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Field (2013) states that both quantitative and qualitative methods are complimentary at best, none competing approaches to solving the world’s problems. Although these methods are quite different from each other. Simply put, quantitative methods are utilized when the research contains variables that are numerical, and qualitative methods are utilized when the research contains variables that are based on language (Field, 2013). Thus, central to quantitative research and methods is to understand the numerical, ordinal, or categorical dataset and what the data represents. This can be done through either descriptive statistics, where the researcher uses statistics to help describe a data set, or it can be done through inferential statistics, where conclusions can be drawn about the data set (Miller, n.d.).

Field (2013) and Schumacker (2014), defined central tendency as an all-encompassing term to help describe the “center of a frequency distribution” through the commonly used measures mean, median, and mode. Outliers, missing values, and multiplication of a constant, and adding a constant are factors that affect the central tendency (Schumacker, 2014). Besides just looking at one central tendency measure, researchers can also analyze the mean and median together to understand how skewed the data is and in which direction. Heavily skewed distributions would heavily increase the distance between these two values, and if the mean less than the median the distribution is skewed negatively (Field, 2013). To understand the distribution, better other measures like variance and standard deviations could be used.

Variance and standard deviations are considered as measures of dispersion, where the variance is considered as measures of average dispersion (Field, 2013; Schumacker, 2014). Variance is a numerical value that describes how the observed data values are spread across the data distribution and how they differ from the mean on average (Huck, 2011; Field, 2013; Schumacker, 2014). The smaller the variance indicates that the observed data values are close to the mean and vice versa (Field, 2013).

Rarely is every member of the population studied, and instead a sample from that population is randomly taken to represent that population for analysis in quantitative research (Gall, Gall, & Borg 2006). At the end of the day, the insights gained from this type of research should be impersonal, objective, and generalizable. To generalize the results of the research the insights gained from a sample of data needs to use the correct mathematical procedures for using probabilities and information, statistical inference (Gall et al., 2006). Gall et al. (2006), stated that statistical inference is what dictates the order of procedures, for instance, a hypothesis and a null hypothesis must be defined before a statistical significance level, which also has to be defined before calculating a z or t statistic value. Essentially, a statistical inference allows for quantitative researchers to make inferences about a population. A population, where researchers must remember where that data was generated and collected from during quantitative research process.

Most flaws in research methodology exist because the validity and reliability weren’t established (Gall et al., 2006). Thus, it is important to ensure a valid and reliable assessment instrument. So, in using any existing survey as an assessment instrument, one should report the instrument’s: development, items, scales, reports on reliability, and reports on validity through past uses (Creswell, 2014; Joyner, 2012). Permission must be secured for using any instrument and placed in the appendix (Joyner, 2012). The validity of the assessment instrument is key to drawing meaningful and useful statistical inferences (Creswell, 2014).

Through sampling of a population and using a valid and reliable survey instrument for assessment, attitudes and opinions about a population could be correctly inferred from the sample (Creswell, 2014). Sometimes, a survey instrument doesn’t fit those in the target group. Thus it would not produce valid nor reliable inferences for the targeted population. One must select a targeted population and determine the size of that stratified population (Creswell, 2014).

Parametric statistics, are inferential and based on random sampling from a distinct population, and that the sample data is making strict inferences about the population’s parameters, thus tests like t-tests, chi-square, f-tests (ANOVA) can be used (Huck, 2011; Schumacker, 2014). Nonparametric statistics, “assumption-free tests”, is used for tests that are using ranked data like Mann-Whitney U-test, Wilcoxon Signed-Rank test, Kruskal-Wallis H-test, and chi-square (Field, 2013; Huck, 2011).

First, there is a need to define the types of data. Continuous data is interval/ratio data, and categorical data is nominal/ordinal data. Modified from Schumacker (2014) with data added from Huck (2011):

Statistic | Dependent Variable | Independent Variable |

Analysis of Variance (ANOVA) | ||

One way | Continuous | Categorical |

t-Tests | ||

Single Sample | Continuous | |

Independent groups | Continuous | Categorical |

Dependent (paired groups) | Continuous | Categorical |

Chi-square | Categorical | Categorical |

Mann-Whitney U-test | Ordinal | Ordinal |

Wilcoxon | Ordinal | Ordinal |

Kruskal-Wallis H-test | Ordinal | Ordinal |

So, meaningful results get reported and their statistical significance, confidence intervals and effect sizes (Creswell, 2014). If the results from a statistical test have a low probability of occurring by chance (5% or 1% or less) then the statistical test is considered significant (Creswell, 2014; Field, 2014; Huck, 2011Statistical significance test can have the same effect yet result in different values (Field, 2014). Statistical significance on large samples sizes can be affected by small differences and can show up as significant, while in smaller samples large differences may be deemed insignificant (Field, 2014). Statistically significant results allow the researcher to reject a null hypothesis but do not test the importance of the observations made (Huck, 2011). Huck (2011) stated two main factors that could influence whether or not a result is statistically significant is the quality of the research question and research design.

Huck (2011) suggested that after statistical significance is calculated and the research can either reject or fail to reject a null hypothesis, effect size analysis should be conducted. The effect size allows researchers to measure objectively the magnitude or practical significance of the research findings through looking at the differential impact of the variables (Huck, 2011; Field, 2014). Field (2014), defines one way of measuring the effect size is through Cohen’s d: d = (Avg(x1) – Avg(x2))/(standard deviation). If d = 0.2 there is a small effect, d = 0.5 there is a moderate effect, and d = 0.8 or more there is a large effect (Field, 2014; Huck, 2011). Thus, this could be the reason why a statistical test could yield a statistically significant value, but further analysis with effect size could show that those statistically significant results do not explain much of what is happening in the total relationship.

In regression analysis, it should be possible to predict the dependent variable based on the independent variables, depending on two factors: (1) that the productivity assessment tool is valid and reliable (Creswell, 2014) and (2) we have a large enough sample size to conduct our analysis and be able to draw statistical inference of the population based on the sample data which has been collected (Huck, 2011). Assuming these two conditions are met, then regression analysis could be made on the data to create a prediction formula. Regression formulas are useful for summarizing the relationship between the variables in question (Huck, 2011).

When modeling predict the dependent variable based upon the independent variable the regression model with the strongest correlation will be used as it is that regression formula that explains the variance between the variables the best. However, just because the regression formula can predict some or most of the variance between the variables, it will never imply causation (Field, 2013). Correlations help define the strength of the regression formula in defining the relationships between the variables, and can vary in value from -1 to +1. The closer the correlation coefficient is to -1 or +1; it informs the researcher that the regression formula is a good predictor of the variance between the variables. The closer the correlation coefficient is to zero, indicates that there is hardly any relationship between the variable (Field, 2013; Huck, 2011; Schumacker, 2014). It should never be forgotten that correlation doesn’t imply causation, but can help determine the percentage of the variances between the variables by the regression formula result, when the correlation value is squared (r2) (Field, 2013).

**References:**

- Creswell, J. W. (2014)
*Research design: Qualitative, quantitative and mixed method approaches*(4^{th}ed.). California, SAGE Publications, Inc. VitalBook file. - Field, A. (2013)
*Discovering Statistics Using IBM SPSS Statistics*(4^{th}ed.). UK: Sage Publications Ltd. VitalBook file. - Gall, M. D., Gall, J., & Borg W. (2006).
*Educational research: An introduction*(8^{th}ed.). Pearson Learning Solutions. VitalBook file. - Huck, S. W. (2011)
*Reading Statistics and Research (6*Pearson Learning Solutions. VitalBook file.^{th}ed.). - Joyner, R. L. (2012)
*Writing the Winning Thesis or Dissertation: A Step-by-Step Guide*(3^{rd}ed.). Corwin. VitalBook file. - Miller, R. (n.d.). Week 1: Central tendency [Video file]. Retrieved from http://breeze.careeredonline.com/p9fynztexn6/?launcher=false&fcsContent=true&pbMode=normal
- Schumacker, R. E. (2014)
*Learning statistics using R*. California, SAGE Publications, Inc, VitalBook file.

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