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Several statistical tests are available to a researcher for the analysis of data collected during research. Each test has different meaning and is better used to analyze various data and variables. Understanding these statistical methods of analyzing the data for psychological research is essential as it makes it easier for the researchers to present the correct results and findings of their research. This paper discusses the use of Z test, t-test for independent samples and t-test for dependent samples
Z-test
This statistical analysis is used for large samples where the standard deviation of the data is known. The z-test is used to test the relationship between samples (Freedman, Pisani, & Purves, 2007). A research question that can be used with a Z-test would be what is the impact of increased teacher’s autonomy in their subject area affect the teacher’s productivity? The dependent variable will be teacher’s productivity, and the independent variable will be autonomy.
T-test for independent samples is majorly used to test two independent samples to show whether the examples have a significant difference between them. To carry out this analysis, the dependent variable should be a continuous one while the independent variable should be categorical. The independent variable should be more than one (Freedman, Pisani, & Purves, 2007). An example of a research question will be to identify the change in the various demographical car buyers because of change in car prices.
T-test for dependent samples tests the changes or difference in mean between variables that are related to each other. In this test, the participants are represented in both groups under analysis (Freedman, Pisani, & Purves, 2007). In both cases, the dependent variable can be numerical, absolute, or continuous variables. An example of research would be to assess the change in perception of employees towards outsourcing before working in a virtual team and after participating in a virtual team.
#1
The Z test is best used when the sample size is larger than 30 and population standard deviation is known. Z tests is used to convert observed data into standardized scores. This shows the number of standard deviation units and which direction they are, away from the mean of a given raw score (Christensen, et al., 2013). For example, a psychologist wants to know whether children who have single parents play more video games than the national average. The independent variable time spent playing video games is and the dependent variable is children of single parents.
The independent samples t test is used when comparing the means of two separate groups. Data from the two groups can be placed side by side in columns. The means of each sample represent independent samples. These samples are not dependent on each other. The two sample scores are not influenced, or dependent on the scores of the other (Pace, 2008). For example, a psychologist wants to know whether reaction times for a control group and an experimental group. The independent variable is reaction time and the dependent variables are control and experimental groups.
The dependent samples t test compares means for observation pairs. Data can be entered in two columns named with appropriate labels. The means of the dependent samples are tested for the difference (Pace, 2008). These samples are dependent because they are related in some way. For example, a psychologist wants to know fast swimmers who swim well in prelims do well in finals, regardless of any experimental manipulation. The independent variable is prelims time and the dependent variable is finals time.
References
Christensen, L. B., Johnson, R. B., Turner, L. A. (07/2013). Research Methods, Design, and Analysis, 12th Edition. [Argosy University]. Retrieved from
https://digitalbookshelf.argosy.edu/#/books/9781323305720/
Pace, L. A. (2008). The Excel 2007 data and statistics cookbook. Anderson, S.C: TwoPaces LLC.
#2
· z test: Are children who participate in after-school extracurricular activities less likely to be involved in juvenile delinquency than children who are not?
· Variable: Juvenile delinquency
· t tests for independent samples: Do children who play video games have a higher IQ than children who do not?
· IQ scores for a control group and an experimental group
· Variable: IQ score
· t test for dependent samples– Measuring depression in patients before psychotherapy begins and assessing depression in the same individuals again when therapy is over. (pre-test and post-test).
· Variable being tested: Depression
· Both z tests and t tests are inferential statistics that allow you to compare two sample means to each other or one sample mean to a population mean or given mean. There are two rules that guide us as to which test to use; use a t test if the sample size is less than 30 AND/OR the population SD is unknown and use a z test if the sample size is larger than 30 AND/OR the population SD is known (Z Test and t Test). The dependent t test also known as the paired-sample t test is used to compare two means for situations in which every participant is in both samples (Nolan&Heinzen). On the other hand an independent sample t testis used to compare two means for situations which each participant is assigned to only one condition (Nolan& Heinzen).
References:
Nolan, S. A., & Heinzen, T. (n.d.). Paired/Dependent T- test. Retrieved February 3, 2018, from
https://rpubs.com/raquelsbf/t-tests
Z Test and t Test. (n.d.). Retrieved February 3, 2018, from
https://myclasses.argosy.edu/d2l/le/content/15839/viewContent/626179/View
3#
Psychological research questions can be analyzed by the use of different statistical test. However, for the purpose of this discussion three different statistical tests will be discussed. Research questions will be designed to utilize three statistical tests, including the z test, t test for independent samples, and t test for dependent samples.
Z test are often used to measure large samples, especially when the sample is more than 30. Also, when using a Z test, the research must already have knowledge of the standard deviation. If the researcher does not know the standard deviation, the research could elect to utilize a t test. When utilizing a t test, the sample size must contain less than 30. T-test for independent samples are used to measure sample proportions and not comparing it to a populations. Opposite of t-test for dependent samples, the samples measured are related in some way.
Chen, Wang, Wang, Ronkainen, and Huang (2016) argue that that an important aspect of athlete’s socializing has a lot to do with the coach’s style of coaching. Autonomy-supportive style and controlling style are the most common styles of coaching represented. Autonomy-supportive style involves the coach allowing the athletes to participate in their athletic process and respect their input (Chen et. al., 2016; Bartholomew, Ntoumanis, & Thogersen-Ntoumani, 2009). A controlling coaching style involves the coaches using an authoritarian and coercive communication, not considering the athletes opinion (Chen et. al., 2016). Chen et. al. (2016), hypothesized the affects of the coaching styles on the athletes prosocial behaviors. Utilizing the information provided be this initial study the first research question utilizing a z test is: Elite tennis athlete’s performance scores will be lower with a coach utilizing a controlling coaching style in comparison to the performance scores of other elite tennis athlete’s. The variables measured will be the performance of the sample group in comparison to the norm of the population. Utilizing the t-test for independent samples, the second research question is: The comparison of a small sample size of elite tennis players with a controlling style coach and another small sample size of elite tennis players with an autonomy-supportive style coach. The performance of each sample group will also be measured. Lastly, utilizing a t test for dependent samples, the third research question is: Elite tennis athlete performance declines will decline after obtaining a coach with a controlling style of coaching. In order to answer this research question the performance of the athlete will be measured prior to the athlete’s having the coach and after the athlete’s have worked with the coach.
Reference
Bartholomew, K. J., Ntoumanis, N. & Thogersen-Ntoumani, C. (2009). A review of controlling motivational strategies from a self-determination theory perspective: implications for sports coaches. International Review of Sport and Exercise Psychology, 2, 215-233.
Chen, Z., Wang, D., Wang, K., Ronkaine, N.J., & Huang, T. (2016). Effects of coaching style on prosocial and antisocial behavior among Chinese athletes. Social Behavior and Personality, 44(11), 1889-1900.
