DH 211 Research Statistics Assignment Ms

DH 211
Research Statistics Assignment

Ms. Eva Dzionek

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Farnoush Pourhadi
Emmanuella Joseph
Nazila Amozgar-Shahidi
Kristan James
Yvette Paul

The Canadian Academy of Dental Health and Community Sciences
November 30/2018

A dental hygienist, working in Simcoe County, is interested in studying the incidence of visible fluorosis in 12–14 year old school children in the region whose families use well water. The County School Board lists 789 children of this age range living in rural areas which are not served by community water supply. The Board is also willing to allow visual examinations of the children to be carried out on school premises. A sample of 20–25% of a population is considered adequate to represent the population.
Describe, briefly, the steps the researcher should take to obtain samples for this study using each of the recognized sampling strategies.
Identify which sampling strategy you would implement and why

A) Type of Samples:

The samples are selected independently and randomly, with no bias from the statistical population. This method of sample selection allows the statistical population with equal probability to be chosen at random (Beatty 2017).

Example for Random Sampling:
The population being sampled are children between age 12-14 year old.
Listing the population = 789 of Simcoe County children
The chosen sample size ranges is between 20 – 25% of the 789 Children = 197 Children
Assigning numbers to cases = A group of 197 Children will be randomly selected.

A sampling method that divides the large population into a sample size population by way of interval sampling. This interval sample is based on the numbers, values or list of items at fixed periodic intervals (Beatty 2017).

Example for Systematic Sampling:
Assigning a number to every element in your population = 1 – 789 Children
Decide on how large your sample size needs to be = 20-25% of 789 Children = 197 Children, then dividing the total population from the sample size = (789÷197= 4)
(4) will be the “nth” sampling number = every 4th person will be chosen from the sample size of 197 students.

Involves participants based on their availability. This type of sample is used when the total population is not attainable for the random sample selection (Beatty 2017).

Example for Convenience Sampling:
Selecting only the children of the Simcoe County will be convenient since the dental hygienist works in Simcoe County and The County School Board is allowing screening of the children to be done on the school premises. Using the County School Board List of 789 Children, from which a sample size of only 20-25% = 197 children are selected for the research.

Judgmental or purposive:
It is based on the researcher’s judgement of which individuals and/or specific groups that they are willing to do research on. The pros are that it is less time consuming because it already targets a specific group, and the cons would be that the research will be bias and not random (Beatty 2017).

Example of Judgmental or purposive:
The dental hygienist decides on choosing only children within the age category of 12-14 years old, and only the ones that are on the Simcoe County School Board list of children = 789 children. Than subdividing that selection down to 20-25% = (789÷25%)= 197 school children, selected area where the incidence of visible fluorosis exists.

Stratified random:
Involves a percentage of a bigger population that is subdivided into smaller groups within a homogeneous population (Strata). The grouping of stratified sampling is organized by shared characteristics or attributes such as gender, ethnicity, location, and age (Beatty 2017).

Example of Stratified random:
The dental hygienist will be sampling the total population of 789 children and subsampling only 20-25% of those children = 197 children sample size that are being used to see how many have visible fluorosis. Subdividing the children into different age category groups from 12-14 years old whose family use well water. By Subdividing the children into age category groups, the age range who developed the most visible fluorosis can be distinctly identified.
B) Identify which sampling strategy you would implement and why.
The sampling strategy that we would implement is the stratified random sample strategy. The reasoning behind this is that the stratified random, is the only type of sample that takes into consideration the total percentage of the population and dividing them into subdivisions of homogeneous; age; and location (Beatty 2017). The total population of 789 children from the age of 12-14 years old, of which only 20-25% are subdivided into being sampled to see how many have visible fluorosis .


The numbers listed below represent the scores received by 18 dental hygiene students on a mid-term oral disease test.

Answer the following, show all calculations where applicable.
Which score represents the following: the mode; the median? Calculate the following values: the range,the mean, the variance, the standard deviation.
Display the scores as a grouped, cumulative relative frequency distribution.
Summarize and briefly discuss the findings

Frequency Table








Midterm scores arranged from lowest to the highest:
46, 56, 62, 63, 66, 73, 73, 75, 79, 79, 79, 83, 84, 86, 87, 88, 91, 96

“Mode: the score or value that occurs most frequently in a set of data; only measure of central tendency that can be used with nominal data” (Beatty 2017, p. 318).

When the midterm scores are placed in order from lowest to highest, the number that occurs the most is 79.

46, 56, 62, 63, 66, 73, 73, 75, 79, 79, 79, 83, 84, 86, 87, 88, 91, 96

“Median: the exact middle score or value in a distribution of scores” (Beatty 2017, p. 318).

When the midterm scores have been placed in order from lowest to highest, the middle value is 79.

46, 56, 62, 63, 66, 73, 73, 75, 79, 79, 79, 83, 84, 86, 87, 88, 91, 96

“Mean: arithmetic average of a group of scores; the sum of the numbers divided by the quantity of scores” (Beatty 2017, p. 318).

Once all the midterm scores have been added up, the value is 1,366. The sum then must be divided by the number of students, which would be 18 students. The mean works out to be 75.8.


“Range: a crude measurement of dispersion that provides an expression of the difference between the highest and lowest values in a distribution of scores” (Beatty 2017, p. 319).

To calculate the range, the lowest value, 46, is subtracted from the highest value, 96. The difference equals 50.


“Variance: a numerical value that demonstrates how widely individual scores in a group vary around the mean; used with interval and ratio data” (Beatty 2017, p. 321).

To calculate the value of the variance, firstly, the mean value, 75.8, is subtracted from each students’ individual score. Secondly, that amount is then squared. Thirdly, that value is divided by the total number of scores, in this case, 18. For the purpose of calculations, the mean value of 75.8 will be rounded to 76.

(76-46) = 302 = 900
(76-56) = 202 = 400
(76-62) = 142 = 196
(76-63) = 132 = 169
(76-66) = 102 = 100
(76-73) = 32 = 18
(76-73) = 32 = 18
(76-75) = 12 = 1
(76-79) = -32 = 9
(76-79) = -32 = 9
(76-79) = -32 = 9
(76-83) = -72 = 49
(76-84) = -82 = 64
(76-86) = -102 = 100
(76-87) = -112 = 121
(76-88) = -122 = 144
(76-91) = -152 = 225
(76-96) = -202 = 400
All above summed = 2,923 “positive square root of the variance” (Beatty 2017, p. 320).

To calculate the standard deviation, the value of the variance will be square rooted.

?162.4= 12.7. Therefore, 12.7 is the value of the standard deviance.

Above summed divided by the total number of scores 2,923÷18=162.4

162.4 is the value of the variance.

“Standard Deviation: a numerical value that demonstrates how widely individual scores in a group vary around the mean; used with interval and ratio data; computed as the positive square root of the variance.” (Beatty 2017, p. 320)


In summary, we were tasked with finding the mean, median, mode, range, variance, and standard deviation pertaining to the results of 18 dental hygiene students’ on their oral disease test. The mean is the sum of all the scores and divided by the amount of scores. The value of the mean is 75.8. The median is the exact middle score, which is 79. The mode is the score that appears most frequently, which is also 79. The range is the difference between the lowest value and the highest, which worked out to be 50. The variance demonstrates how widely the scores vary around the mean. The value for the variance is 162.4. Lastly, standard deviation is a number used to demonstrate how spread out the values are from the mean, which is the average. The standard deviation is 12.7. It is a low value, which indicates that the majority of the test scores are close to the average. According to the scores graphed above, a majority of the students achieved a grade between 71 and 80 percent. In conclusion, it is important to be able to calculate such data because as a dental professional, or an instructor, it is valuable to know where your clients, and students are in order to help them succeed (Beatty, 2017).


Beatty CF. Community oral health practice for the dental hygienist. 4th ed. St. Louis, MO: Elsevier Saunders; 2017:188, 192-199, 318-321