Preliminary Data Indicating a Relationship Between Primary Nocturnal
Enuresis and Handedness
by Mark A. Murphy
copyright 2000, Mark A. Murphy
(Research initiated November 1998, originally submitted December 4,
2000 to "Pedriatrics" medical journal, not accepted. Submitted August
16, 2001 to the "Journal of Paediatrics and Child Health", awaiting review)
(this version is a draft, comments welcome, please send to murphy@tarleton.edu)
Abstract
A survey of college students indicates a significant
relationship between the manifestations of monosymptomatic primary nocturnal
enuresis and left-handedness. There was no significant relationship
between sex and handedness, and only a marginal relationship between sex
and enuresis, with males being more prone to enuresis at just under the
p= 0.05 level. The significance of the relationship between enuresis
and handedness, in conjunction with a review of the literature, indicates
that there is a possibility that both conditions may share at least one
genetic origin. Preliminary data is presented to support this argument
with a short discussion of previous research into both areas.
Introduction
Left-handedness has been associated with many
physical and mental conditions including shortened lifespan and sleep apnea
(Hoffstein, 1993), Attention Deficit Disorder (Comings & Comings 1987),
cognitive deficits in development of Alzheimer’s disease (Doody, et al,
1999), and homosexuality (Bailey, 1999). In addition to being more
likely to die younger, left-handers have higher injury rates in sports,
at home and work, and while driving (U.S. News & World Report, 1993).
There is a definite decline of left-handedness with increased age (Stellman,
et al, 1997). Aside from being associated with shorter lifespan,
this decline may be due, in part, to social pressure to change handedness
in order to conform to the right-handed norm, a situation not as strictly
enforced in the West today (Klar, 1996).
It is estimated that 5-7 million children
in the United States suffer from primary nocturnal enuresis (PNE) (Cendron,
1999), the most common form of bedwetting (von Gontard, et al, 1997).
While no discussion or study of a direct relationship between left-handedness
and nighttime bed wetting was found, there appeared to be a sufficient
amount of anecdotal evidence, concurrent manifestations, and literature
on shared phenotypical traits to warrant formation of the hypothesis that
they are related, and to conduct tests of that hypothesis.
The concept for this study began as anecdotal
evidence pointing to a relationship between PNE and left handedness.
The author was seeking medical treatment advice for an 8-year-old son who
suffered from nightly bedwetting episodes. The author has a brother
who is left-handed and had pre-pubescent enuresis, and the author’s spouse
had a sister who was a left-handed enuretic. Since the son was left-handed,
the author asked the physician treating the boy if there was possibly a
genetic link or correlation between the two. The physician said he
had never heard of a link, but that he so happened to be left-handed and
was enuretic prior to puberty as well. This started a concept that
was perpetuated by the fact that when the author sought advice or potential
partner with a medical background for a preliminary study on the correlation,
the first person consulted also responded that she was a left-handed sufferer
of PNE. As Coren (1993) has said, “Serendipity plays a role in science”.
The purpose of this study was to collect preliminary
data to support or refute the hypothesis that an actual relationship exists
between left-handedness and monosymptomatic PNE, not to provide genetic
or cultural models, nor to further any school of thought as to origins
of PNE and handedness. A small, introductory discussion of the genetic
vs. cultural origin controversy is presented, but to understand the arguments
in depth, a detailed review of over 70 years of research literature is
required, which is beyond the scope of this preliminary study. Sources
for various, detailed studies of genetics, handedness and PNE are referenced.
Monosymptomatic PNE is the onset or continuation
of consistent bedwetting after age 5 and up to age 15. These patients
exhibit no obvious physiological reason for PNE, such as reduced bladder
capacity (Johnson, 1998). Patients with obstructive sleep apnea (OSA)
are shown to have increased urine output at night due to level increases
of the hormone atrial natriuretic peptide (ANP), which may play a role
in PNE in children (Krieger, 1995). PNE also has been associated
with a decreased nighttime secretion of antidiuretic hormone (Cendron,
1999). While children with secondary nocturnal enuresis (that which
is caused by a pathology) often exhibit behavioral disorders and psychosocial
stress, those with PNE are usually better socially adjusted (von Gontard,
et al, 1998). By the age of 5, the bladder should be in a relatively
mature state and the child should be exhibiting adult pattern urinary control
(Johnson, 1998). About 11% of children between the ages of 5 and
17 report bed-wetting at least once in the previous year. Boys have
a slight tendency to wet more than girls (Byrd & Weitzman, 1996).
Approximately 90% of the population are right-handed
(Corballis, 1997, U.S. News & World Report, 1993). Animals show
almost an even preference for right and left side dominance, with the exception
of great apes which are about 2:1 right to left “handed” (Corballis, 1997),
while humans uniquely prefer the right (Bello, 1986). The ratio of
left-handed men to left-handed women has been described at about 3:1 (U.S.
News & World Report, 1993), but Cerone & McKeever (1999) indicate
no hand preference class by sex interaction. The male to female ratio
for PNE sufferers is also 3:1 (Arnell, et al, 1997), perhaps coincidentally.
Perinatal exposure to testosterone appears to have an effect on handedness,
but it is not clear if neonatal or prenatal exposure has the most effect
(Clark, et al, 1996; Coren, 1998). Handedness has been associated
with faster maturational development of the left cerebral hemisphere (Gabbard,
1995), and cerebral dominance (Annett, 1964; Corballis, 1997), but hand
preference seems to have no relationship to cognitive ability in developed
individuals (Cerone & McKeever, 1999).
There are several definitions of handedness
and ways to determine sidedness, laterality or sinistrality, including
indices created by various researchers using a wide variety of tests and
motor skill evaluations (Klar 1996, Coren & Searleman 1987, French
& Richards 1990, Annette 1964). With the use of questionnaires
in handedness studies, it has been shown that no particular bias due to
anxiety by left-handers will contaminate the results (Beaton & Moseley,
1991; French & Richards, 1990). In the present study respondents
were surveyed as to whether they considered themselves left-handed or not.
Some bias may be possible in older respondents especially because of former
school trends and attitudes that forced conformation to right-handedness.
Today's attitudes are more culturally accepting of left-handedness (Klar,
1996). However, the social and cultural pressures associated with
PNE may present a different problem.
Genetic causes and phenotypical manifestations
of handedness and PNE have been studied, but always separately. The
closest study found containing both, though not necessarily in concert,
revealed that enuresis is present in 19-36% of Tourette Syndrome patients,
and that 30-35% of Tourette Syndrome patients were left-handed (Comings
& Comings, 1987). The candidate gene or genes responsible for enuresis
have been likely identified, specifically assigned to chromosomes 13q,
probably 12q (Eiberg, 1995a; Arnell, et al, 1997), and possibly 8q (von
Gontard, et al, 1997; Hollmann, et al, 1998). The genetic locus of
mutation resulting in an allele for handedness is believed to have arisen
as a characteristic of Homo sapiens development about 200,000 years ago.
This could have been the result of the development of an opposable thumb,
but may have been a result of the ability to create speech by lateralizing
brain communication centers (Corballis, 1997). Archaeology has shown
5000-year-old cave paintings, use of paleolithic tools and Cro-Magnon man
studies also display the 90% right hand tendencies of humans (Bello, 1986,
Corballis, 1997).
The simple Mendelian model does not hold for
a handedness gene at a single locus (Corballis, 1997). However, despite
conflicting twin studies, definite familial patterns have emerged with
respect to handedness as evidenced by the legendary Kerr family of Scotland.
In the Middle ages, “Kerr-handed” people carried shields in the right hand,
swords in the left, thus making it more likely to take a fatal blow to
the heart. Kerr castle staircases wound up in a counter-clockwise
spiral to give them the edge in a sword fight. More recent studies
of the Kerr clan show about 30% left-handers compared to about 10% in the
general population (Coren, 1993). Annett (1996), Klar (1996) and
others have presented a model for a single gene that controls handedness.
They specify that this gene/locus actually specifies cerebral laterality
and that individuals lacking this gene have a 50% chance of being left-handed.
Hollmann, et al (1998) also state that PNE
has been shown to be familial in nature, but that there has been no statistically
significant association between linkage to a chromosome interval and type
of enuresis. More than 50% of PNE may be familial (Super & Postlethwaite,
1997). It has been suggested that recessive genes code for handedness,
but recent analyses of larger families indicate an autosomal dominant inheritance
with high penetrance, which may be influenced by other genes and environmental
factors (Norgaard, et al, 1997). One gene that controls the likelihood
of handedness may be located on chromosome 12 (Eiberg, 1995b). It
is not likely that the gene or genes are located on the sex chromosome,
but genes located there may influence handedness or cerebral asymmetry
(Corballis, 1997).
Some researchers believe that exact searches
for candidate genes of PNE on chromosomes 12q and 13q should concentrate
on those areas associated with sleep abnormalities (Super & Postlethwaite,
1997). PNE sufferers have higher incidences of defective sleep arousal
mechanisms (Neveus, et al 1999) and sleep-related breathing disorders (Messner,
1999), while older children with PNE are more difficult to rouse from sleep
than younger sufferers (Super & Postlethwaite, 1997). Arousal
response to bladder distension develops with age (Watanabe, 1995).
Left-sided people also have greater occurrences of sleep disturbances (Coren
& Searleman, 1987). Surprisingly, left-handedness also appears
associated with severe sleep apnea or obstructive sleep apnea (OSA), which
may help to explain a higher mortality rate amongst left-handed people
(Hoffstein, 1993). Enuresis, though an unusual symptom in adult OSA,
is a classic symptom of childhood OSA (Kramer, et al, 1998).
In fact, certain types of secondary enuresis are resolved with surgical
treatment of OSA, but this is not true of PNE (Wang & Vordemark, 1994).
Method
The primary data-gathering mechanism was the use
of a survey of 168 university students at Tarleton State University, all
respondents in a voluntary and anonymous exercise. A college student
population was chosen for this survey because it was surmised that most
would be of a post-pubescent age, possibly old enough to overcome some
of the emotional trauma associated with PNE, yet young enough to clearly
remember wetting the bed and remember siblings who did the same.
In one category, numbers of siblings and their statistics were used with
the same weight as the conditions of the primary respondents. Also
at this approximate age level there should be less bias due to social pressures
of switching handedness (Klar, 1996) and a general decline of left handedness
with increased age (Stellman, et al 1997, Coren 1993). Preliminary
interviews of left handed persons for this study who were older than about
35 indicated that many had forgotten whether or not they wet the bed between
5 and 15 years of age, and several failed to recall if any siblings did
as well.
Observations were grouped into different categories
for comparison, the main comparison being the handedness of the survey
respondent to the manifestation of monosymptomatic primary nocturnal enuresis
(table A). A slight modification of this comparison included those
listed as ambidextrous to be left-handed (table B). Studies have
included ambidextrous individuals as left-handed (Klar, 1996.) Another
category included the summed data from both the respondents directly and
the information provided by them on their siblings (table C). Other
comparisons were made of sex to PNE (table D) and sex to handedness (table
E).
Chi-square analyses of two by two tables were
used to analyze the data of each category. Probability based on the
chi-square determination was calculated at the 95% (p=0.05) confidence
level, with some comparisons at other levels (see tables). Handedness
has been associated with disease and disease risk factors (Stellman,
et al, 1997) and comparisons have been made of left handedness to sleep
disorders (Hoffstein, 1993), both with the use of chi-square analysis.
Neveus, et al (1999) used chi-square for simple comparisons of sex, enuresis
and sleep disorders. Szeszko, et al (1997) determined no significant
difference between gifted and non-gifted children in distribution of left
and right handed writing with the use of chi square comparison.
The following questions were asked on the
survey: What is your sex? What is your age? (grouped 18-25, 26-35,
36-49, 50-65, over 65). Are you left, right or both-handed?
How many of your siblings are/were left handed? How many of your
siblings are/were right-handed? Did you wet the bed between the ages
of 5 and 15? How many of your right-handed siblings experienced bed
wetting after age 5 but before age 15? How many of your left-handed
siblings experienced bed wetting after age 5 but before age 15? Answers
were tabulated and totaled with chi-square analysis performed for the different
categories as mentioned.
Results
The number of respondents totaled 168. Age
category totals were as follows: 99 respondents were 18-25 years old, 37
were 26-35, 27 were 36-49, 4 were 50-65, and 1 was over 65. Of these,
131 considered themselves right-handed, 32 left-handed and 5 both-handed.
Those who answered affirmative to bed wetting between the ages of 5 and
15 were 34, while 134 responded in the negative. Males totaled 43
and females totaled 125, which may have been skewed due to the majority
of participants apparently being nursing students, though an effort was
made to distribute the survey campus-wide. See the attached tables
for other totals, relationships and descriptive chi-square analyses of
those relationships.
At the 95% confidence level, a significant
relationship was seen between being left-handed and suffering from PNE.
This was true in both the respondent data excluding ambidextry, the respondent
data including ambidextry, and the respondent plus sibling data including
ambidextry. The respondent data set excluding ambidexterity neared
the 97.5% confidence level. The respondent plus sibling data showed
a significant relationship through the 99.9% confidence level, possibly
because this was a larger population of individuals. The relationship
between sex and PNE, though not significant (at p= 0.05) was closer to
the 95% level than to the 90% level. No relationship at all could
be determined for sex and handedness with this data set. Age was
not taken into account, nor was the effect of familial sibling relationship
to probability, though enuresis has been found to be more often a shared
sibling trait (Hollmann, et al, 1998).
Discussion
Based on this preliminary survey data, it appears
that there is a significant relationship between handedness and PNE.
Combined with current literature and studies, the possibility is presented
that PNE and handedness may have some genetic connection. No significant
relationship can be shown for sex and PNE, or for sex and handedness, with
this data set. Future studies need to be performed, with a larger
population and possibly with a more defined classification of handedness
using one of several accepted indices. It is suggested that clinical
data is needed on PNE patient populations to further or contest the hypothesis.
Some anxiety of enuretic sufferers could have
contributed to a bias of the study, though the surveys were completely
anonymous. No anxiety bias on the questionnaires was expected due
to handedness (Beaton & Moseley, 1991; French & Richards, 1990).
Another possible bias contributor was the subjective description of PNE
in the survey, especially when using data based on memory of sibling characteristics.
No bias determination of the effects of age, or the relationship of handedness
and enuresis between siblings was attempted. Some anecdotal evidence
suggests that males participants may have a harder time admitting to having
certain conditions, such as enuresis, as compared with females. This
must also be considered as a possible bias in future studies.
Acknowledgements
Special thanks to Diana Kunce, R.N., Dok Woods, R.N. and the Tarleton
State University Nursing Department for assisting in dissemination and
collection of the surveys. Thanks to Bobby Donohue, M.D., John Calahan,
Ph.D. and Nancy Easterling for reviews and comments on this paper.
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Table A
Chi Square Comparison of Handedness to PNE
(Respondent only, ambidextrous removed)
Left Right Totals
Wet 11 22 33
Dry 21 109 130
Totals 32 131 163
Table A Analysis
Degrees of freedom (df) = (rows - 1) x (columns - 1)
df = (2-1) x (2-1) = 1
Expected frequencies for each cell
Row 1 Column 1
Observed value (O) = 11
Expected value (E) = (row total x column total) / grand total
E = (33 x 32) / 163 = 6.47852760736196
Chi-square = (O - E)squared / E
Chi-square = ((11 - 6.47852760736196) **2) / 6.47852760736196
Chi-square = 3.1556109406953
Total chi-square now = 3.1556109406953
Row 1 column 2
Observed value (O) = 22
Expected value (E) = (row total x column total) / grand total
E = (33 x 131) / 163 = 26.521472392638
Chi-square = (O - E)squared / E
Chi-square = ((22 - 26.521472392638) **2) / 26.521472392638
Chi-square = 0.770836260322515
Total chi-square now = 3.92644720101781
Row 2 column 1
Observed value (O) = 21
Expected value (E) = (row total x column total) / grand total
E = (130 x 32) / 163 = 25.521472392638
Chi-square = (O - E)squared / E
Chi-square = ((21 - 25.521472392638) **2) / 25.521472392638
Chi-square = 0.801039700330344
Total chi-square now = 4.72748690134816
Table A Analysis (cont.)
Row 2 column 2
Observed value (O) = 109
Expected value (E) = (row total x column total) / grand total
E = (130 x 131) / 163 = 104.478527607362
Chi-square = (O - E)squared / E
Chi-square = ((109 - 104.478527607362) **2) / 104.478527607362
Chi-square = 0.195673819928023
Total chi-square now = 4.92316072127618
Probability (P):
Critical values for chi at df = 1:
Sig levels 0.20 0.10 0.05 0.025 0.01 0.001
Crit value 1.64 2.71 3.84 5.02 6.64 10.83
Sig. 0.20: chi is greater than or equal to 1.64
Sig. 0.10: chi is greater than or equal to 2.71
Sig. 0.05: chi is greater than or equal to 3.84
Degrees of freedom: 1
Chi-square = 4.92316072127618
p is less than or equal to 0.05.
The distribution is significant.
Table B:
Chi Square Comparison of Handedness to PNE
(Respondent only, ambidextrous included as left-handed)
Left Right totals
Wet 12 22 34
Dry 25 109 134
totals 37 131 168
Table B Analysis
Degrees of freedom (df) = (rows - 1) x (columns - 1)
df = (2-1) x (2-1) = 1
Expected frequencies for each cell:
Row 1 column 1
Observed value (O) = 12
Expected value (E) = (row total x column total) / grand total
E = (34 x 37) / 168 = 7.48809523809524
Chi-square = (O - E)squared / E
Chi-square = ((12 - 7.48809523809524) **2) / 7.48809523809524
Chi-square = 2.71861988038459
Total chi-square now = 2.71861988038459
Row 1 column 2
Observed value (O) = 22
Expected value (E) = (row total x column total) / grand total
E = (34 x 131) / 168 = 26.5119047619048
Chi-square = (O - E)squared / E
Chi-square = ((22 - 26.5119047619048) **2) / 26.5119047619048
Chi-square = 0.767854470032288
Total chi-square now = 3.48647435041687
Row 2 column 1
Observed value (O) = 25
Expected value (E) = (row total x column total) / grand total
E = (134 x 37) / 168 = 29.5119047619048
Chi-square = (O - E)squared / E
Chi-square = ((25 - 29.5119047619048) **2) / 29.5119047619048
Chi-square = 0.689799074127433
Total chi-square now = 4.17627342454431
Row 2 column 2
Observed value (O) = 109
Expected value (E) = (row total x column total) / grand total
Table B Analysis (cont.)
E = (134 x 131) / 168 = 104.488095238095
Chi-square = (O - E)squared / E
Chi-square = ((109 - 104.488095238095) **2) / 104.488095238095
Chi-square = 0.194828746127595
Total chi-square now = 4.3711021706719
Probability (P):
Critical values for chi at df = 1:
Sig levels 0.20 0.10 0.05 0.025 0.01 0.001
Crit value 1.64 2.71 3.84 5.02 6.64 10.83
Sig. 0.20: chi is greater than or equal to 1.64
Sig. 0.10: chi is greater than or equal to 2.71
Sig. 0.05: chi is greater than or equal to 3.84
Degrees of freedom: 1
Chi-square = 4.3711021706719
p is less than or equal to 0.05.
The distribution is significant.
Table C:
Chi Square Comparison of Respondent and Sibling Handedness vs. PNE
Left Right totals
Wet 28 63 91
Dry 67 403 470
totals 95 466 561
Table C Analysis
Degrees of freedom (df) = (rows - 1) x (columns - 1)
df = (2-1) x (2-1) = 1
Expected frequencies for each cell:
Row 1 column 1 ...
Observed value (O) = 28
Expected value (E) = (row total x column total) / grand total
E = (91 x 95) / 561 = 15.4099821746881
Chi-square = (O - E)squared / E
Chi-square = ((28 - 15.4099821746881) **2) / 15.4099821746881
Chi-square = 10.2860955350119
Total chi-square now = 10.2860955350119
Row 1 column 2
Observed value (O) = 63
Expected value (E) = (row total x column total) / grand total
E = (91 x 466) / 561 = 75.5900178253119
Chi-square = (O - E)squared / E
Chi-square = ((63 - 75.5900178253119) **2) / 75.5900178253119
Chi-square = 2.09695080649385
Total chi-square now = 12.3830463415058
Row 2 column 1
Observed value (O) = 67
Expected value (E) = (row total x column total) / grand total
E = (470 x 95) / 561 = 79.5900178253119
Chi-square = (O - E)squared / E
Chi-square = ((67 - 79.5900178253119) **2) / 79.5900178253119
Chi-square = 1.99156317805551
Total chi-square now = 14.3746095195613
Row 2 column 2
Observed value (O) = 403
Expected value (E) = (row total x column total) / grand total
E = (470 x 466) / 561 = 390.409982174688
Table C Analysis (cont.)
Chi-square = (O - E)squared / E
Chi-square = ((403 - 390.409982174688) **2) / 390.409982174688
Chi-square = 0.406005368916893
Total chi-square now = 14.7806148884782
Probability (P):
Critical values for chi at df = 1:
Sig levels 0.20 0.10 0.05 0.025 0.01 0.001
Crit value 1.64 2.71 3.84 5.02 6.64 10.83
Sig. 0.20: chi is greater than or equal to 1.64
Sig. 0.10: chi is greater than or equal to 2.71
Sig. 0.05: chi is greater than or equal to 3.84
Sig. 0.025: chi is greater than or equal to 5.02
Sig. 0.01: chi is greater than or equal to 6.64
Sig. 0.001: chi is greater than or equal to 10.83
Degrees of freedom: 1
Chi-square = 14.7806148884782
p is less than or equal to 0.001.
The distribution is significant.
Table D:
Chi Square Comparison of Sex to PNE
Male Female totals
Wet 13 21 34
Dry 30 104 134
totals 43 125 168
Table D Analysis
Degrees of freedom (df) = (rows - 1) x (columns - 1)
df = (2-1) x (2-1) = 1
Expected frequencies for each cell:
Row 1 column 1
Observed value (O) = 13
Expected value (E) = (row total x column total) / grand total
E = (34 x 43) / 168 = 8.70238095238095
Chi-square = (O - E)squared / E
Chi-square = ((13 - 8.70238095238095) **2) / 8.70238095238095
Chi-square = 2.12235359259983
Total chi-square now = 2.12235359259983
Row 1 column 2
Observed value (O) = 21
Expected value (E) = (row total x column total) / grand total
E = (34 x 125) / 168 = 25.297619047619
Chi-square = (O - E)squared / E
Chi-square = ((21 - 25.297619047619) **2) / 25.297619047619
Chi-square = 0.730089635854342
Total chi-square now = 2.85244322845417
Row 2 column 1
Observed value (O) = 30
Expected value (E) = (row total x column total) / grand total
E = (134 x 43) / 168 = 34.2976190476191
Chi-square = (O - E)squared / E
Chi-square = ((30 - 34.2976190476191) **2) / 34.2976190476191
Chi-square = 0.538507627973092
Total chi-square now = 3.39095085642726
Row 2 column 2
Observed value (O) = 104
Expected value (E) = (row total x column total) / grand total
Table D Analysis (cont.)
E = (134 x 125) / 168 = 99.7023809523809
Chi-square = (O - E)squared / E
Chi-square = ((104 - 99.7023809523809) **2) / 99.7023809523809
Chi-square = 0.185246624022744
Total chi-square now = 3.57619748045001
Probability (P):
Looking up critical values for chi at df = 1:
Sig levels 0.20 0.10 0.05 0.025 0.01 0.001
Crit value 1.64 2.71 3.84 5.02 6.64 10.83
Sig. 0.20: chi is greater than or equal to 1.64
Sig. 0.10: chi is greater than or equal to 2.71
Degrees of freedom: 1
Chi-square = 3.57619748045001
For significance at the .05 level, chi-square should be greater than
or equal to 3.84.
p is less than or equal to 0.10.
The distribution is not significant.
Table E:
Chi Square Comparison of Sex to Handedness
Male Female totals
Right 31 100 131
Left 12 25 37
totals 43 125 168
Table E Analysis
Degrees of freedom (df) = (rows - 1) x (columns - 1)
df = (2-1) x (2-1) = 1
Expected frequencies for each cell
Row 1 column 1
Observed value (O) = 31
Expected value (E) = (row total x column total) / grand total
E = (131 x 43) / 168 = 33.5297619047619
Chi-square = (O - E)squared / E
Chi-square = ((31 - 33.5297619047619) **2) / 33.5297619047619
Chi-square = 0.190866112111452
Total chi-square now = 0.190866112111452
Row 1 column 2
Observed value (O) = 100
Expected value (E) = (row total x column total) / grand total
E = (131 x 125) / 168 = 97.4702380952381
Chi-square = (O - E)squared / E
Chi-square = ((100 - 97.4702380952381) **2) / 97.4702380952381
Chi-square = 0.0656579425663392
Total chi-square now = 0.256524054677791
Row 2 column 1
Observed value (O) = 12
Expected value (E) = (row total x column total) / grand total
E = (37 x 43) / 168 = 9.47023809523809
Chi-square = (O - E)squared / E
Chi-square = ((12 - 9.47023809523809) **2) / 9.47023809523809
Chi-square = 0.675769207745952
Total chi-square now = 0.932293262423743
Row 2 column 2
Observed value (O) = 25
Table E Analysis (cont.)
Expected value (E) = (row total x column total) / grand total
E = (37 x 125) / 168 = 27.5297619047619
Chi-square = (O - E)squared / E
Chi-square = ((25 - 27.5297619047619) **2) / 27.5297619047619
Chi-square = 0.232464607464608
Total chi-square now = 1.16475786988835
Probability (P):
Critical values for chi at df = 1:
Sig levels 0.20 0.10 0.05 0.025 0.01 0.001
Crit value 1.64 2.71 3.84 5.02 6.64 10.83
Degrees of freedom: 1
Chi-square = 1.16475786988835
For significance at the .05 level, chi-square should be greater than
or equal to 3.84.
p is less than or equal to 1.
The distribution is not significant.