Now consider Table 3. In that table, find where it states 0.76**. What does that 0.76 mean, and what does the double asterisk mean? (Phrase your interpretations in the context of the problem at hand. That is, how they relate to the variables under discussion.) We don’t discuss correlation until the last week of the semester, but the basics are pretty straightforward and I think with a solid knowledge of the foundations of hypothesis testing you will be capable of giving a good answer here TABLE 3 Pearson correlations between nocturnal sleep fragmentation metrics and night-time actigraphic sleep variablesKRAVariablesKRAFragTST (h)WASO (min)SE (%)SOL (min)Awakenings0.43**-0.32*0.36**-0.32*0.110.53**Frag-0.40**0.59**-0.84**0.57**0.49**TST-0.020.36**0.030.22sleep is fragmented and physiologically sub-optimal during the day.Furthermore, frequent nappers may have a fragmented sleep due toenvironmental factors (e.g., noise, light, temperature, etc.) resultingin tiredness during the daytime, although this was not indicated bythe participant in the comment section on the sleep diary or duringthe interview.WASODespite finding a significant association between nap frequencyand KRA, we found no significant association between nap frequencyand standard measures of night-time sleep quality (WASO, awaken-ings, and SE). However, some previous studies reported significant,negative associations between nap frequency and night-time sleepquality (Goldman et al., 2008; Ye et al., 2015). Similar to our find-ings, McDevitt et al. (2012) found no significant association betweennap frequency and actigraphy-assessed night-time sleep quality in27 university students who were stratified into three nap frequencygroups. It is possible that the non-significant association betweennap frequency and nocturnal sleep quality in their study and oursmay be due to differences in methodology and/or lack of power todetect group differences. Of note, the failure to find differences innocturnal sleep between our moderate and non-nappers could beexplained by the lack of a distinction between planned voluntaryor intentional naps and unplanned accidental naps (i.e., dozing off-0.61**0.210.76**SE-0.70**-0.47**SOL0.26*Note: Awakenings, number of awakenings; Frag, actigraphy fragmentation index; KRA, novel fragmentation metric; SE, sleep efficiency; SOL, sleeponset latency; TST, total sleep time; WASO, wake after sleep onset.N = 62, *p < 0.05, **p < 0.01 two-tailed.Awakeningsinvoluntarily during the day while watching television or reading)(Ficca et al., 2010). Some studies have reported that nappers tendto under report their napping habits (Yoon et al., 2003), particularlyself-reported unplanned nap episodes during the day (Ficca et al.,2010). This underestimates total napping (as it reflects only plannednaps) and its consequences on night-time sleep fragmentation andsleep quality. A distinction between planned and unplanned napsmay have revealed nuances in the night-time sleep between themoderate and non-nappers.As expected, in our sample, late evening naps in close prox-imity to bedtime were associated with more sleep fragmentationand worse actigraphic sleep quality (SOL, WASO, and awakenings)but with a higher TST than early naps. Ye et al. (2015) reportedthat young adults taking naps in the evening (6:00-9:00 p.m.) hadthe poorest night-time sleep quality. Although napping has oftenbeen considered detrimental to night-time sleep, early naps areless likely to interfere with night-time sleep (Campbell et al., 2005;Lavie & Weler, 1989). Lavie and Weler (1989) assessed sleep in asmall sample of nine young adults and found that early nappershad higher SE, and longer slow-wave sleep duration than latenappers. Similarly, Campbell et al. (2005) demonstrated that asingle afternoon 2-h nap opportunity (2:00-4:00 p.m.) increased

Variables KRA Frag TST WASO SE SOL Awakenings KRA - Frag 0.43** - TST(h)…

Answered: Now consider Table 3. In that table,…

MATLAB: An Introduction with Applications

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Now consider Table 3. In that table, find where it states 0.76**. What does that 0.76 mean, and what does the double asterisk mean? (Phrase your interpretations in the context of the problem at hand. That is, how they relate to the variables under discussion.) We don’t discuss correlation until the last week of the semester, but the basics are pretty straightforward and I think with a solid knowledge of the foundations of hypothesis testing you will be capable of giving a good answer here

TABLE 3 Pearson correlations between nocturnal sleep fragmentation metrics and night-time actigraphic sleep variables
KRA
Variables
KRA
Frag
TST (h)
WASO (min)
SE (%)
SOL (min)
Awakenings
0.43**
-0.32*
0.36**
-0.32*
0.11
0.53**
Frag
-0.40**
0.59**
-0.84**
0.57**
0.49**
TST
-0.02
0.36**
0.03
0.22
sleep is fragmented and physiologically sub-optimal during the day.
Furthermore, frequent nappers may have a fragmented sleep due to
environmental factors (e.g., noise, light, temperature, etc.) resulting
in tiredness during the daytime, although this was not indicated by
the participant in the comment section on the sleep diary or during
the interview.
WASO
Despite finding a significant association between nap frequency
and KRA, we found no significant association between nap frequency
and standard measures of night-time sleep quality (WASO, awaken-
ings, and SE). However, some previous studies reported significant,
negative associations between nap frequency and night-time sleep
quality (Goldman et al., 2008; Ye et al., 2015). Similar to our find-
ings, McDevitt et al. (2012) found no significant association between
nap frequency and actigraphy-assessed night-time sleep quality in
27 university students who were stratified into three nap frequency
groups. It is possible that the non-significant association between
nap frequency and nocturnal sleep quality in their study and ours
may be due to differences in methodology and/or lack of power to
detect group differences. Of note, the failure to find differences in
nocturnal sleep between our moderate and non-nappers could be
explained by the lack of a distinction between planned voluntary
or intentional naps and unplanned accidental naps (i.e., dozing off
-0.61**
0.21
0.76**
SE
-0.70**
-0.47**
SOL
0.26*
Note: Awakenings, number of awakenings; Frag, actigraphy fragmentation index; KRA, novel fragmentation metric; SE, sleep efficiency; SOL, sleep
onset latency; TST, total sleep time; WASO, wake after sleep onset.
N = 62, *p < 0.05, **p < 0.01 two-tailed.
Awakenings
involuntarily during the day while watching television or reading)
(Ficca et al., 2010). Some studies have reported that nappers tend
to under report their napping habits (Yoon et al., 2003), particularly
self-reported unplanned nap episodes during the day (Ficca et al.,
2010). This underestimates total napping (as it reflects only planned
naps) and its consequences on night-time sleep fragmentation and
sleep quality. A distinction between planned and unplanned naps
may have revealed nuances in the night-time sleep between the
moderate and non-nappers.
As expected, in our sample, late evening naps in close prox-
imity to bedtime were associated with more sleep fragmentation
and worse actigraphic sleep quality (SOL, WASO, and awakenings)
but with a higher TST than early naps. Ye et al. (2015) reported
that young adults taking naps in the evening (6:00-9:00 p.m.) had
the poorest night-time sleep quality. Although napping has often
been considered detrimental to night-time sleep, early naps are
less likely to interfere with night-time sleep (Campbell et al., 2005;
Lavie & Weler, 1989). Lavie and Weler (1989) assessed sleep in a
small sample of nine young adults and found that early nappers
had higher SE, and longer slow-wave sleep duration than late
nappers. Similarly, Campbell et al. (2005) demonstrated that a
single afternoon 2-h nap opportunity (2:00-4:00 p.m.) increased

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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