Statistics and Measurement

Statistics and Measurement

Introduction

You will discuss the basics of research design and how variables are measured. You will also focus on how various measures of central tendency and variability are used to describe a sample.

You may want to conduct a study investigating whether playing video games affects academic performance. You could ask participants in your study how many hours per day they spend playing video games and you could also ask them their grade point average (GPA). To answer this research question, you would need to use a correlational analysis to examine the relationship between the number of hours spent playing video games and GPA. A correlational analysis is an example of an inferential statistics test. However, you also want to describe the sample. You could also ask participants in the study about their age, sex, and ethnicity. You will notice, as you read the results of research in peer-reviewed psychology journals and news articles, that the data from individual participants are not mentioned; rather, you summarize the data from your sample using descriptive statistics. As the name suggests, descriptive statistics describe the data. For instance, you may summarize the data by stating that 15 men and 25 women participated in the study and that the mean age of the women was 19.5 years and the mean age of the men was 21.2. You will usually report the standard deviation, along with the mean. You could also report the number (or percentage) of people representing each ethnicity.

How you describe the data depends on the level of measurement. As mentioned in Gavin (2008), the four levels of measurement are nominal, ordinal, interval, and ratio. In the study described above, sex and ethnicity are nominal-level variables. Age and GPA are measured at the interval level and the number of hours spent playing video games is measured at the ratio level. 

Another important concept in statistics involves normal distributions. As discussed in Gavin's (2008) Chapter 4, when the sample size is greater than 30, the distribution of the data approximates what is called a normal distribution. This distribution is shaped like a bell and is symmetrical. In the case of a perfectly normal distribution, the mean, median, and mode would all be the same value.

In addition to looking at a distribution of raw scores, you can also convert individual scores to z-scores. To calculate a z-score, you subtract an individual’s score from the mean of the sample, and then divide it by the sample standard deviation:

The z-score can tell us how many standard deviations a particular score is above or below the mean. The distribution of z-scores is called the standard normal distribution (z-scores are also called standard scores). The distribution of z-scores has a mean of 0 and a standard deviation of 1. Because it is symmetrical, 50% of the scores are above the mean, and 50% are below the mean. 

Below is Figure 4.6 from Gavin (2008) which shows how data from an IQ test could be converted to z-scores. 

You are expected to apply the information from these resources when you prepare your assignments.

Reference(s)

· Gavin, H. (2008).  Understanding research methods and statistics in psychology. London: SAGE Publications Ltd. 

Assignment: Discuss Descriptive Statistics in Research

Statistics and Measurement

Introduction

You will discuss the basics of research design and how variables are measured. You will also focus on how various measures of central tendency and variability are used to describe a sample.

You may want to conduct a study investigating whether playing video games affects academic performance. You could ask participants in your study how many hours per day they spend playing video games and you could also ask them their grade point average (GPA). To answer this research question, you would need to use a correlational analysis to examine the relationship between the number of hours spent playing video games and GPA. A correlational analysis is an example of an inferential statistics test. However, you also want to describe the sample. You could also ask participants in the study about their age, sex, and ethnicity. You will notice, as you read the results of research in peer-reviewed psychology journals and news articles, that the data from individual participants are not mentioned; rather, you summarize the data from your sample using descriptive statistics. As the name suggests, descriptive statistics describe the data. For instance, you may summarize the data by stating that 15 men and 25 women participated in the study and that the mean age of the women was 19.5 years and the mean age of the men was 21.2. You will usually report the standard deviation, along with the mean. You could also report the number (or percentage) of people representing each ethnicity.

How you describe the data depends on the level of measurement. As mentioned in Gavin (2008), the four levels of measurement are nominal, ordinal, interval, and ratio. In the study described above, sex and ethnicity are nominal-level variables. Age and GPA are measured at the interval level and the number of hours spent playing video games is measured at the ratio level. 

Another important concept in statistics involves normal distributions. As discussed in Gavin's (2008) Chapter 4, when the sample size is greater than 30, the distribution of the data approximates what is called a normal distribution. This distribution is shaped like a bell and is symmetrical. In the case of a perfectly normal distribution, the mean, median, and mode would all be the same value.

In addition to looking at a distribution of raw scores, you can also convert individual scores to z-scores. To calculate a z-score, you subtract an individual’s score from the mean of the sample, and then divide it by the sample standard deviation:

The z-score can tell us how many standard deviations a particular score is above or below the mean. The distribution of z-scores is called the standard normal distribution (z-scores are also called standard scores). The distribution of z-scores has a mean of 0 and a standard deviation of 1. Because it is symmetrical, 50% of the scores are above the mean, and 50% are below the mean. 

Below is Figure 4.6 from Gavin (2008) which shows how data from an IQ test could be converted to z-scores. 

You are expected to apply the information from these resources when you prepare your assignments.

Reference(s)

· Gavin, H. (2008).  Understanding research methods and statistics in psychology. London: SAGE Publications Ltd. 

Assignment: Discuss Descriptive Statistics in Research