Mental health and psychosocial status in mothers of children with Attention Deficit Hyperactivity Disorder (ADHD): differences by maternal ADHD tendencies

DOI: https://doi.org/10.21203/rs.3.rs-1809370/v1

Abstract

This study aimed to clarify differences in mental health, psychosocial status, and mental health-related factors among mothers of ADHD children between those with and without ADHD tendencies of their own. The data from 149 mothers of children with ADHD, collected through an online survey, were analyzed. Mothers with ADHD tendencies had poorer mental health, more ADHD children, and felt a lack of understanding of their surroundings than mothers without ADHD tendencies. There were differences in mental health-related factors depending on the mother's ADHD tendencies. Therefore, individualized interventions based on the presence or absence of the mother's ADHD tendencies may be important to maintain mental health in mothers of ADHD children.

Introduction

Attention deficit hyperactivity disorder (ADHD) is a neurodevelopmental disorder characterized by inattention, hyperactivity, and impulsivity. Therefore, mothers of children with ADHD experience higher parenting stress [1] and more mental health problems [2-6] than those of children with neurotypical development. Poor mental health leads to dysfunctional parenting skills, such as corporal punishment, lack of discipline, overly strict discipline [7-9], worsening children’s ADHD symptoms, behavioral problems, and oppositional defiant disorder [10-13]. Furthermore, previous studies also reported that parents of children with ADHD had an increased risk of family separation, such as divorce [14-15] and difficulties in their employment [14] compared to parents of children without ADHD.

Therefore, it is important to maintain mental health in mothers of children with ADHD. Previous studies have reported factors related to their mental health. For example, depressive symptoms in mothers of children with ADHD and caregivers were related to children’s features (e.g., severity of behavioral disturbance, hyperactivity-impulsivity dominant and mixed features, child’s introversion problems [16-18]), mothers’ socioeconomic attributes (e.g., low income, being the sole caregiver in the family, baseline marital status [17, 18]), and parenting stress [1]. 

On the other hand, Genetic factors are strongly involved in ADHD psychopathology, and 25–50% of ADHD children have ADHD parents [19, 20]. Furthermore, adult ADHD is often associated with secondary disorders such as depression and anxiety disorders [21, 22], impaired work functioning [23], and financial difficulties [23]. Therefore, mothers of children with ADHD, especially those with ADHD tendencies of their own, may have more children with ADHD, high parenting stressors, poor socioeconomic status, and mental health problems.

However, it has not been studied how mental health, psychosocial status, and mental health-related factors of ADHD children’s mothers differ due to the mother’s ADHD tendencies. Therefore, this study aimed to clarify the differences in mental health, psychosocial status, and mental health-related factors among mothers of ADHD children between those with and without ADHD tendencies of their own. We hypothesized that mothers with ADHD tendencies would have poorer mental health and worse psychosocial status, such as unmarried, lower income, and higher parenting stressors compared to mothers without ADHD tendencies, and that mental health-related factors would differ by the presence or absence of maternal ADHD tendencies.

Methods

Study design and participants

An online survey was conducted between September 24, 2021, and October 19, 2021. Eligible participants were mothers of children (under 18) with ADHD that had been diagnosed by medical experts. The survey link was distributed to the participants by two peer groups for parents of children with developmental disabilities, a provider of after-school care services, and a support group for children with developmental disabilities. A checkbox was set up on the top page of the survey form to confirm that mothers of children with ADHD diagnosed by medical experts were the targets of the survey. Only those who clicked on this checkbox were allowed to participate in the survey. Of the 164 respondents who responded during the survey period, 149 were included in the analysis after excluding six respondents with incomplete data and nine who did not live with their children.

Survey instrument

Attributes, ADHD tendencies, ADHD child’s attributes and severity of ADHD symptoms, parenting stressors, and mental health were assessed.

Attributes

Attributes included age, education, marital status, occupation, living with a spouse, household income, medication status, number of children, and number of children with ADHD. The mothers’ medication use for mental health problems (antidepressants, anxiolytics, hypnotics) and ADHD (ADHD medications) were questioned. A list of the generic drug names of such medications approved in Japan was provided in the questionnaire. 

ADHD tendencies

Part A of the Adult ADHD Self Report Scale (ASRS-v1.1) [24] was used to define ADHD tendencies. The ASRS is a validated scale to screen adults for ADHD. The tool comprises 18 items, with six items for screening (Part A) and 12 additional questions (Part B). Respondents are considered positive on the ASRS when they answer four or more Part A questions at the threshold level [24]. The ASRS Part A screening has a sensitivity of 68.7% and specificity of 99.5% [24]. Cronbach’s alpha coefficient of the ASRS Part A in the present study was 0.831. In this study, mothers who tested positive on the ASRS Part A screening were defined as having ADHD tendencies.

ADHD child’s attributes and severity of ADHD symptoms

The attributes of child with ADHD included age, sex, diagnosis of comorbid developmental disorders (ASD, LD, DCD, other), and severity of ADHD symptoms. If the respondents had more than two children with ADHD, they were asked to respond regarding the child with the highest burden. The Japanese version of the home form of the ADHD-RS [25] was used for the severity of ADHD symptoms. The total ADHD-RS score was defined as the severity of ADHD symptoms. A higher score indicated more severe ADHD symptoms. Cronbach’s alpha coefficient of the ADHD-RS in the present study was 0.878. 

Parenting stressors

The Developmental Disorder Parenting Stressor Index (DDPSI) [26] was used for parenting stressors. The DDPSI is designed to measure stressors in parents of children with developmental disabilities and has an 18-item questionnaire composed of four factors: (1) difficulties in understanding the child and coping with the child’s needs, (2) anxiety about the child’s future and independence, (3) inadequate understanding of the childʼs disorder from others, and (4) conflicting emotions with regard to the childʼs disorder. A higher score indicated higher stress experienced by the respondents. Cronbach’s alpha coefficients of the four factors in the respondents were 0.721–0.868.

Mental health

The Japanese version of the Kessler 6-Item Psychological Distress Scale (K6) [27] was used. This scale is used in the Comprehensive Survey of Living Conditions conducted triennially by the Ministry of Health, Labour, and Welfare in approximately 300,000 Japanese households to investigate basic matters of national life, such as health, medical care, welfare, pension, and income. Cronbach’s alpha coefficient of K6 for the respondents was 0.866.

Statistical methods

The 149 respondents were divided into two groups according to the presence or absence of ADHD tendencies assessed by the ASRS Part A screening. Group comparisons were conducted for attributes, ADHD child’s attributes and severity of ADHD symptoms, parenting stressors, and mental health. A student’s t-test was used to compare quantitative variables, and Pearson's chi-square test or Fisher–Freeman–Halton test was used to compare qualitative variables.

We then analyzed the association between mental health (K6 scores) and the variables of attributes, ADHD child’s attributes and severity of ADHD symptoms, and parenting stressors in each group. Pearson’s correlation analysis was used for associations with quantitative variables. Student’s t-test, Welch’s t-test, or one-way analysis of variance was used for associations with qualitative variables.

SPSS Statistics version 27 for Mac was used for all statistical analyses, and the statistical significance level was set at 5%.

Results

Characteristics differences by maternal ADHD tendencies

The characteristics by maternal ADHD tendencies are shown in Table 1. Mothers with ADHD tendencies had significantly more children with ADHD (p=0.007), higher scores on “inadequate understanding of the childʼs disorder from others” stressor (p=0.029), and higher K6 scores (10.4 ± 4.7 vs. 7.8 ± 5.3, p=0.009) than those without ADHD tendencies.

[Table 1 will be here]

Factors associated with mental health in mothers with ADHD tendencies

Table 2 presents the results about factors associated with mental health in mothers with ADHD tendencies. Significant associations were found between K6 scores and the following items: age (r=-0.401, p=0.014), “difficulties in understanding the child and coping with the child’s needs” stressor (r=0.469, p=0.003), and “inadequate understanding of the childʼs disorder from others” stressor (r=0.332, p=0.045).

[Table 2 will be here]

Factors associated with mental health in mothers without ADHD tendencies

Table 3 presents the results about factors associated with mental health in mothers without ADHD tendencies. Significant associations were found between K6 scores and the following items: medications for mental health problems (yes vs. no:12.4±6.6 vs. 7.0±4.6, p=0.006), the severity of ADHD symptoms in child with ADHD (r=0.271, p=0.004), “difficulties in understanding the child and coping with the child’s needs” stressor (r=0.504, p<0.001), “anxiety about the child’s future and independence” stressor (r=0.421, p<0.001), “inadequate understanding of the childʼs disorder from others” stressor (r=0.294, p=0.002), and “conflicting emotions with regard to the childʼs disorder” stressor (r=0.360, p<0.001).

[Table 3 will be here]

Discussion

Currently, mothers of children with ADHD are known to experience higher parenting stress [1] and more mental health problems [2-6] than those of children with typical development. However, it is unknown how the mental health and psychosocial status among mothers of children with ADHD differ according to the presence or absence of their own ADHD tendencies. This study aimed to clarify the differences in mental health, psychosocial status, and mental health-related factors between mothers with and without ADHD tendencies.

First, the results of this study showed that mothers with ADHD tendencies had significantly poorer mental health, a higher number of children with ADHD, and higher stressor regarding “an inadequate understanding of the child’s disorder from others” compared to mothers without ADHD tendencies.

Regarding mental health, our results support previous studies reporting that adults with ADHD have a higher incidence of depression and other psychiatric disorders than adults without ADHD [21, 22]. In addition, our finding that mothers with ADHD tendencies had more ADHD children is also consistent with the genetic psychopathology of ADHD [19, 20]. Furthermore, the result that “inadequate understanding of the childʼs disorder from others” stressor was higher in mothers with ADHD tendencies may reflect social life difficulties that adults with ADHD have, such as “I get into arguments or fights easily,” “I lose friends easily because of my impulsive behavior, ” and “I am quick to lose my temper with my partner or loved one,” as reported in a previous study [23]. 

Contrary to our hypothesis, there were no differences in socioeconomic status, such as marital status or household income, between the two groups, which might be due to the small sample size of this study.

Second, the results of this study showed that mental health-related factors differed according to the presence or absence of ADHD tendencies in mothers. Among mothers with ADHD tendencies, younger individuales had poorer mental health. This suggests that younger mothers with ADHD tendencies are especially at high risk for poor mental health among mothers of children with ADHD. Additionally, in mothers with ADHD tendencies, parenting stressors of “difficulties in understanding the child and coping with the child’s needs” and “inadequate understanding of the childʼs disorder from others” were related to poor mental health. When combined with the finding that mothers with ADHD tendencies had a higher stressor of “inadequate understanding of the child’s disorder from others” than mothers without ADHD tendencies; improving this stressor seems particularly important for mothers with ADHD tendencies to prevent mental health problems. Moreover, medication use was not related to mental health in mothers with ADHD tendencies, contrary to previous findings that poor mental health is associated with antidepressant medication use [28-31]. This may indicate that mothers with ADHD tendencies do not have adequate access to medical resources even when they have mental health problems; therefore, it is necessary to support by experts in medical institutions and welfare centers.

On the other hand, in mothers without ADHD tendencies, poor mental health was related to medications, more severe ADHD symptoms in their child, and various kinds of parenting stressors such as “difficulties in understanding the child and coping with the child’s needs,” “anxiety about child’s futures and independence,” “inadequate understanding of the childʼs disorder from others” and “conflicting emotions with regard to the childʼs disorder.” Regarding medications in mothers without ADHD tendencies, unlike mothers with ADHD tendencies, our finding supports previous findings that poor mental health is associated with antidepressant medication use [28-31]. In addition, our findings suggest that varied parenting stressors and severity of child’s ADHD symptoms are the main factors related to poor mental health among mothers without ADHD tendencies. Therefore, it seems to be particularly important to improve these parenting stressors to maintain the mental health of mothers without ADHD tendencies.

This study had some limitations. First, as this was a cross-sectional study, causal relationships were not possible to prove. Longitudinal research is necessary to verify causal relationships. Second, since the voluntary nature of the online survey might have led to a selection bias, the respondents of this study may not be representative of the population. Thus, future studies should be conducted using a larger representative study sample. Third, data were collected using self-report questionnaires. Therefore, a reporting bias cannot be ruled out. Further studies using expert assessments of clinical symptoms and diagnostic criteria are needed in the future.

Despite these limitations, this is the first study to cralify differences in mental health, psychosocial status, and mental health-related factors among mothers of children with ADHD, depending on the presence or absence of mothers’ own ADHD tendencies. The results of this study showed as following. Mothers with ADHD tendencies had poorer mental health and psychosocial status than mothers without ADHD tendencies. Some factors related to the maternal mental health, which are parenting stressors such as “difficulties in understanding the child and coping with the child’s needs” and “inadequate understanding of the childʼs disorder from others” were common regardless of the mother's ADHD tendencies, while other factors differed depending on the mother’s ADHD tendencies. Threfore, to maintain the mental health of mothers with ADHD children, individualized interventions based on the presence or absence of the mother's ADHD tendencies, while improving common factors, are seemed to be important. These findings should help explore measures of mental health promotion in mothers of children with ADHD in the future.

 

Conclusions

Mothers with ADHD tendencies were found to have poorer mental health, more children with ADHD, and a higher stressor regarding “inadequate understanding of the childʼs disorder from others” compared to mothers without ADHD tendencies. Poor mental health in mothers with ADHD tendencies was related to younger age and higher parenting stressors such as “difficulties in understanding the child and coping with the child’s needs” and “inadequate understanding of the childʼs disorder from others.” Poor mental health in mothers without ADHD tendencies was related to medication use, more severe ADHD symptoms in the child, and higher parenting stressors such as “difficulties in understanding the child and coping with the child’s needs,” “anxiety about child’s futures and independence,” “inadequate understanding of the childʼs disorder from others,” and “conflicting emotions with regard to the childʼs disorder.”


Summary

Mothers of children with ADHD are known to have poor mental health and more psychosocial difficulties than mothers of children without ADHD and it is important to improve mental health problems in mothers of ADHD children. Whereas genetic factors are known to be involved in the psychopathology of ADHD and it is possible that mothers with ADHD tendencies of their own may especially have more mental health problems and psychosocial difficulties. Therefore, this study aimed to clarify differences in mental health, psychosocial status, and mental health-related factors among mothers of children with ADHD depending on the presence or absence of their own ADHD tendencies. Data from 149 mothers of children with ADHD obtained through a cross-sectional online survey were analyzed. The presence or absence of ADHD tendencies in the mothers was defined by ASRS screening. Mothers with ADHD tendencies had poorer mental health, more ADHD children, and felt a lack of understanding of their surroundings than mothers without ADHD tendencies. Poor mental health in mothers with ADHD tendencies was related to younger age and higher parenting stressors regarding “difficulties in understanding the child and coping with the child’s needs” and “inadequate understanding of the childʼs disorder from others.” Poor mental health in mothers without ADHD tendencies was related to medication use, more severe ADHD symptoms in their child, and higher parenting stressors such as “difficulties in understanding the child and coping with the child’s needs,” “anxiety about child’s futures and independence,” “inadequate understanding of the childʼs disorder from others” and “conflicting emotions with regard to the childʼs disorder.” The findings of this study imply the need for individualized interventions based on the presence or absence of ADHD tendencies in mothers to maintain the mental health among mothers of children with ADHD.

 

Declarations

Acknowledgments We wish to thank Eiko Okano, Hideko Dobashi, Kazuhisa Tanaka, and Tomoyuki Maeda for their support with data collection. We would like to thank Editage (www.editage.com) for English language editing.

Author Contributions Tatsuro Marumoto: Conceptualization, Methodology, Validation, Data curation, Formal analysis, Writing original draft, Writing review & editing. Takafumi Monma: Validation, Formal analysis, Writing review & editing. Yukinori Sawae: Data curation, Writing review & editing. Fumi Takeda: Conceptualization, Methodology, Validation, Formal analysis, Writing review & editing, Project administration, Supervision.

Funding This research did not receive any specific grants from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability The data are not available due to privacy and ethical restrictions.

Declarations

Conflict of interest Tatsuro Marumoto is an employee of Takeda Pharmaceutical Company Limited.

Ethical approval This study was approved by the Research Ethics Committee of the Faculty of Health and Sport Sciences of the University of Tsukuba, Japan (approval number: Tai 021-8; approval date: June 19, 2021).

Informed consent Informed consent was obtained from all individual participants included in the study.

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Tables

Table 1. Characteristics of respondents

 

 

 

Maternal ADHD tendencies

p-value




No(n=112)

Yes(n=37)

 

 

 

Mean±SD or n(%)

Mean±SD or n(%)

Attributes









Age


43.3

±5.0

42.7

±4.9

0.522

a


Education

High school or below

20

(17.9)

8

(21.6)

0.065

b



Vocational college/Junior college

35

(31.3)

19

(51.4)





University or above

55

(49.1)

10

(27)





Other

2

(1.8)

0

(0)




Marital status

Married 

102

(91.1)

30

(81.1)

0.176

b



Unmarried

2

(1.8)

2

(5.4)





Divorced/Widowed

8

(7.1)

5

(13.5)




Occupation

Employed

74

(66.1)

31

(83.8)

0.060

c



Unemployed

38

(33.9)

6

(16.2)




Household income

Less than 4 million

19

(17)

9

(24.3)

0.063

b



4.01-8 million 

50

(44.6)

21

(56.8)





8.01 million or more 

42

(37.5)

6

(16.2)





Do not know

1

(0.9)

1

(2.7)




Living with a spouse

Yes

97

(86.6)

28

(75.7)

0.128

c



No

15

(13.4)

9

(24.3)




Number of children

1

27

(24.1)

7

(18.9)

0.143

c



2

66

(58.9)

18

(48.6)





3 or more

19

(17)

12

(32.4)




Number of ADHD children

1

92

(82.1)

22

(59.5)

0.007

c



2 or more

20

(17.9)

15

(40.5)



 

Medications for mental health problems

Yes

16

(14.3)

7

(18.9)

0.600

c

 

 

No

96

(85.7)

30

(81.1)

 

 

 

ADHD medications

Yes

2

(1.8)

1

(2.7)

1.000

d

 

 

No

110

(98.2)

36

(97.3)

 

 

ADHD child’s attributes and severity of ADHD symptoms









Age


10.0

±3.2

10.5

±3.3

0.449

a


Sex

Male

91

(81.3)

29

(78.4)

0.811

c



Female

21

(18.8)

8

(21.6)




Comorbid developmental disorders

Yes

90

(80.4)

30

(81.1)

1.00

c



No

22

(19.6)

7

(18.9)




Severity of ADHD symptoms

 

25.6

±9.9

27.5

±11.2

0.332

a

Parenting stressors

 

 

 

 

 

 

 

 

Difficulties in understanding the child and coping with the child’s needs

 

8.4

±4.4

9.5

±4.6

0.194

a

 

Anxiety about the child’s future and independence

 

10.4

±3.8

11.2

±3.3

0.251

a

 

Inadequate understanding of the childʼs disorder from others

 

4.8

±3.1

6.1

±3.1

0.029

a

 

Conflicting emotions with regard to the childʼs disorder

 

5.2

±2.6

6.1

±2.3

0.087

a

Mental health

 

 

 

 

 

 

 

 

K6 score

 

7.8

±5.3

10.4

±4.7

0.009

a

a: Student’s t-test, b: Fisher-Freeman-Halton test, c: Pearson’s chi-square test, d: Fisher's exact test.

SD: standard deviation

Table 2. Relationship between mental health and psycho-social status in mothers with ADHD tendencies

 

 

 

n

K6 score

r

p-value




 

 

 

Mean±SD

Attributes





 




Age


37

42.7

±4.9

-0.401

0.014

a


Education

High school or below

8

12.5

±6.8

 

0.618

b



Vocational college/Junior college

19

10.1

±4.2

 





University or above

10

9.4

±3.7

 




Marital status

Married 

30

10.5

±5.3

 

0.187

b



Unmarried

2

10.0

±1.4

 





Divorced/Widowed

5

10.2

±1.3

 




Occupation

Employed

31

10.6

±4.9

 

0.617

c



Unemployed

6

9.5

±4.3

 




Household income

Less than 4 million

9

10.7

±2.7

 

0.253

b



4.01-8 million 

21

10.2

±5.7

 





8.01 million or more 

6

11.3

±3.9

 





Do not know

1

7.0

±0

 




Living with a spouse

Yes

28

10.3

±5.3

 

0.697

d



No

9

10.8

±2.2

 




Number of children

1

7

10.9

±4.2

 

0.448

b



2

18

9.6

±4.2

 





3 or more

12

11.3

±5.9

 




Number of ADHD children

1

22

10.4

±4.3

 

0.949

c



2 or more

15

10.5

±5.5

 



 

Medications for mental health problems

Yes

7

13.3

±5.6

 

0.074

c

 

 

No

30

9.7

±4.4

 

 

 

 

ADHD medications

Yes

1

10.0

±0.0

 

0.932

c

 

 

No

36

10.4

±4.8

 

 

 

ADHD child’s attributes and severity of ADHD symptoms

 

 

 

 

 

 

 

 

Age

 

37

10.5

±3.3

-0.176

0.297

a

 

Sex

Male

29

10.1

±4.8

 

0.522

c

 

 

Female

8

11.4

±4.8

 

 

 

 

Comorbid developmental disorders

Yes

30

11.1

±4.6

 

0.052

c

 

 

No

7

7.3

±4.3

 

 

 

 

Severity of ADHD symptoms

 

37

27.5

±11.2

0.218

0.195

a

Parenting stressors

 

 

 

 

 

 

 

 

Difficulties in understanding the child and coping with the child’s needs

 

37

9.5

±4.6

0.469

0.003

a

 

Anxiety about the child’s future and independence

 

37

11.2

±3.3

0.252

0.132

a

 

Inadequate understanding of the childʼs disorder from others

 

37

6.1

±3.1

0.332

0.045

a

 

Conflicting emotions with regard to the childʼs disorder

 

37

6.1

±2.3

0.308

0.064

a

a: Pearson’s correlation analysis, b: One-way analysis of variance, c: Student’s t-test, d: Welch’s t-test

SD: standard deviation

Table 3. Relationship between mental health and psycho-social status in mothers without ADHD tendencies

 

 

 

n

K6 score

r

p-value




 

 

 

Mean±SD

Attributes





 




Age


112

43.3

±5.0

-0.105

0.272

a


Education

High school or below

20

7.1

±5.6

 

0.099

b



Vocational college/Junior college

35

6.8

±4.9

 





University or above

55

8.6

±5.4

 



 

 

Other

2

10.0

±2.8

 

 

 


Marital status

Married 

102

7.9

±5.4

 

0.962

b



Unmarried

2

6.5

±2.1

 





Divorced/Widowed

8

7.1

±5.1

 




Occupation

Employed

74

7.4

±5.3

 

0.251

c



Unemployed

38

8.6

±5.3

 




Household income

Less than 4 million

19

8.0

±5.1

 

0.255

b



4.01-8 million 

50

7.1

±5.6

 





8.01 million or more 

42

8.3

±5.0

 





Do not know

1

16.0

±0

 




Living with a spouse

Yes

97

7.6

±5.1

 

0.229

c



No

15

9.3

±6.1

 




Number of children

1

27

7.1

±4.6

 

0.388

b



2

66

8.0

±5.2

 





3 or more

19

8.2

±6.5

 




Number of ADHD children

1

92

7.7

±5.2

 

0.548

c



2 or more

20

8.5

±5.5

 



 

Medications for mental health problems

Yes

16

12.4

±6.6

 

0.006

c

 

 

No

96

7.0

±4.6

 

 

 

 

ADHD medications

Yes

2

12.5

±5.0

 

0.206

c

 

 

No

110

7.7

±5.3

 

 

 

ADHD child’s attributes and severity of ADHD symptoms

 

 

 

 

 

 

 

 

Age

 

112

10.0

±3.2

-0.124

0.194

a

 

Sex

Male

91

7.6

±5.4

 

0.358

c

 

 

Female

21

8.8

±4.9

 

 

 

 

Comorbid developmental disorders

Yes

90

8.0

±5.2

 

0.378

c

 

 

No

22

6.9

±5.5

 

 

 

 

Severity of ADHD symptoms

 

112

25.6

±9.9

0.271

0.004

a

Parenting stressors

 

 

 

 

 

 

 

 

Difficulties in understanding the child and coping with the child’s needs

 

112

8.4

±4.4

0.504

<0.001

a

 

Anxiety about the child’s future and independence

 

112

10.4

±3.8

0.421

<0.001

a

 

Inadequate understanding of the childʼs disorder from others

 

112

4.8

±3.1

0.294

0.002

a

 

Conflicting emotions with regard to the childʼs disorder

 

112

5.2

±2.6

0.360

<0.001

a

a: Pearson’s correlation analysis, b: One-way analysis of variance, c: Student’s t-test, d: Welch’s t-test

SD: standard deviation