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Sleep, 18(S}:342-345

© 1995 American Sleep Disorders Association and Sleep Research Society

Daytime Sleepiness

Mean Versus Median for the Multiple Sleep Latency

Test Selim R. Benbadis, Michael Perry, Barbara R. Wolgamuth, John Turnbull and Wallace

B. Mendelson

Cleveland Clinic Foundation Sleep Disorders Center, Department of Neurology,

Cleveland,

Ohio, U.S.A.

Summary: Since its introduction in the mid-1970s, the mUltiple sleep latency test (MSLT) has become the standard

method for evaluating hypersomnolence. The mean sleep latency is usually calculated and constitutes the traditional basis for interpretation. Mean and median are both measures of the central tendency of a distribution, but because

the trials of the MSLT are limited to 20 minutes, the median may be more appropriate. The objective of this study

was to compare the value of the mean versus the median sleep latency in the interpretation of the MSLT. We retrospectively analyzed

100 MSL Ts performed for evaluation of excessive daytime sleepiness. Patients' ages ranged

from 6 to 84 years (mean 43). Mean and median sleep latencies were calculated according to standard formulas.

We classified each record into one

of three categories, using both the mean and the median sleep latencies: normal

(> 10 minutes), moderate (205 and 10 minutes), and severe sleepiness "5 minutes). Of the 100 MSLTs, 89

remained in the same category (normal, moderate, severe) whether mean or median was used. In II cases, the category changed. All shifts were by one category, that is, no shift occurred between normal and severe. This study suggests that, despite valid theoretical arguments for the use of the median, both measures are equally acceptable for clinical purposes. Key Words:

MSLT -Daytime sleepiness-Central tendency-Mean.

Resume: Depuis son introduction par l'ecole califomienne, Ie test de latence multiple de sommeil (TLMS) est

devenu la methode de reterence dans Ie bilan des etats d'hypersomnolence. En general, la moyenne des latences d'endormissement est calculee, et constitue la base de l'interpretation. La moyenne et la mCdiane mesurent la tendance centrale d'une distribution, mais du fait que les siestes du TLMS sont limitees a 20 minutes, la mCdiane

peut sembler plus adequate. Le but de ce travail etait de com parer la valeur de la moyenne et de la mCdiane dans

l'interpretation du TLMS. Nous avons etudie de fa,bilan d'hypersomnolence. Les patients etaient ages de 6 a 84 ans (moyenne 43). Moyenne et mCdiane ont ete

calculees selon les formules standards. En utilisant d'une part la moyenne et d'autre part la mCdiane, nous avons

classe chaque enregistrement en 3 categories d'hypersomnolence: normal (> 10 minutes), moderee (20 5 et 10

minutes), et severe " 5 minutes). Sur les 100 tests, 89 n'ont pas change de categorie quel que soit Ie parametre

utilise.

Dans II cas, la classification a change, et toutes ont change d'une seule categorie (aucun changement ne

s'est produit entre normale et severe). Nous concluons que, en depit des arguments statistico-mathematiquesjustifies en faveur de la mediane, moyenne et mCdiane sont toutes deux acceptables en pratique clinique. Since its introduction at the Stanford University Sleep Research Center in the mid-1970s, the multiple sleep latency test (MSL T) has become the standard method for evaluating hypersomnolence (1). Beginning with early studies, accepted rules for interpretation have been based on the mean sleep latency: values greater than 10 are usually considered normal, whereas values less than 5 are considered indicative of pathological sleepiness. Values between 5 and

10 represent a gray

Accepted for publication February 1995.

Address correspondence

and reprint requests to Selim R. Ben badis, Department of Neurology, Medical College of Wisconsin,

9200 West Wisconsin Avenue, Milwaukee, WI 53226, U.S.A.

zone and can be viewed as indicative of moderate sleepiness (1-3).

Mean and median are both measures of the central

tendency of a distribution. The term mean, or average, usually refers to arithmetic mean, and this is most widely used in the

MSLT. Because the trials of the

MSLT are limited to 20 minutes, the distribution is truncated, and the median may be a more appropriate measure than the mean.

In the published guidelines

for the

MSLT (2), both mean and median are cited as

possible measures, but their respective merit has not been assessed.

The objective of this study was to com

pare the value of the mean and the median sleep latency in the clinical interpretation of the MSLT.

342 Downloaded from https://academic.oup.com/sleep/article/18/5/342/2749676 by guest on 23 October 2023

MEAN VS. MEDIAN FOR THE MSLT 343

PATIENTS AND METHODS

Patients

We retrospectively analyzed the data from 100

MSLTs performed on 100 patients for evaluation of

excessive daytime sleepiness (EDS). Ages ranged from

6 to 84 years [mean 43, standard deviation (SD)

16].

There were 63 males and 37 females.

MSLT method

MSLTs were recorded on Grass model

78 poly

graphs. Electrodes were attached with collodion, using the following montage: four channels of electroen cephalogram (EEG) using midline placement and in cluding an occipital electrode, four channels of elec trooculogram using left and right outer canthus, left above eye and left under eye, one electromyograph (EMG) channel (mental to submental), and one elec trocardiogram (EKG) channel. MSLTs were per formed during the day following an overnight poly somnogram and included at least four trials. If only one sleep onset rapid eye movement (REM) period (SOREMP) occurred in the first four naps, then a fifth trial was recorded. All trials were separated by

90 min

utes, during which patients were instructed to stay awake. All MSLTs were scored using 30-second epochs and according to standard criteria for sleep staging (4). Three epochs of stage 1 or one epoch of any other sleep stage were required to establish sleep onset.

Mean and median sleep latencies were calculated

according to standard formulas (5). Although several types of mean may be employed, the arithmetic mean is most commonly used; it is calculated by adding the observations and dividing the sum by the number of observations. The median is defined as the middle ob servation, that is, half the observations are smaller and half are larger. It is calculated by first arranging the observations from smallest to largest. The median is the middle value if there is an odd number of obser vations, and the mean of the two middle values ifthere is an even number of observations.

For the purpose

of this study, we then classified each record into one of three categories, using both the mean sleep latency and the median sleep latency. The cate gories of sleepiness, according to either mean or me dian, were: normal (N) if> 10 minutes, moderate (M) if 2: 5 and $10 minutes and severe (S) if < 5 minutes.

Each record was therefore assigned two classifica

tions: one using the mean, and one using the median.

If there was a discrepancy between the two classi

fications, patients' charts were reviewed to gather rel evant history. # patIents 2 2 d<-3 -3§d<·2 -2"dMean-Median difference (d) in minutes # of patients with • Mean>Median 0 MeanRESULTS

Of the 100 MSLTs, using the more traditional mean

sleep latency, 26 were classified as normal, whereas 35 showed evidence of moderate sleepiness (2: 5 and $10) and 39 showed evidence of severe sleepiness (mean < 5). Seven patients showed one SOREMP only, and

26 patients showed 2 or more

SOREMPs. The mean

was greater than the median in

67 patients, the median

was greater than the mean in 28 and mean and median were equal in

5. The distribution of the differences,

mean minus median, is shown in Fig. 1. The differences ranged from -4.0 to +4.1 (average +0.35, SD 1.42).

In 89 patients, classification remained the same

whether mean or median was used. In 11, the category changed, and these data are shown in Table

1. Ages

ranged from 8 to

61 years (mean 42.7, SD 16.4). There

were six males and five females. All shifts were by one category, that is, between

Nand M or between M and

S' no shift occurred between normal and severe sleep

Four of these "shifting" cases showed at least

one

SOREMP; three had a diagnosis of narcolepsy and

one of severe obstructive sleep apnea. In

10 of the 11 "shifting" cases, the mean was greater

than the median. The absolute value of the difference between mean and median ranged from 0.6 to 5 (mean

2.3, SD

1.1).

DISCUSSION

From a statistical point of view

Mean and the median are equally easy to compute,

particularly with a small number of observations, as

Sleep, Vol. 18, No.5, 1995 Downloaded from https://academic.oup.com/sleep/article/18/5/342/2749676 by guest on 23 October 2023

344 S. R. BENBADIS ET AL.

TABLE I. Data on patients whose MSLT would be classified differently using the mean or the median sleep latency

Sleep latency (minutes) Mean minus

Patient

median no. Age/sex Nap I Nap 2 Nap 3 Nap 4 Nap 5 Mean Median difference SOREMpa I

60/M 1.5 5.5 2 9.5 6 4.9 (S)b 5.5 (M) -0.6 None

2

371M 18 4 5.5 3 7.63 (M) 4.75 (S) +2.88 None

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