Assignment 2 – Statistical Concepts & Research Methods

Ty’jah M. Hill

Department of Counseling, Nova Southeastern University

PYCL 0507: Research and Evaluation

Dr. Elda Veloso

February 25, 2022

Scales of Measurement

The nominal measurement scale determines the identity of the data (Renze, 2021). However, there is no numerical value (Renze, 2021). The data can be arranged but not multiplied, divided, added, or removed. It’s also unattainable to quantify the distinction between data points. For example, nominal data includes names, which means that the difference is that there is no natural ordering of nominal values (Renze, 2021). However, you can put it in alphabetic order, but it doesn’t change the actual data order. Nominal data can determine the pattern.

The ordinal scale describes data set in a specific order. The critical difference is that ordinal values have a natural ordering (Renze, 2021). It can also test two ordinal values for their order and specify the median. Interval data is a type of numerical data. It is the measured quantity of things. Interval data allow for a degree of distinction between two values.

The zero point on an interval scale by chance; doesn’t represent a minimum natural quantity of what is in that measure (Renze, 2021). As well, it determined both the mode and the median. We can also add or subtract interval data. What’s more, we can also choose the arithmetic mean.The ratio scale adds, subtract, divide, and multiply data. Ratio scales are distinguished from interval scales by the presence of a true zero. The zero denotes the absence of a value point in the data (Renze, 2021). The properties of all four measurement scales contain scale measurement scales.

Measures of Central Tendency

Measures of central tendency are the middle, or the average, of a data set (Bhandari, 2022). The three most common measurements of central tendency are the mode, median, and mean (Bhandari, 2022). The most recurring value is the mode of the cluster. It tells the sample’s most popular choice or most common characteristics. A data set can often have no mode, one mode, or more than one mode, depending on how many different values duplicate most frequently(Bhandari, 2022).

To find the mode, order the values from low to high. Then, Identify the value or values that occur most often. The median is the value in the middle of a data set ordered. It’s a measurement of the central tendency that splits the lowest 50% from the highest 50% of values (Bhandari, 2022). The median is the most useful measure of central tendency for skewed distributions or outliers (Bhandari, 2022). The mean of a dataset is the sum of all values divided by the total number of values.

Measures of Variability

Variability refers to the distance between data points and the distribution’s center (Bhandari, 2022). The range describes the data spread from the lowest to the highest value. Subtract the lower value from the highest value in the data set. The standard deviation measures the dataset’s average variability (Bhandari, 2022).

The average of squared deviations from the mean is the variance.

The distance between a score and the mean is its deviation from the mean. The variance is equal to the square of the standard deviation. Variance units are far more significant than those used to represent a standard data set value.

Frequencies

Table 1

Table 2

Graph 1

Table 3

Table 4

Graph 2

Table 5

Descriptive Statistics

N Minimum Maximum Mean Std. Deviation Variance Skewness

Statistic Statistic Statistic Statistic Statistic Statistic Statistic Std. Error

Grades 7 36.00 98.00 74.5714 23.56450 555.286 -.908 .794

Valid N (listwise) 7 Table 6

Descriptive Statistics

N Minimum Maximum Mean Std. Deviation Variance Skewness

Statistic Statistic Statistic Statistic Statistic Statistic Statistic Std. Error

Hours slept 7 4 10 6.96 2.128 4.530 -.502 .794

Valid N (listwise) 7 References

Bhandari, P. (2022, January 5). Central tendency: Mean, median and Mode. Scribbr. Retrieved February 26, 2022, from https://www.scribbr.com/statistics/central-tendency/Renze, M. (2021, June 28). Nominal, ordinal, interval, and ratio data. Matthewrenze. Retrieved February 26, 2022, from https://matthewrenze.com/articles/the-four-subtypes-of-data-in-data-science/

SPSS software. IBM. (n.d.). Retrieved February 27, 2022, from https://www.ibm.com/analytics/spss-statistics-software