STRENGTH ABILITIES: MODELING OF IMMEDIATE AND DELAYED TRAINING EFFECT OF STRENGTH LOADS IN BOYS AGED 8 YEARS

The purpose of the study was to obtain regression models of immediate and delayed training effect of strength loads in boys aged 8 years, based on a full factorial experiment. Materials and methods. The study participants were 48 boys aged 8 years. The experiment was performed using a 22 factorial design. The study materials were processed by the IBM SPSS 22 statistical analysis program. The study examined the impact of four variants of strength load on the immediate (ITE) and the delayed (DTE) training effect of orthogonal strength exercises modes and rest intervals in boys aged 8 years. Results. The study results show that in the proposed matrix of the 22 full factorial design, the chosen step of variation of factors is sufficient to study the influence of different modes of strength exercises on the dynamics of ITE in boys aged 8 years. Based on the data analysis, the study obtained regression models of load for calculating the ITE1, ITE2, and DTE. The obtained regression models make it possible to calculate the number of repetitions and rest interval to achieve the most rational load variant. Conclusions. The analysis of regression equations shows the interrelation between training effects: ITE1 —> ITE2 —> DTE. The value of ITE1, ITE2, and DTE at station I (exercises to strengthen arms and shoulders) and station II (exercises to strengthen abdominal muscles) depends on the increase in the number of repetitions in a set and the duration of the rest interval. The value of ITE1, ITE2 at station ІІІ (exercises to strengthen back muscles) depends on the increase in the number of repetitions in a set and the duration of the rest interval. The value of DTE – on the increase in the number of repetitions in a set and the reduction of the rest interval duration. The value of ITE1 at station IV (exercises to strengthen leg muscles) depends on the increase in the number of repetitions in a set and the reduction of the rest interval duration. To strengthen the DTE, it is necessary to reduce the number of repetitions in a set and the duration of the rest interval.

The importance of developing methodological approaches to normalization and management of training loads in physical education classes in order to improve the effectiveness of teaching is pointed out in the studies by Khudolii, Iermakov, and Bartik (2020), Ivashchenko, Berezhna, and Cieślicka (2020), Ivashchenko and Sirichenko (2020).
Thus, the problem of normalization of strength loads in primary schoolchildren's physical education classes is relevant and requires additional research.
The purpose of the study was to obtain regression models of immediate and delayed training effect of strength loads in boys aged 8 years, based on a full factorial experiment.

Study participants
The study participants were boys aged 8 years (n = 48). The children and their parents were fully informed about all the features of the study and gave their consent to participate in the experiment.

Study organization
To solve the tasks set, theoretical and empirical methods were used: analysis and generalization of scientific and methodo logical literature; modeling, pedagogical observation and experiment, regression analysis.
To determine the dynamics of strength training effects in boys aged 8 years, the study carried out an experiment according to the plan given in Table 1. Variant І of the combined method was used to strengthen arm and shoulder muscles (station I), abdominal muscles (station II), back muscles (station III), and leg muscles (station IV). At each station, the following methods were used: dynamic effort method, maximal effort method, isometric effort method, repeated effort method. The modes of performance for each group, for the indicated stations are given in Table 1. The study examined the impact of four variants of strength load on the immediate training effect (ITE 1 ) after performing exercises at four stations, the immediate training effect (ITE 2 ) after training, and the delayed training effect (DTE) 24 hours after training.

Statistical analysis
The study materials were processed using the IBM SPSS 22 statistical analysis program. The Yates' algorithm was used to calculate the regression coefficients.
The study protocol was approved by the Ethical Committee of H. S. Skovoroda Kharkiv National Pedagogical University.

Results
Tables 2-7 show the results of the 2 2 full factorial design. The study examined the impact of four variants of strength load on the ITE 1 after performing exercises at four stations, the ITE 2 after training, and the DTE 24 hours after training.
The results of analysis of the immediate training effect (ITE 1 ) after performing exercises at four stations: station 1 "Exercises to strengthen arms and shoulders"; station II "Exercises to strengthen abdominal muscles"; station III "Exercises to strengthen back muscles"; station ІV "Exercises to strengthen leg muscles" are given below (see Tables 2-3).
The analysis of the regression equations given in Table 2 made it possible to determine the influence of strength loads on the immediate training effect (ITE 1 ) of different modes of exercises in boys aged 8 years. After training at stations I-IV, the following data were obtained: • after training at station I -exercises to strengthen arms and shoulders -the ITE 1 is most influenced by the number of repetitions in a set (х 1 ) (exercise No. 1) and the rest interval (х 2 ) (exercise No. 2). To strengthen the ITE 1 , it is necessary to increase the number of repetitions in a set and the duration of the rest interval; • after training at station II -exercises to strengthen abdominal muscles -the ITE 1 is most influenced by the rest interval (х 2 ), the number of repetitions in a set (х 1 ), and the interaction between the number of repetitions in a set and the rest interval (х 1 х 2 ). To strengthen the ITE 1 , it is necessary to increase the number of repetitions in a set and the duration of the rest interval; • after training at station III -exercises to strengthen back muscles -the ITE 1 is most influenced by the rest interval (х 2 ), the interaction between the number of repetitions in a set and the rest interval (х 1 х 2 ), and the number of repetitions in a set (х 1 ). To strengthen the ITE, it is necessary to increase the number of repetitions in a set and the duration of the rest interval; • after training at station IV -exercises to strengthen leg muscles -the ITE 1 is most influenced by the rest interval (х 2 ), the interaction between the number of repetitions in a set and the rest interval (х 1 х 2 ), and the number of repetitions in a set (х 1 ). To strengthen the ITE, it is necessary to increase the number of repetitions in a set and reduce the duration of the rest interval. The analysis of variance given in Table 3 made it possible to determine the percentage influence of the factors on the immediate training effect (ITE 1 ) of different modes of exer- Table 3. Results of the analysis of variance for the 2 2 FFE in studying the influence of different strength training modes on the change in the immediate training effect (ITE 1 ) in boys aged 8 years (n = 40) (х 1 -amount of training, х 2 -rest interval). The first variant of the combined method of strength development.  • after training at station I -exercises to strengthen arms and shoulders -the ITE 1 is most influenced by the number of repetitions in a set (х 1 ) -79.6% (exercise No. 1) and the rest interval (х 2 ) -56.1% ; • after training at station II -exercises to strengthen abdominal muscles -the ITE is most influenced by the rest interval (х 2 ) -66.4%; • after training at station III -exercises to strengthen back muscles -the ITE is most influenced by the rest interval (х 2 ) -68.4%; • after training at station IV -exercises to strengthen leg muscles -the ITE is most influenced by the rest interval (х 2 ) -90.5%. The data of analysis of the immediate training effect (ITE 2 ) after training are given in Tables 4-5.

Place of training
The analysis of the regression equations given in Table 4 made it possible to determine the influence of strength loads on the immediate training effect (ITE 2 ) of different modes of exercises in boys aged 8 years. After training, the following data were obtained: • exercises to strengthen arms and shoulders -the ITE 2 is most influenced by the interaction between the number of repetitions in a set and the rest interval (х 1 х 2 ) (exercise No. 1) and the rest interval (х 2 ) (exercise No. 2). To strengthen the ITE 2 , it is necessary to increase the number of repetitions in a set and the duration of the rest interval; • exercises to strengthen abdominal muscles -the ITE 2 is most influenced by the rest interval (х 2 ), the number of repetitions in a set (х 1 ), and the interaction between the number of repetitions in a set and the rest interval (х 1 х 2 ). To strengthen the ITE 2 , it is necessary to increase the number of repetitions in a set and the duration of the rest interval; • exercises to strengthen back muscles -the ITE 2 is most influenced by the rest interval (х 2 ), the number of repetitions in a set (х 1 ), and the interaction between the number of repetitions in a set and the rest interval (х 1 х 2 ). To strengthen the ITE, it is necessary to increase the number of repetitions in a set and the duration of the rest interval; • exercises to strengthen leg muscles -the ITE 2 is most influenced by the rest interval (х 2 ), the interaction between the number of repetitions in a set and the rest interval (х 1 х 2 ), and the number of repetitions in a set (х 1 ). To strengthen the ITE, it is necessary to reduce the number of repetitions in a set and the duration of the rest interval.
The analysis of variance given in Table 5 made it possible to determine the percentage influence of the factors on the immediate training effect (ITE 2 ) of different modes of exercises in boys aged 8 years. After training, the following data were obtained: • exercises to strengthen arms and shoulders -the ITE 2 is most influenced by the interaction between the number of repetitions in a set and the rest interval (х 1 х 2 ) -88.8% (exercise No. 1) and the rest interval (х 2 ) -67.1%; • exercises to strengthen abdominal muscles -the ITE is most influenced by the rest interval (х 2 ) -79.3%; • exercises to strengthen back muscles -the ITE is most influenced by the rest interval (х 2 ) -90.5%; • exercises to strengthen leg muscles -the ITE is most influenced by the rest interval (х 2 ) -65.5%.
The results of analysis of the delayed training effect (DTE) 24 hours after training are given in Tables 6-7.  The analysis of the regression equations given in Table 6 made it possible to determine the influence of strength loads on the delayed training effect (DTE) of different modes of exercises in boys aged 8 years. 24 hours after training, the following data were obtained: • exercises to strengthen arms and shoulders -the DTE is most influenced by the number of repetitions in a set (х 1 ), the rest interval (х 2 ), the interaction between the number of repetitions in a set and the rest interval (х 1 х 2 ) (exercise No. 1), and the interaction between the number ТМФВ, 2020, том 20, № 4 ISSN 1993-7989 (print). ISSN 1993-7997 (online). Теорія та методика фізичного виховання. Том 20, № 4 of repetitions in a set and the rest interval (х 1 х 2 ) (exercise No. 2). To strengthen the DTE, it is necessary to increase the number of repetitions in a set and the duration of the rest interval; • exercises to strengthen abdominal muscles -the DTE is most influenced by the interaction between the number of repetitions in a set and the rest interval (х 1 х 2 ), the rest interval (х 2 ), the number of repetitions in a set (х 1 ). To strengthen the DTE, it is necessary to increase the number of repetitions in a set and the duration of the rest interval; • exercises to strengthen back muscles -the DTE is most influenced by the rest interval (х 2 ), the interaction between the number of repetitions in a set and the rest interval (х 1 х 2 ), and the number of repetitions in a set (х 1 ).
To strengthen the DTE, it is necessary to increase the number of repetitions in a set and reduce the duration of the rest interval; • exercises to strengthen leg muscles -the DTE is most influenced by the number of repetitions in a set (х 1 ), the interaction between the number of repetitions in a set and the rest interval (х 1 х 2 ), and the rest interval (х 2 ). To strengthen the DTE, it is necessary to reduce the number of repetitions in a set and the duration of the rest interval. The analysis of variance given in Table 7 made it possible to determine the percentage influence of the factors on the delayed training effect (DTE) of different modes of exercises in boys aged 8 years. 24 hours after training, the following data were obtained: • exercises to strengthen arms and shoulders -the DTE is most influenced by the number of repetitions in a set (х 1 ) -62.2% (exercise No. 1) and the interaction between the number of repetitions in a set and the rest interval (х 1 х 2 ) -73.9%; • exercises to strengthen abdominal muscles -the DTE is most influenced by the interaction between the number of repetitions in a set and the rest interval (х 1 х 2 ) -55.2%; • exercises to strengthen back muscles -the DTE is most influenced by the rest interval (х 2 ) -99.8%; • exercises to strengthen leg muscles -the DTE is most influenced by the number of repetitions in a set (х 1 ) -46.1% and the interaction between the number of repetitions in a set and the rest interval (х 1 х 2 ) -44.2%.

Discussion
The study assumed that a full factorial experiment would allow to determine the influence of strength loads on the immediate training effect (ITE) and the delayed training effect (DTE) of different modes of exercises in boys aged 8 years.
The study results show that in the proposed matrix of the 2 2 full factorial design, the chosen step of variation of factors is sufficient to study the influence of different modes of strength exercises on the dynamics of ITE in boys aged 8 years (Table 1). Based on the data analysis, the study obtained regression models of load for calculating the ITE 1 (Table 2), ITE 2 (Table 4), and DTE (Table 6).
The studies by Iermakov, Ivashchenko, Khudolii, and Chernenko (2020), Ivashchenko, Khudolii, Prusik, and Giovanis (2020), Ivashchenko, Nosko, and Ferents (2019) substantiated the influence of different load variants on the dynamics of the immediate and delayed training effect on the basis of discriminant analysis. Iermakov, Ivashchenko, Khudolii, and Chernenko (2020) found the interrelation of training effects. The obtained data indicate that each of the variants of strength load can be effectively used depending on the educational tasks of both one and a series of physical education classes, and also show that the ITE and DTE of strength exercises depend on the initial level of fitness and the total amount of strength exercises in a physical education class. Ivashchenko, Khudolii, Prusik, and Giovanis (2020) point out that in the first variant of strength load, the greatest contribution to the dynamics of training effects is made by training at the first station "exercises to strengthen arms and shoulders"; in the second variant, the greatest contribution to the dynamics of training effects is made by training at the third station "exercises to strengthen back muscles";  in the third variant, the greatest contribution to the dynamics of training effects is made by training at the first station "exercises to strengthen arms and shoulders" and the third station "exercises to strengthen back muscles"; in the fourth variant, the greatest contribution to the dynamics of the ITE is made by training at the first "exercises to strengthen arms and shoulders" and the third "exercises to strengthen back muscles" stations; the most significant changes in the DTE are connected with training at the fourth station "exercises to strengthen leg muscles". The obtained regression models make it possible to calculate the number of repetitions and rest interval to achieve the most rational load variant. These data supplement the results presented in the studies by Iermakov, Ivashchenko, Khudolii, and Chernenko (2020), Ivashchenko, Khudolii, Prusik, and Giovanis (2020) and form a methodology for studying training loads, which differs from the methods used in the studies by Arazi et al. (2012), Ratamess et al. (2012), Miranda et al. (2010) in that research is conducted using an active 2 k FFE and materials are processed with the help of regression and discriminant analysis.
The results supplement the information of Ivashchenko and Cieślicka (2017), Cieślicka and Ivashchenko (2017) about the effectiveness of using factorial designs in studying training effects of strength loads in children; that of Ivashchenko, Khudolii, Iermakov, Chernenko and Honcharenko (2018), Marchenko and Kovalenko (2020) about the reliability of obtained regression equations for modeling the process of motor skills and motor abilities development in schoolchildren.
The effectiveness of using a 2 k full factorial experiment is confirmed by data of Tort-Martorell (2009, 2012), Ivashchenko, Nosko, and Ferents (2019). The main purpose of designs is to neutralize the influence of unknown factors, the authors recommend using designs with three and four factors. The results of presented research (Tables 2-7) show the effectiveness of using a 2 2 FFE in studying the ITE of strength loads in boys aged 8 years.
The obtained results specify the conceptual approaches to experiment planning in studying the effectiveness of children's physical education, factorial designs are an objective tool for obtaining data to calculate regression models of training effects in children (Khudolii, Ivashchenko, Iermakov, Nosko, & Marchenko, 2019;Khudolii, 2019;Ivashchenko, 2020).
In addition, strength training of schoolchildren is considered as a necessary condition of the educational process (Kapkan, Khudolii, & Bartik, 2019a,b). Based on the analysis of regression equations, it is possible to choose a load by focus, based on discriminant analysis -to choose a total load.

Conclusions
The study results show that in the proposed matrix of the 22 full factorial design, the chosen step of variation of factors is sufficient to study the influence of different modes of strength exercises on the dynamics of ITE in boys aged 8 years. Based on the data analysis, the study obtained regression models of load for calculating the ITE 1 , ITE 2 , and DTE. The obtained regression models make it possible to calculate the number of repetitions and rest interval to achieve the most rational load variant.
The analysis of regression equations shows the interrelation between training effects: ITE 1 -> ITE 2 -> DTE. The value of ITE 1 , ITE 2 , and DTE at station I (exercises to strengthen arms and shoulders) and station II (exercises to strengthen abdominal muscles) depends on the increase in the number of repetitions in a set and the duration of the rest interval. The value of ITE 1 , ITE 2 at station ІІІ (exercises to strengthen back muscles) depends on the increase in the number of repetitions in a set and the duration of the rest interval. The value of DTE -on the increase in the number of repetitions in a set and the reduction of the rest interval duration. The value of ITE 1 at station IV (exercises to strengthen leg muscles) depends on the increase in the number of repetitions in a set and the reduction of the rest interval duration. To strengthen the DTE, it is necessary to reduce the number of repetitions in a set and the duration of the rest interval.