Tentative Quantitative Research Question

**Part 1**

In order to ensure that this assignment which covers both part I and II of activity 7 is effectively completed the need to work with a tentative qualitative research question is inevitable. Therefore, the proposed tentative qualitative research question for this activity is: How does the use of whiteboards in high school classrooms influence students’ performance?

**Question one**

The importance of validity in quantitative research has been long accepted, but in qualitative research, the acceptance has been marked by more contentious discussions. Therefore, at present both internal and external validity play a significant role by acting as a methodological criterion for assessing the quality of practice oriented research (Bleijenbergh *et al.,* 2011). Comparatively, both internal and external validity are essential in determining whether a research is well designed or not and ensures that the obtained results are appropriate for generalization to the particular population of interest (Jackson, 2012).

In contrast, i**nternal validity is referred **to** ****the ability of a research design towards providing an adequate hypothesis testing meaning that it has the **ability to ascertain the explanation for results being tested and rule out all plausible explanations (Onwuegbuzie & Johnson, 2006). On the other hand, e**xternal validity is referred **to** ****the ability of a research design towards providing results that are likely to be generalized to other populations or situations**. Further contrast show that internal validity is often used for the determination of the validity of causal conclusions or causal reasoning as well as the measurement procedure validity where the measured effect must be purely as a result of the independent variable and not any other variables (Schillewaert *et al.,* 1998). In contrast, external validity of the research results is used to determine whether inferences concerning a specific research’s cause and effect relations can be generalized to other populations or settings (Schreuder *et al.,* 2001).

There are many research questions for which external validity is a primary concern, especially those concerned with general issues within the society or particular segments of the society. For instance, a study on consumer behavior will tend to pose concerns depending on the sample population used and the populations or settings where the results need to be generalized (Winer, 1999). Examples of the research questions include: (1) what are consumer behavior among self-employed persons towards leisure spending? (2) Which factors that influence student performance in a mixed classroom? Furthermore, there are also numerous research questions, for which internal validity is a primary concern, particularly those concerning experimental or controlled studies. In these research questions, the effect being measured or quantified must only be caused by the independent variable. Examples of the research questions include: (1) how does purchasing power influence consumer behavior among University students in the United States? (2) How does gender influence performance of high school students in the United States?

Moreover, there are strategies that can be used by researchers in order to make strong claims about the applicability of their findings to a target population. First, the researchers should ensure that their studies consist of significantly large sample populations which are randomly selected (using probability sampling strategies) in order to make sure there is an appropriate representativeness of the target population (Jackson, 2012). Second, the researchers should adopt triangulation approach where mixed research designs, methods, tools, instruments and techniques are used in order to ensure that flaws of one are solved the other one as well as allowing comparison to be made (Onwuegbuzie & Johnson, 2006). This results to significant improvement of the research findings’ credulity, validity and reliability allowing the researchers to make strong claims about the applicability of their findings to a target population.

**Question two**

**The way in which a sample population is obtained and managed or handled plays a crucial role in determining the research design and results of a study. In comparison, both random selection and random assignment are used as sampling techniques in order the desired sample population is obtained from the target population **(Bleijenbergh *et al.,* 2011)**. In contrast, random** selection refers to how a sample population for a study is drawn from a target population while r**andom assignment refers to** how the sample population drawn from the target population is assigned to different groups or treatments in the study. It is possible to combine both random selection and random assignment in a single study; for instance, where a randomly selected sample population is further subdivided into smaller groups for additional treatment through random assignment (Schreuder *et al.,* 2001). Moreover, there are situations when only one of them can be used in a study. For instance, a sample of 100 can be nonrandomly selected from a population of 1000; let’s say the first 100 on the list, followed by random assignment this sample which is nonrandom to treatment versus control. Or, a sample of 100 can be randomly selected from a population of 1000 followed nonrandom assignment to treatment or control (Schillewaert *et al.,* 1998).

However, there are possible consequences of failing to do random selection or random assignment in particular situations. This is mainly because random selection is mostly concerned with sampling. Therefore, in most cases random selection is associated with the external validity or the ability of research results to be generalized (Winer, 1999). This means that the sample population should be randomly selected in order to ensure that the research participants are an appropriate representative of the target population. Failure to this, external validity will be very low or absent suggesting that the results can no longer be generalized (Schillewaert *et al.,* 1998). Moreover, random assignment is mostly concerned with the research design. For instance, when research participants are randomly assigned to treatments, by definition this becomes an experimental design (Schreuder *et al.,* 2001). Thus, in most cases random assignment is associated with internal validity because it ensures that similar conditions and treatments are provided for each particular group of participants (Winer, 1999). Failure to this, the experimental design becomes weak and the internal validity is eventually lowered (Bleijenbergh *et al.,* 2011).

**Question three**

When it comes to the determination of the statistically significant difference between measured values of two groups, the sample size becomes very crucial. This is due to the fact that statistical testing aims to uncover an existing significant difference between values measured from two groups (Pelham & Blanton, 2006). Simply, this involves a comparison of values from samples between one group and another (probably a control). In this process, sample size plays an important role because as the sample size increases the chances of finding a statistically significant difference also increases. As a result researchers always strive to select larger sample sizes, so that a specific mean difference uncovering chances are maximized, which also tend to be statistically significant. The reason why larger sample sizes increase the chances of achieving statistical significance difference is due to the fact that they are a more reliable reflection of the population mean (Trochim, 2009). Therefore, it is always recommended to ensure that the selected sample population is directly proportional to the target population which is determined using existing statistical procedures, but the larger the sample sizes the better (Pelham & Blanton, 2006).

**Question four**

Collection of information by researchers adopts a wide range of methods, ranging from surveys commonly used in the social sciences through to experimental designs commonly used in the physical sciences. However, for the collected information or data to be valid and reliable, the sampling method should be properly designed and executed in order to ensure that sampling errors are significantly reduced. Two sampling methods exist such as probability sampling and non-probability sampling. Comparatively, both probability sampling and non-probability sampling are concerned with selection of the sample population (Trochim, 2009). In contrast, probability sampling occurs when the researcher know the probability for the inclusion of each and every member of the population into the sample population while in non-probability sampling the researcher can not specify the probability for the inclusion of any given member of the population into the sample population (Pelham & Blanton, 2006).

However, both probability sampling and non-probability sampling have different advantages and disadvantages. For instance, probability sampling has various advantages such as: (1) it is possible to make valid generalization of the results from the samples to the population; (2) in probability sampling there is less bias and the samples are usually more representative (i.e. external validity is always higher); and (3) with probability sampling it is possible to estimate the accuracy of the sample which means the level of confidence can be estimated (Trochim, 2009). The disadvantage of probability sampling is that it is often time consuming and tedious (Trochim, 2009).

On the other hand, non-probability sampling is not as popular as probability sampling despite their major advantage of being convenient and inexpensive (Trochim, 2009). This is due to its disadvantages such as: (1) biasness where some individuals have higher chances of being selected than others while others do not have any chance of being selected; (2) since the members of the population having higher chances for inclusion in the sample are not known, then it is not known whether or not the selected sample is an accurate representative of the population; and (3) with non-probability sampling the results from samples cannot be generalized to the population. In fact, if there is any population that exist it is not possible to determine which a non-probability sample represents (Pelham & Blanton, 2006).

**Part 2**

This part presents calculations concerning power analyses carried out using the G*Power Software.

**Question one**

*Sample size:* 66

*Alpha:* 0.05

*Beta:* 0.15

*Argument:* Considering that half of the sample size is approximately 32 while the alpha and beta are 0.05 and 0.15 respectively. Therefore, if the above factors are considered it is undoubtedly worthy to do the study with the smaller sample size since the resulting values for alpha and beta are satisfactory since the effect size is small.

**Question two**

*Sample size:* 177

*Alpha:* 0.17

*Beta:* 0.30

*Rationale selected beta/alpha ratio:* The selected beta/alpha ratio which is 4 was determined by dividing the provided beta value and alpha value such as 0.2 divided by 0.05 which gives us 4.

*Argument:* Considering that this study involves three groups and the resulting alpha and beta values of 0.17 and 0.30 respectively, it is worthy to do the study with the smaller sample size of 87 which imply that each group shall consist of 29 individuals.

**Question three**

The research question outlined at the beginning of this activity can be addressed using two research designs such as simple random sampling and random stratified sampling. The former involves selecting research participants in a random manner, but following a specific preset criterion while the latter involves clustering of the randomly selected research participants into strata on basis of particular characteristics.

*Simple random sampling*

The factors considered in the calculation of the estimated sample size are:

- Two-tailed t-test with two independent groups of equal size
- Medium effect size
- Alpha = 0.05
- Beta = 0.8

The total sample size is 84 meaning each group consist of 42 individuals.

The reason why a medium effect size was selected is due to the fact that the confidence level is 2-tailed and the sample population is divided into two groups. Also the identified alpha and beta values were to ensure sufficient sample was selected for valid and reliable findings and conclusions.

*Random stratified sampling *

The factors considered in the calculation of the estimated sample size are:

- One-tailed t-test with two independent groups of equal size
- Small effect size
- Alpha = 0.05
- Beta = 0.3

The total sample size is 128 meaning each group consist of 64 individuals.

The reason why a small effect size was chosen is mainly because the influence is anticipated to be relatively small in the selected research design where the samples size is grouped into strata consisting of people with particular characteristics. However, the identified alpha and beta values were to ensure sufficient sample was selected for valid and reliable findings and conclusions.

**References**

Bleijenbergh, I., Korzilius, H., & Verschuren, P. (2011). Methodological criteria for the internal validity and utility of practice oriented research. *Qual Quant,* 45(3), 145–156.

Jackson, C. (2012). Internal and External Validity in Experimental Games: A Social Reality Check. *European Journal of Development Research**,* 24(3), 71–88.

Onwuegbuzie, A.J., & Johnson, R.B. (2006). The Validity Issue in Mixed Research. *Research in the Schools,* 13(1), 48-63.

Pelham, B.W., & Blanton, H. (2006). *Conducting Research in Psychology: Measuring the Weight of Smoke, 3 ^{rd} Edition.* Washington, DC: Wadsworth Publishing.

Schillewaert, N., Langerak, F., & Duhamel, T. (1998). Non-probability sampling for WWW surveys: A comparison of methods. *Journal of the Market Research Society,* 40(4), 307-322.

Schreuder, H.T., Gregoire, T.G., & Weyer, J.P. (2001). For what applications can probability and non-probability sampling be used? *Environmental Monitoring and Assessment, *66(2), 281–291.

Trochim, W.M.K. (2009). Design: *Research Methods Knowledge Base, 2 ^{nd} Edition.* Boston, MA: Sage Publications.

Winer, R.S. (1999).Experimentation in the 21st century: The importance of external validity. *Academy of Marketing Science Journal,* 27(3), 349-358.

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