However unlike male results, our female data shows a variety of predictor variables correlated with a large and significant amount of vertical jump power variance [4]. It is therefore important to explain how our predictor variables correlated to such high amounts of vertical jump power variance. Longitudinal training to enhance force output in men will also increase their vertical jump heights [9]. Such training also impacts the shape of power- and displacement-time curves produced by vertical jumps [9]. However, a larger sample comprised of nearly equal numbers of men and women saw the “greater force-higher jump height” relationship was less clear, which implies vertical jumps done by women are less the product of PF values and instead an interplay among an array of kinetic and temporal variables that maximize performance [11].

Like the current study, subjects (46 men, 51 women) performed countermovement vertical jumps on an instrumented force plate [11]. Per jump 18 kinetic- and temporal-based performance variables were collected [11]. Unlike the current study in which power serves as a criterion measure, they first identified it as a performance variable and subsequently a strong correlate to vertical jump performance [11]. Yet when power was excluded as an independent variable, their best three-predictor model only explained 66.2% of the vertical jump height variance [11]. The authors concluded while a high PF helped achieve maximum jump height, it certainly was not the only important variable. Since some subjects had low jump heights in spite of their high PF values, it was also concluded the pattern and timing of force application were more important than PF results [11]. In particular, the ability to exert high forces at joint angles as they near full extension and rotate at high velocities were considered advantageous [11].

Unfortunately the aforementioned study did not examine disparities, or identify different correlates to jump performance, by gender [11]. But based on their results [11], as compared to studies with only men [4, 9] or the current investigation with only female subjects, women appear to rely on temporal variables to a greater extent to maximize their vertical jump performance. From their large mixed-gender sample, Dowling and Vamos noted two temporal variables (duration of maximum force to takeoff: $r=$ $-$ 0.27; duration of maximum positive power to takeoff: $r=$ $-$ 0.41) which each correlated to small yet significant amounts of jump height variance [11]. Since men rely more heavily upon PF values to attain higher vertical jump heights, it is interesting to speculate how similar Downing and Vamos’ results would have been to the current study if they conducted intra-gender analyses [4, 9, 11, 35]. In support of our results, a recent study with female athletes showed vertical jump performance correlated significantly to tests that measured their acceleration ( $r=$ 0.80) and agility ( $r=$ 0.78) [27]. Thus to improve jump performance, women appear to rely relatively less on kinetic-based variables than men [27]. Tables 2 and 3 results affirm this assertion. PF, the best predictor of male jump heights, did not have the highest univariate correlation when either female jump height or power was the criterion [4, 9]. While some of our variables were better predictive indices than PF, it is of interest to note why some were better than others. In addition some variables expressed relative to BM had univariate correlations with our criterion measures that were higher than similar indices expressed as absolute values. Finally it is noteworthy to discuss why our predictor variables correlated to far more vertical jump power, as compared to jump height, variance.

In regards to some temporal variables serving as better correlates, our results show TTPF was among the better predictors of jump height variance, while TTPF/BM had a strong ( $r=$ $-$ 0.502) univariate correlation to jump power. In contrast TTPFa was generally a weak correlate to each of our criterion measures. These outcomes reinforce the importance of the countermovement, or eccentric, phase of jump performance. It is during the countermovement, which prestretches the prime movers involved in the jump, that leads to the subsequent attainment of maximum height and power values. The jump’s countermovement permits the strong contribution to vertical jump performance by allowing the knee and hip extensors to prestretch immediately prior to the ascent, which subsequently causes greater motor unit recruitment and higher height attainment [13, 28]. In contrast TTPFa is only measured over the concentric phase, which is perhaps why it was a weaker correlate in the current study. Countermovements have such an influence on TTPF and jump performance values that it was controlled for in prior investigations [9, 18, 28]. Thus in our study, it is likely the countermovement phase had an important role that led to high TTPF-jump height and TTPF/BM-jump power univariate correlations.

Our results revealed AUC/BM and PF/BM were among the stronger correlates to vertical jump height, while TTPF/BM had a strong inverse relationship to vertical jump power values. In contrast, data collected from men showed predictor variables expressed relative to BM were weak correlates to jump performance [4]. As it pertains to some of our performance variables expressed relative to BM serving as strong predictors of the variance seen in our criterion measures, precedent does exist for this occurrence [11]. In addition, jump studies that assessed the impact of various interventions showed variables normalized to BM often produce significant changes sooner, or to a greater extent, than those expressed as absolute measures because data variability is reduced [9, 28]. With jump data obtained from men and women with a force plate, a significant correlation was noted between maximum height and power outputs relative to subjects’ BM [11]. A chronic training intervention done by men for its impact on vertical jump height noted variables that had the greatest improvements over time were force and power values normalized to BM [9]. A study of countermovement depth and volitional effort on jump height in ten men saw large inter-treatment power and torque disparities when expressed relative to BM, yet these differences were not significant likely due to the sample size examined [28].

Finally it is of interest to note why the current study performance variables predicted far more vertical jump power, as compared to jump height, variance. Differences in amount of variance explained by the current study criterion measures is unusual given the high correlations ( $r=$ 0.92–0.93) between jump power and height seen previously [5, 11]. While jump heights represent absolute vertical displacement, power is the product of force and velocity. Given the power formula, it is not difficult to ascertain why the current kinetic- and temporal-based performance variables could correlate to force and velocity measures. Our Table 3 results show PF ( $r=$ 0.527) and AUC ( $r=$ 0.666) had the highest univariate correlations to vertical jump power variance. Unlike PF, AUC is a measure of work performed per unit time and a performance variable that integrates force and time. Thus in terms of its formula, AUC is more akin to power measurements than is PF, so it is easy to see why it had the highest Table 3 univariate correlation with vertical jump power. In addition, the AUC formula is somewhat similar to the measurement of impulse ( $\Delta$ force/ $\Delta$ time); the latter is associated with greater vertical jump performances [11, 20]. Thus perhaps the similarities in AUC and impulse formulas led to the former having a high univariate correlation to vertical jump power. Since less jump data have been collected from female subjects, and due to the apparent differences in the way men and women create vertical impulses, additional research on correlates to jump performance done by women is warranted.

Given our methods and sample size, we believe our study provides a general representation of factors that contribute to vertical jump performance in women. However particularly in regards to their physical characteristics and training histories, limitations to our study include a rather heterogeneous sample of female subjects. Since women participate in a broad variety of sports in modern-day athletics, future research in this area may wish to use a similar study design with a more homogenous group of female athletes, such as those that participate or specialize in a singular sport or activity. With such an approach, future study results may identify factors that best predict vertical jump performance and perhaps, in turn, offer insights on the athletic performance of their subjects.

Footnotes

Acknowledgments

We wish to thank our subjects for their participation.

Conflict of interest

The authors of this paper have no conflicts of interest to report.

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Performance-based correlates to vertical jump height and power values in women

Abstract

BACKGROUND AND OBJECTIVE:

METHODS:

RESULTS:

CONCLUSIONS:

Keywords

1. Introduction

2. Method

2.1 Subjects

2.2 Procedures

3. Results

Table 1 Subject’s descriptive data for our eight predictor variables and two criterion measures

Footnotes

Acknowledgments

Conflict of interest

References

Table 1
Subject’s descriptive data for our eight predictor variables and two criterion measures