Lecture 7: Measurements and probability The Islamic University of Gaza- Higher Studies Deanery Research Methodology (MMCD 6304) Lecture 7: Measurements and probability Mohammed Alhanjouri

Measurements and probability The term ‘measurement’ is mainly used to quantify quantitative questions. I prefer to use the terms ‘evaluation’ or ‘assessment’ to process exploratory questions.

A. Level of measurement In order to be able to select the appropriate method of analysis, you need to understand the level of measurement. For each type of measurement, there is/are an appropriate method/s that can be applied and not others. Measurement is a procedure in which a researcher assigns numerals (numbers or other symbols) to empirical properties (variables) according to rules. Four principle levels of measurement, namely, nominal, ordinal, interval and ratio. Your primary data collection should belong to one or more of these levels.

1. Nominal scale Nominal numbering implies belonging to a classification or having a particular property and a label. It does not imply any idea of rank or priority. Nominal numbering is also conventional integers, that is positive and whole numbers Example:

2. Ordinal scale This is a ranking or a rating data which normally uses integers in ascending or descending order. Example:

Ordinal scale (cont.) Example: In this example the score of 9 was given the first rank. As three people share the score of 10, you need to share the ranking, such as: (2+3+4) / 3 = 9/3 = 3 For subject one and four this means the rank 5 and 6 are shared, i.e.: (5+6) / 2 = 11/2 = 5.5

3. Interval scale 4. Ratio scale The numbering system in the ordinal and nominal measurement is purely an arbitrary label for identifying each type of person. If you have a set of observations or data where the distance between each observation is constant, then this type of measurement is called an interval level of measurement. Often used examples are minutes, kilograms, number of words recalled in a memory test or percentage marks in the exam. The interval between 20 to 30 minutes is the same as 50 to 60 minutes. 4. Ratio scale The ratio scale is similar to the interval scale except it involves the kind of numerical scale which has a natural zero such as age, salary, time and distance. However, you do not need to bother about the difference between interval and ratio scales. For the level of statistics described in this book, both measurements are treated in exactly the same way.

B. Probability statement The subject of probability is an important term to understand when you start to analyze your results. We use the word ‘probably’ almost everyday to express our views on certain things. Consider the following statements: It will probably rain next week (historical records) 5, 10, 20, 50 % and so on I will most probably visit my friend tomorrow (based on your experience) 80, 90, 95 % I will definitely pass my math exam (historical records) 100% The second statement may be based on your experience, but the first and third statements are based on historical records. The term ‘probability’ can, therefore, be defined as the percentage that an event occurs in a number of times.

The term ‘probability’ can, therefore, be defined as the percentage that an event occurs in a number of times. In observational or experimental studies, if 1000 tosses of a coin result in 529 heads, the relative frequency of heads is 529/1000= 0.529. If another 1000 tosses result in 493 heads, the relative frequency in the total of 2000 tosses is (529 + 493)/2000= 0.511. According to the statistical definitions, by continuing in this manner we should ultimately get closer and closer to a number which we call the probability of a head in a single toss of the coin. From results so far presented this should be 0.5 to one significant figure. To obtain more significant figures, further observations/experiments must be made.