Questions on Introduction to Quantitative Measurements

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Introduction to Quantitative Measurement Unit 1 Written Assignment UNIVERSITY OF THE PEOPLE HS 4510-01 Biostatistics AY-2024-T2 Instructor: Adaugo Eziyi Date: 19/11/2023

1. Number of past road accidents is a ratio variable, because it has a meaningful zero point and can be compared using ratios. For example, a person who had 4 accidents has twice as many accidents as a person who had 2. This variable is also discrete, because it can only take integer values. History of past road accident is a nominal variable, because it is a categorical variable that does not have any inherent order. For example, whether a person had a head-on collision, a rear-end collision, or a side-impact collision does not imply any ranking. This variable is also discrete, because it can only take a finite number of values. Heartbeats per minute is a ratio variable, because it has a meaningful zero point and can be compared using ratios. For example, a person who has 80 beats per minute has twice as many beats as a person who has 40. This variable is also continuous, because it can take any value within a range. Time taken to complete a race is a ratio variable, because it has a meaningful zero point and can be compared using ratios. For example, a person who took 10 minutes to complete a race took twice as long as a person who took 5 minutes. This variable is also continuous, because it can take any value within a range. Race is a nominal variable, because it is a categorical variable that does not have any inherent order. For example, whether a person is Asian, Black, White, or Hispanic does not imply any ranking. This variable is also discrete, because it can only take a finite number of values.

ABO blood type is a nominal variable, because it is a categorical variable that does not have any inherent order. For example, whether a person has type A, B, AB, or O blood does not imply any ranking. This variable is also discrete, because it can only take a finite number of values. Injury severity score that takes values from 1 to 5, with 1 being “very minor”, 2 “minor”, 3 “moderate”, 4 “serious”, 5 “very serious” is an ordinal variable, because it is a categorical variable that has an inherent order. For example, an injury with score 5 is more severe than an injury with score 4. This variable is also discrete, because it can only take integer values. 2. This scenario's incidence and prevalence numbers suggest that women are more likely to contract and recover from the disease. The incidence rate is the number of new cases of an illness in a population over time, while the prevalence rate is the percentage of persons with the disease. If women have a greater incidence rate than men, more women are contracting the disease. However, if prevalence rates reveal no sex differences, women and men have equal disease rates. Women may be more likely to survive or recover from the condition than men, or vice versa. It could also mean migration, misdiagnosis, or underreporting alter incidence and prevalence rates. 3. To calculate the given expression, we need to multiply each element of X, Y, and Z according to their corresponding positions, and then square the result of Z. Here is a step-by-step solution:

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2 √ [Σ Xi Yi Zi2] = 2 √ [(1 * 0.25 * 2)2 + (-2 * -0.5 * 3)2 + (4 * 8 * 6)2 + (-2 * 2 * 3)2 + (0 * 2 * 1)2 + (1 * 5 * 1)2] = 2 √ [42 + 182 + 11522 + (-122) + (02) + (52)] = 2 √ [16 + 324 + 132496 + 144 + 0 + 25] = 2 √ [133005] = 730.28 4. Age groups | Number of participants | Proportion of female | Relative frequency of participants 15 years or younger | 10 | 0.4 | 0.2 16-25 years | 25 | 0.6 | 0.5 26-30 years | 10 | 1.0 | 0.2 31 years or older | 2 | 1.0 | 0.04 - Are the age groups mutually exclusive? Yes, the age groups are mutually exclusive because each participant belongs to only one age group and there is no overlap between the groups. - Based on the number of participants, can you argue for or against this sample being representative of the age groups in city A? No, based on the number of participants, we cannot argue for or against this sample being representative of the age groups in city A

because we do not know the population size and distribution of city A. We would need to compare the sample proportions with the population proportions to determine if the sample is representative or not. - How many males and females were included in the study? There were 19 males and 28 females included in the study. We can find this by multiplying the number of participants by the proportion of female for each age group and then adding up the results for females and subtracting them from the total number of participants for males. - Calculate the relative frequencies in the first right column. The relative frequencies are calculated by dividing the number of participants in each age group by the total number of participants in the sample. For example, for the first age group, the relative frequency is 10/50 = 0.2. The relative frequencies are shown in the table above. - The information displayed in the above table relates to which statistical paradigm: descriptive or inferential? Explain your answer. The information displayed in the above table relates to descriptive statistics because it summarizes and displays the data collected from the sample using measures such as frequency, proportion, and percentage. Descriptive statistics do not make any conclusions or predictions about the population based on the sample data, unlike inferential statistics (Illowsky et al, 2022). References: Illowsky, B., Dean, S., Birmajer, D., Blount, B., Boyd, S., Einsohn, M., Helmreich, J., Kenyon, L., Lee, S., & Taub, J. (2022). Introductory statistics. openstax. https://openstax.org/details/books/introductory-statistics