]. Soc. Cosmet. Chern., 27, 379-398 (September 1976)
`
`Combability Measurements on Human Hair
`
`MARIO L. GAROIA, Ph.D. and JOSE DIAZ, B.S.#
`
`Presented May 29, 1975, SCC Seminar, St. Louis, Missouri
`
`Synopsis: An instrumental method for MEASURING the effect of cosmetic products or
`any other treatment of the COMBABILITY of HUMAN HAIR has been developed. The
`required
`instrumentation, experimental procedure, and
`interpretation of
`the data
`are presented in detail. The method involves the continuous recording of the forces,
`which oppose the motion of a comb through a swatch of hair. The data thus produced
`consists of graphs showing the forces opposing (or generated by) combing as a function
`of the position of the comb along the length of the swatch. Examples of applications
`are presented.
`
`INTRODUCTION
`
`Combability can be defined as the subjective perception of the relative ease
`or difficulty with which human hair can be combed. It depends on the magni(cid:173)
`tude and on the fluctuations of the forces that oppose combing.
`Combability is an important attribute, which is always considered when
`judging the "condition" of human hair. Improved combability is perceived as
`the hair being in better condition. Another concept closely associated with
`combability is that of manageability. Still another factor related to combability
`is that of the mechanical damage, which is done to hair with the combing
`process, which is accelerated if the hair is hard to comb or to untangle. It fol(cid:173)
`lows that combability, due to its close connection with other desirable hair
`qualities, is a very important factor in judging the performance of many hair
`care products.
`The method described in this paper was developed in our laboratories for
`the purpose of quantitatively evaluating combability. It has been extensively
`tested with a wide variety of hair products and treatments and is now used as
`a standard test during product development and for claim substantiation in
`finished products. A number of instrumental methods for evaluating combabil(cid:173)
`ity have been reported in the literature (1-3). Some of the similarities and
`differences between those methods and ours will be discussed later. It is our
`opinion that our method has advantages in its simplicity and in the type of
`information that can be obtained by using it.
`
`-~Clairol Inc. Research Labs., 2 Blachley Road, Stamford, Con:ri. 06902.
`
`379
`
`

`

`380
`
`JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS
`
`In what follows, the method is first described in full detail so that it can
`easily be used by any interested laboratory. This description is followed by a
`selected number of experimental results, interpretation of the data, and a
`general discussion of the method.
`
`METHOD
`
`Experimentally, the method consists of suspending a hair swatch from a
`force-measuring device, inserting a comb close to the root end of the swatch,
`setting the comb in a straight combing motion through the swatch at a con(cid:173)
`stant speed, and continuously recording the forces that resist its motion during
`this transit from the point of insertion till it clears the tip end of the swatch.
`The data resulting from this operation consist of a graph showing the load
`(in grams) opposing (or generated by) combing as a function of the position
`of the comb along the length of the swatch. We call this graph a 'Combing
`Curve.'
`Com bing curves can be recorded using dry or wet hair. Typical examples
`of these curves can be seen in Fig. 1 (dry) and Fig. 2 (wet). Dry combing
`curves are recorded using swatches, which have been previously hand
`combed. In spite of the precombing, they show gradually increasing comb(cid:173)
`ing forces which reach maximum values at or near the tip end of the swatch.
`Wet combing curves are recorded using swatches which have been purpose(cid:173)
`ly tangled by immersing them in water. The resulting curve shows a high in(cid:173)
`cidence of tangles all through the length of the swatch. In some cases, the
`combing forces are higher close to the tip end of the swatch.
`In our method, combab~lity is measured by means of two parameters, which
`can be directly obtained from the combing curves. The first parameter is
`'peak combing load' (PCL). This is the highest load (in grams) that is re(cid:173)
`corded during the combing of the swatch. Points P in Figs. 1 and 2 are ex(cid:173)
`amples of PCLs. If desired, PCL can be converted to peak combing forces
`(PCF) (in dynes) by multiplying them by the acceleration of gravity
`( =980. em/ sec2 ). The second parameter is the average combing load ( ACL).
`This is the average load during one combing of the swatch. It is expressed in
`grams • em units) by the distance in centimeters traveled by the comb
`through the swatch.
`Both of these parameters give us a quantitative measure of how difficult
`(or easy) it is to comb a swatch of hair. Our method is based on measuring
`the changes that occur in such parameters when the hair is treated with a
`product. Decreases in PCL and/ or ACL, which indicate improvements in
`combability (and vice versa) correlate with what is perceived when the hair
`is combed by hand.
`As could be expected, the absolute values of the PCLs and ACLs depend
`on a large number of factors such as speed of combing, handling of the
`hair, dimensions of the hair swatch, curliness of the hair, comb dimensions,
`comb material, etc., which cannot be totally controlled. It is for these reasons
`
`

`

`MEASUHEMENTS ON HUMAN HAIR
`
`381
`
`..,
`p
`
`70
`
`BO
`
`150 -1!1
`
`-40
`
`D
`(
`030
`.J
`
`~ac
`iii
`~ ID
`u
`
`D
`
`14C
`
`12C
`
`ICC -Cl
`
`- BC·
`
`D
`(
`QBC·
`.J
`
`~4C
`iii
`~ao
`u
`
`0
`
`D
`
`0
`
`DISTANCE FROM TOP
`ICM J
`Figure 1. Dry combing curves, B before
`treatment, A after treatment with com(cid:173)
`mercial creme rinse. Combing loads ap(cid:173)
`pear plotted against distance of comb from
`top end of swatch
`
`Figure 2. Wet combing curves, B before
`treatment, A after treatment with com(cid:173)
`mercial creme rinse. Combing loads ap(cid:173)
`pear plotted against distance of comb
`from top end of swatch
`
`that changes in the values of these parameters are more important and
`more reproducible than their absolute values. It also follows that great
`care has to be taken so that comparisons-as, for example, before and after
`the use of a product-are done under experimental conditions that are,
`insofar as possible, identical. If done carefully, however, this method al(cid:173)
`lows us to measure changes in combing forces of the order of ± 20 per cent.
`Average changes are calculated by averaging the individual values measured
`on a set of replicate swatches.
`
`Equipment
`
`The instrumentation consists of an lnstron Tensile Tester (Metric Table
`Model, TM-M#) to which some attachments have been added (see Fig. 3).
`The Instron load cell B which has a range of 0 to 2,000 g is used. Other re(cid:173)
`cording tensile testing instruments could be similarly adapted.
`The attachments to the lnstron Tester shown in Fig. 3 are as follows (c)
`Comb Stand: the comb stand is an L-shaped aluminum part designed to hold
`different types of combs, it is mounted on the traveling crossbar of the ln(cid:173)
`stron by means of two screws; (b) Comb: the comb used in our measure(cid:173)
`ments consists of 8 cylindrical stainless steel teeth (unpolished), 2.2 mm in
`diameter, mounted (with an interteeth distance of 1.5 mm) on an aluminum
`frame. Two removable bars of the same material and diameter as the teeth are
`
`l>Jnstron Corp., Canton, MA.
`
`

`

`382
`
`JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS
`
`c_
`
`d
`
`: : :
`
`I
`
`I
`
`I
`
`I
`
`I
`
`Figure 3. Part of lnstron Tensile Tester showing combing attachments: (a) clamp; (b)
`comb; (c) L-shaped stand; (d) crossbar; (e) hair swatch; (f) load cell
`
`mounted perpendicular to them in order to keep the hair in place during
`combing (Fig. 4). (a) Clamps: the hair as used for these measurements is
`mounted on specially designed aluminum clamps (Fig. 4). These clamps pro(cid:173)
`duce approximately rectangular cross-sectional swatches .They have a hole on
`the top from which they are hung on a 1.5 mm diameter metal rod, which is
`connected to the load cell of the Instron. At the clamp, the dimensions of the
`cross-section of the hair swatch are 2.8 em in length and approximately 2 mm
`in width. At
`least
`two
`regular hand combs should be at hand
`for each measurement. One of the combs should only be used for clean un(cid:173)
`t:r:ea"[;ed hair swatches. The other one should be used for the treated swatches.
`Ordinary hard rubber or nylon combs are suitable.
`The measurements are done under standard temperature and humidity con(cid:173)
`ditions (70 ± 2°F, 65 ± 2 per cent RH). This requires the availability of a
`temperature and humidity controlled room wherein the tensile tester can be
`located and operated.
`
`

`

`MEASUREMENTS ON HUMAN HAIR
`
`383
`
`Sample Preparation
`
`The preparation of swatches consists of mounting the hair that has been
`selected to be used in the measurements, on the clamps previously described.
`The uniformity of this operation is facilitated by proceeding as follows: start
`by securing enough hair for a complete set of measurements. Six swatches
`are recommended in routine evaluations of products. If changes in comba(cid:173)
`bility are very small, more swatches might be required to ascertain statistically
`significant changes. About 10 g of hair are required to prepare each swatch.
`Although if could be desirable to use perfectly straight hair, this is not prac(cid:173)
`tical because it is difficult and expensive to obtain such hair. Virgin European
`hair with its natural soft curl is perfectly suitable for these measurements and
`should be used.
`If possible, all the hair to be used in 1 set of measurements should come
`from the same batch of commercially purchased hair. Blending the hair is not
`necessary and is not recommended because the coherence of the hair's natura]
`curl is lost, and this results in excessive tangling.
`The length of the individual hairs to be used should be uniform. A good
`length to start with in preparing swatches is 11 in.
`Measure the length of the hair in inches. On a top loading balance weigh
`Cto ± 0.2 g) individual bundles of hair (one for each swatch) so that each
`
`COMB
`
`top view
`
`side view
`
`CLAMP
`
`:I
`
`iliJ w
`thl
`rJ ~
`b;d
`
`top view
`
`side view
`
`c
`I
`
`1
`I
`I
`I
`INCHES
`
`2
`I
`
`Figure 4. Top and side views of comb and clamp used in measurements
`
`

`

`384
`
`JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS
`
`bundle's weight in grams is approximately equal to its stretched length in
`inches times (0.7); that is, the linear density of each bundle should be ap·
`proximately 0.7 g/in. Handle the bundles gently so that the hair's natural curl
`is not unnecessarily disturbed.
`Place the rootend section of a bundle in the throat of the clamp and dis(cid:173)
`tribute the hair evenly throughout its width. Allow approximately 1 in of hair
`beyond the throat of the clamp. Secure the male part of the clamp to the
`other part by means of the 2 screws. Proceed in the same way with the rest of
`the bundles. Cut the excess (root end) hair close to the top of the clamp's
`jaws. Stretch the hair swatch with the hands and cut the tip end of the hair
`at a distance of 6.5 in. from the closest end of the clamp. This can be done
`conveniently using a laboratory guillotine.-(!, The amount of hair freely hang(cid:173)
`ing from the clamp will weigh 4.5 to 5.0 g.
`The hair mounted on the clamps should be cleaned in order to remove
`dirt, grease, or any foreign material that might be present on the hair when it
`is purchased. The cleaning is done using a 15 per cent aqueous solution by
`weight of sodium lauryl ether sulfate. The (unadjusted) pH of this solution is
`in the range of 7 to 8. The solution is liberally applied twice to each swatch
`as if it were a shampoo. After the second application, the swatches are thor(cid:173)
`oughly rinsed under running deionized water (at room temperature) for 30
`min. For our purposes, this cleaning treatment is more realistic and less ar(cid:173)
`bitrary than the commonly used precleaning of hair with various organic sol(cid:173)
`vents.
`After cleaning, the swatches are combed and hung to dry and equilibrate
`to the standard conditions of 700F (21.1 OC) and 65 per cent RH for 24 hours
`in a controlled environment room or chamber.
`
`Experimental Procedure
`
`The experimental procedure consists of measuring the PCLs and/ or ACLs
`of the same hair swatches wet and/ or dry before a treatment and after the
`treatment.
`Measurements on Untreated Hair-Wet Measurements as follows. Step 1:
`turn on the Instron, allow it to warm up, and calibrate, following its operation
`manual. Step 2: place each of the swatches to be measured in deionized water
`at room temperature (70oF) for at least 10 min and for no more than 30 min
`prior to the measurements. This can be done by supporting the swatches by
`the clamps and allowing them to hang freely inside a large beaker(-= 3000 ml)
`full of deionized water. Step 3: take the first swatch out of the water and comb
`it until no detangling is noticed on further combing. Start this operation using
`
`~Harvard Apparatus Co., Inc., Dover, MA.
`
`

`

`MEASU HEMENTS ON HUMAN I-lAIR
`
`385
`
`the wide-tooth section of a hand comb and finish using the thin-tooth section.
`Step 4: immerse the hair swatch 3 consecutive times in a separate beaker con(cid:173)
`taining deionized water at room temperature. The purpose of this step is to
`generate a certain degree of tangling of the swatch under controlled condi(cid:173)
`tions. This step is very important and care should be taken to perlorm it in
`the same way each time. It should be done by holding the swatch through the
`clamp and gently dipping it in and out of the water 3 times. After the third
`immersion, squeeze out the excess water twice with the fingers. Step 5: with
`the crossbar sufficiently out of the way (below), hang the hair swatch from
`the load cell hook and adjust the pen of the recorder so that the swatch plus
`the clamp read zero. To do this, use the balance control of the recorder, which
`does not affect its calibration. Step 6: remove the swatch from the load cell
`and hang it by its clamp close to the lnstron. Displace the crossbar upward
`to the starting position. At this point, the teeth of the comb should be at a dis(cid:173)
`tance of 2.5 em from the lower edge of the hair swatch clamp. Step 7: hang
`the hair swatch from the load cell, and using two fingers to :Hatten the swatch,
`push-guide the hair into the comb. If done carefully, this operation insures a
`fairly even distribution of the hair between the interteeth spaces. Also, be(cid:173)
`cause the width of the swatch at the c1amp is 2.8 em, and the distance between
`the 2 outer teeth of the comb is 3 em, it is simple to have all the hair "in" the
`comb. Place the thin metal rod below the teeth, perpendicular to them, to pre(cid:173)
`vent the hair from coming out of the comb during the measurements. Step 8:
`once the hair is properly placed in the comb, the actual measurement can be
`started. This consists of continuously recording the force that is required to
`move the comb down through the hair swatch at a constant speed. This is
`done by setting the crossbar in downward motion while continuously record(cid:173)
`ing the load. If a recorder integrator is available, it should be functioning so
`that the area under the com bing curve is measured. The com bing speed will
`be set at 10 em/min and the chart speed at 10 em/min. The sensitivity for the
`recorder will be set according to the values of the forces encountered. Step
`9: repeat steps 4 through 8 twice for the same swatch in order to record tripli(cid:173)
`cate runs. Step 10: repeat steps 2 through 9 for the remaining swatches. Step
`11: after the wet measurements are completed, comb the swatches using the
`hand comb, hang them through the clamps and allow them to dry and condi(cid:173)
`tion for at least 24 hours at 65 per cent RH and 70°F.
`Dry Measurements: Dry measurements comprise steps 12 and 13. Step 12:
`Start the dry measurements by taking the first conditioned hair swatch and
`combing it with the hand comb until no detangling is noticed on further
`combing. Proceed then with steps 5 through 9 as before. Step 13: repeat step
`12 for the remaining swatches.
`Treatment: Give the treatment to the hair mounted on the clamps following
`the recommended instructions for the product. Use deionized water whenever
`
`

`

`386
`
`JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS
`
`water is needed. The amount of product to be applied to each hair swatch is
`calculated taking into account the amount recommended for a head of hair,
`using 100 g of hair as the average weight of hair for adult females, and weight
`of hair in each hair swatch. The following formula is applied for this purpose.
`
`Weight of product
`to apply per swatch
`
`(weight of hair swatch) X
`100
`
`Amount of product)
`recommended for a
`head of hair
`
`(
`
`If rinsing with water is the last step of the treatment, care should be given to
`this operation. Rinsing should be sufficient to eliminate excess product, but
`not so intense so that the effect of a product could be completely eliminated.
`The way in which the product is used in actual practice should be followed.
`For example, shampoos are rinsed until foam is no longer evident; the same
`should then be accomplished with the rinsing given to the hair swatches. Once
`the conditions are specified, care should be exercised in rinsing each of the
`swatches in the same way. Rinsing conditions should specify volume of water,
`temperature of the water, rinsing time, and method (Rowing water or immer(cid:173)
`sion).
`Measurements of Treated Hair: Wet measurements on treated hair should
`be done right after the treatment, preceded only by a 5-min period in
`which the treated swatch is allowed to relax immersed in water. The rest of
`the wet treated swatches should be left hanging from their clamps while they
`wait for the 5-min relaxation period and subsequent measurement. The
`main reason for doing the wet measurements right after the treatment is be(cid:173)
`cause, in practice, the hair has to be combed after any treatment, and it is at
`that point that the user will associate the product with its effect on wet comb(cid:173)
`ability. Obviously, wet measurements can be done at a later time if this will
`contribute additional information on the effect of the product.
`
`Calculations
`
`Once the measurements are completed the data required to calculate chang(cid:173)
`es in combability are obtained from the combing curves.
`The PCL for each run corresponds to the highest load recorded for that run
`and is read directly from the corresponding combing curve. The load for a
`full-scale deflection use for recording obviously has to be taken into account.
`The ACL for each run is calculated by first measuring the area under the
`corresponding combing curve (in grams em • units) and then dividing the
`value for the area by the distance in centimeters that the comb travels through
`the hair in that run. This distance is read directly from the curve.
`It has been our experience, in developing this method, that per cent changes
`in PCL are similar in value to per cent changes in ACL. For this reason, and
`
`

`

`MEASUREMENTS ON HUMAN HAIR
`
`387
`
`Table I
`Combability Results on Bleached Hair
`Before and After the Use of a Semipermanent Dye Product
`A
`- - - - - · - - - - - · - - -
`Wet Measurements 70°F)
`Peak Combing Load (G)
`
`Average
`Column
`970.
`1183.
`738.
`1195.
`1208.
`1607.
`
`After Treatment (AT)
`Average
`Run Number
`Column
`2
`3
`1
`707.
`980.
`820.
`320.
`360.
`664.
`463.
`366.
`515.
`460.
`422.
`664.
`722.
`650.
`900.
`616.
`472.
`500.
`480.
`436.
`440.
`350.
`530.
`440.
`
`Per cent
`Change
`-27.1
`-60.9
`-30.2
`-39.6
`-60.9
`-72.7
`
`Swatch
`Number
`1
`2
`3
`4
`5
`6
`
`Before Treatment (BT)
`Run Number
`2
`3
`1
`1050.
`700.
`1160.
`1125.
`1500.
`925.
`525.
`690.
`1000.
`1175.
`1200.
`1210.
`850.
`1950.
`825.
`1550.
`1425.
`1845.
`- - - - - - - - - - - -
`Average BT = 1150, average AT = 553.
`553.- 1150.)
`_
`1150
`
`h
`P
`er cent c ange =
`
`(
`
`X 100 = -52. per cent.
`
`B
`
`Dry Measurements (65 per cent RH, 70°F)
`Peak Combing Load (G)
`
`Swatch
`Number
`1
`2
`3
`4
`5
`6
`
`Before Treatment
`Run Number
`2
`.530.
`390.
`340.
`365.
`800.
`550.
`
`I
`800.
`416.
`500.
`488.
`1180.
`620.
`
`3
`784.
`304.
`275.
`399.
`500.
`650.
`
`Column
`Average
`705.
`370.
`372.
`417.
`827.
`607.
`
`After Treatment
`Average
`Run Number
`Column
`2
`3
`1
`258.
`220.
`238.
`236.
`247.
`140.
`196.
`200.
`19q.
`2f.3.
`140.
`200.
`.310.
`255.
`275.
`280.
`210.
`370.
`400.
`327.
`187.
`155.
`256.
`200.
`
`Per cent
`Change
`-66.3
`-47.0
`-46.2
`-32.9
`-39.5
`-32.9
`
`Average BT = 550, average AT= 240.
`240. - 550.)
`550.
`
`Per cent c ange =
`h
`
`(
`
`00
`X 1
`
`= -
`
`56
`
`per cent.
`
`because they are more readily calculated, the use of PCL values is recom(cid:173)
`mended. The computations are best illustrated by considering examples.
`
`Example I
`
`The data, which appears in Table I are typical and correspond to an experi(cid:173)
`ment that was done for the purpose of determining the effect of an experi(cid:173)
`mental semipermanent dye product on the wet and dry combability of
`bleached hair.
`
`

`

`388
`
`JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS
`
`The columns with headings Run 1-3 contain the PCL values for each of
`the 3 replicate runs that were recorded for each swatch.
`The average column consists of the averages of the runs for each swatch.
`The average before treatment (BT) and average after treatment (AT)
`values are the averages of the average values appearing in the average col(cid:173)
`umns. The per cent change in PCL is calculated using the expression
`t h
`· PCL
`100 _
`- per cen c ange m
`
`(Average PCL AT- Average PCL BT)
`Average PCL BT
`
`X
`
`If average combing loads are measured instead of peak combining loads,
`the data are treated in an identical manner.
`The results of the above set of measurements are summarized as follows.
`Effect of experimental direct dye base on combability: average per cent
`change in dry PCL · · · -56. per cent; average per cent change in wet
`PCL · · · -52. per cent.
`The percent change columns on the right hand side of Table I give the per
`cent changes for the individual swatches. We have chosen not to use these
`numbers, i.e., their averages, to calculate the total per cent change in PCL,
`due to the treatment. These numbers, however, give, on inspection, a practical
`indication of the reproducibility of the experiment and/ or treatment effects.
`
`Example II
`
`In most cases, combability measurements involve the comparison of the
`e1ects on combability of two or more products. Even when this is not the
`case, a product whose effect on combability has been previously measured, is
`normally included in the experiments. This is recommended because it
`serves as an internal standard which will detect any bias in the results due to
`differences in the hair. Hair from the same source should always be used in
`any comparative study.
`A comparison between products can be done by measuring the effect on
`combability of each product individually as in example I and then comparing
`the average per cent changes. If the effects on combability of two products
`are sufficiently different, that is, of the order of (per cent change PCL)
`Product A- (per oent change PCL) Product B ~ 20 per cent, and if the per
`cent change in PCL for most of the replicate swatches is uniform, the
`validity of the observed difference frequently can be decided by simple
`inspection of the data. If there is any doubt and/ or the data are going
`to be used as part of documentation supporting claims for a product, the
`statistical significance of the differences must always be established. This
`is best accomplished by doing an analysis of variance on the data ( 4).
`Such an analysis is illustrated as follows with data that were used to com(cid:173)
`pare the effect of· shampoo A (Table II) to. that of shampoo B . (Table III)
`on the combability of dry human hair. As can be seen in the Tables, 8
`
`

`

`Table II
`Effect of Shampoo A on the Dry Combability of Untreated Brown Hair
`
`Peak Combing Load (Grams) 70°F, 65 Per Cent Relative Humidity
`After Treatment with Shampoo A
`Before Treatment
`Run 1 Run 2 Run 3 Run 4 Run 5 Average Column
`Run 1 Run 2 Run 3 Run 4 Run 5 Average Column Per cent Change
`183.
`133.
`190.
`153.
`181.
`173.
`223.
`155.
`160.
`193.
`173.
`166.
`-
`8.
`173.
`173.
`ll5.
`249.
`198.
`233.
`143.
`150.
`228.
`333.
`310.
`162.
`-35.
`80.
`75.
`68.
`73.
`70.
`65.
`58.
`50.
`.58.
`103.
`90.
`70.
`-4.
`ll5.
`125.
`137.
`120.
`100.
`148.
`125.
`123.
`143.
`170.
`148.
`127.
`-
`7.
`145.
`126.
`ll3.
`98.
`138.
`138.
`ll5.
`158.
`llO.
`108.
`140.
`127.
`0
`73.
`130.
`123.
`100.
`75.
`135.
`88.
`160.
`128.
`140.
`ll5.
`97.
`-25.
`158.
`123.
`125.
`193.
`213.
`138.
`100.
`253.
`170.
`90.
`93.
`141.
`-11.
`50.
`38.
`50.
`55.
`40.
`50.
`35.
`38.
`53.
`60.
`50.
`44.
`-12.
`
`Swatch 1
`Swatch 2
`Swatch 3
`Swatch 4
`Swatch 5
`Swatch 6
`Swatch 7
`Swatch 8
`
`Average before treatment =
`Average after treatment= ll6.8.
`
`er cent c ange =
`h
`P
`
`ll6.8 - 138.)
`_
`X
`138
`
`(
`
`100
`
`= -
`
`15
`. per cent.
`
`

`

`Table Ill
`Effect of Shampoo B on the Dry Combability of Untreated Brown Hair
`
`Peak Combing Load (Grams) 70°F, 65 Per Cent Rebtive Humidity
`Before Treatment
`Mter Treatment with Shampoo .B
`Run 1 Run 2 Run 3 Run 4 Run 5 Average Column
`Run 1 Run 2 Run 3 Run 4 Run 5 Average Column
`138.
`113.
`178.
`150.
`255.
`110.
`195.
`93.
`213.
`143.
`173.
`144.
`173.
`148.
`165.
`108.
`200.
`175.
`154.
`145.
`155.
`108.
`145.
`118.
`170.
`165.
`215.
`190.
`230.
`268.
`202.
`240.
`181.
`133.
`155.
`145.
`120.
`130.
`120.
`150.
`140.
`105.
`132.
`185.
`136.
`130.
`150.
`110.
`100.
`70.
`95.
`90.
`95.
`90.
`100.
`65.
`60.
`105.
`90.
`84.
`80.
`60.
`85.
`80.
`75.
`76.
`66.
`65.
`45.
`65.
`60.
`95.
`100.
`115.
`80.
`105.
`125.
`100.
`180.
`154.
`100.
`175.
`145.
`145.
`45.
`65.
`57.
`llO.
`80.
`65.
`85.
`55.
`60.
`100.
`60.
`88.
`
`Per cent Change
`+20.
`-6.
`-10.
`+ 3.
`-7.
`-13.
`+54.
`-35.
`
`Swatch 9
`Swatch 10
`Swatch 11
`Swatch 12
`Swatch 13
`Swatch 14
`Swatch 15
`Swatch 16
`
`Average before treatment= 123.2.
`Average after treatment= 124.5.
`124.5 - 123.2)
`123
`
`
`Per cent change=
`
`(
`
`X 100 = +1 per cent.
`
`_2
`
`

`

`MEASUREMENTS ON HUMAN HAIR
`
`391
`
`Table IV
`Analysis of Variance for Data in Table II
`
`Source of Variance
`l~etween rows
`Between columns
`Row X column ,interaction
`Residual
`Total
`
`Sums of Squares
`185,415.7
`9,052 .. 5
`14,459.6
`73,495.6
`282,423.4
`
`Degrees of Freedom
`n1 ~ 1 = 7
`n~-1=1
`(nt-1)x('lb-1)=7
`n1n2(na- 1) = 64
`n1n2n3- 1 = 73
`
`Mean Squares
`26,488.
`9,052.5
`2,065.7
`1,148.4
`
`n1 equals number of rows equals 8 (one for each swatch).
`n2 equals number of columns equals 2 (one for each treatment).
`n1 equals number of replications equals 5 (five for each swatch).
`
`swatches were used and 5 replicate runs were done on each swatch:
`It can be seen in Table II that the use of shampoo A resulted in a decrease of
`the forces required to comb 7 out of 8 swatches used. On the other hand,
`Table III shows that of the 8 swatches that were treated with shampoo B, 3
`showed an increase and 5 a decrease in their PCLs.
`Analysis of Variance for Data in Table II. The statistical parameters needed
`to perform the analysis are shown in Table IV. The following operations are
`done to determine the significance of the different components of variance.
`Step 1. Significance of the interaction (between rows and columns) against
`the residual: 2,065.7/1,148.4 = 1.79. For degrees of freedom ( df) N1 = 7,
`N2 = 64 the above ratio is not significant at the 95 per cent confidence level.
`(Fisher variance ratio test. ) This means that the data do not show any de(cid:173)
`tectable statistically significant interaction between the treatment and the
`PCLs of the swatches. If the interaction had been significant, it would
`indicate that the effect of the product is a function of a characteristic of some
`of the swatches, in our case their initial before treatment average PCL. This
`seldom occurs if all the swatches are prepared from the same homogeneous
`batch of hair. If it does, it indicates inhomogeneity of the hair, and the best
`solution is to prepare more swatches and exclude from the set of swatches
`those that have extremely high values for their initial before treatment PCL.
`This should be done on the complete set of swatches participating in the
`experiment. The set would then be randomly divided in half into subsets
`to be used with each product.
`Step 2. Pooling of the sums of squares of the interaction and residual and
`their degrees of freedom: (14,459.6 + 73,495.6)/(7 + 64) = 1,238.8. This num(cid:173)
`ber is now treated as a new mean square for the residual.
`Step 3. Significance of the variance due to differences between columns
`(i.e., due to shampoo A treatment). The value of the ratio of the mean
`square of the between columns term and that of the new residual determines
`the significance of the "between columns" variance: 9,052.5/1,238.8 = 7.31.
`For degrees of freedom N1 = 1 and N2 = 71 the value of the ratio indicates
`
`

`

`392
`
`JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS
`
`Table V
`Analysis of Variance for Data in Table III
`
`Source of Variance
`Letween rows
`Between columns
`Row X column interaction
`Residual
`Total
`
`Sums of Squares
`133,028.0
`32.5
`13,401.0
`.59,972.0
`206,433.5
`
`Degrees of Freedom
`nl-1=7
`n2-1=1
`(n1-1)x(n2-l) =7
`n1n2(na- 1) = 64
`n,n2n3 - 1 = 73
`
`Mean Squares
`19,004.0
`32.5
`1,914.4
`937.1
`
`n1 equals number of rows equals 8 (one for each swatch).
`n2 equals number of columns equals 2 (one for each treatment).
`na equals number of replications equals 5 (five for each swatch).
`
`statistical significance at the 99 per cent confidence level. This means that the
`decrease in PCL measured experimentally ( -15. per cent) can be considered
`statistically significant at the 99 per cent confidence level.
`Analysis of Variance for the Data in Table III. The parameters needed to
`perform the analysis appear in Table V.
`Step 1. Significance of the interaction: 1,914.4/937.1 = 2.04. For N 1 = 7,
`N2 = 64 the interaction is not significant at the 95 per cent confidence level.
`Step 2. Pooling of sums of squares and degrees of freedom: (13,401. +
`59,972.)/(7 + 64) = 1,033.4.
`Step 3. Significance of the variance due to between columns differences:
`32.5/1,033.4 = 0.31. For N 1 = 1, N 2 = 71 is not significant.
`These results confirm that the changes noticed on combing loads (Table
`III) after the use of shampoo B do not indicate any effect due to this treat(cid:173)
`ment.
`The analysis of variance provides us with a criteria to establish the statisti(cid:173)
`cal significance of the observed changes in combing forces. In order to com(cid:173)
`pare the effect of shampoo A to that of shampoo B we can proceed as follows.
`Step a. Calculate the difference between the average after and average be(cid:173)
`fore treatment values for each shampoo,i.e.,
`
`average difference for shampoo A = D A = 116.8 - 138. = -21.2 g
`average difference for shampoo B = Dn = 124.5 - 123.2 = 1.3 g
`
`Step b. Calculate the standard error (standard deviation) of the difference
`in the means, i.e., D A and Dn using the formula (.5)
`
`Standard error =
`
`a- X y2 =urn
`__
`yn
`
`

`

`MEASUREMENTS ON HUMAN HAIR
`
`393
`
`is the common standard deviation of each of the before and
`where a-
`after treatment means, and n ( 40) is the number of observations used
`to calculate the means. In our case, a- will be given by the square root
`of the residua] mean square calculated in Step 2 of the analysis of variance').
`vVe will have the following:
`
`A
`h
`f
`a-rna or s ampoo =
`
`B
`h
`f
`a-mb or s ampoo =
`
`35.2 X 1.41
`.32 =
`6
`
`7 85
`.
`
`32.1 X 1.41
`.32
`6
`
`=
`
`716
`.
`
`If desired, these numbers can be used to estimate confidence level limits
`( ± L) for the differences, i.e., ±L = t X a-m· The residual variance used
`to calculate the standard errors has 7 4 degrees of freedom. The correspond(cid:173)
`ing value for t for the 95 per cent confidence level is 2.0, hence
`
`±LA= ±2. X 7.85 = +15.7
`
`±LB = ±2. X 7.16 = ±14.3
`
`and the changes in combing forces for shampoos can be expressed as follows:
`
`Change in PCF shampoo A= -21.2 ± 15.7 g
`Change in PCF shampoo B =
`Step c. In order to calculate the significance of the difference between the
`two average differences for each shampoo we perform a t test. The value for