MFT 8304 Quantitative Design, Statistics, and Analysis

Factorial ANOVA Report Findings

"Tests of Between-Subjects Effects" There was a statistically significant three-way interaction between gender, risk and drug, F(2, 60) = 7.406, p = .001.

Citations

(Field, 2013) (Creswell, 2014)

1. Initial Observation and research question

Having made casual observation about the world, collect datat to see whethere this observation is true. To do this, define one or more variable to measure.

Independence of Observational Error From Potential Confounding Effects

In statistics, a confounder is a variable that influences both the dependent variable and independent variable causing a spurious association.

Examples of Statistical Assumptions

Independence of observations from each other Independence of observational error from potential confounding effects Exact or approximate normality of observations Linear regression.

Linear Regression

Linear regression is a linear approach for modelling the relationship between a scalar dependent variable y and one or more explanatory variables (or independent variables) denoted X.

Independence of Observations From Each Other

Two events are independence, statistically independent, if the occurrence of one does not affect the probability of occurrence of the other. Two random variables are independent if the realization of one does not affect the probability distribution of the other.

Multiple Regression

You could use multiple regression to understand whether exam performance can be predicted based on revision time, test anxiety, lecture attendance and gender. Alternately, you could use multiple regression to understand whether daily cigarette consumption can be predicted based on smoking duration, age when started smoking, smoker type, income and gender. You might want to know how much of the variation in exam performance can be explained by revision time, test anxiety, lecture attendance and gender "as a whole", but also the "relative contribution" of each independent variable in explaining the variance.

Repeated Measures ANOVA SPSS brief steps

analyze, general linear model, repeated measures. Name your independent variable. Add number of times it is measured. Name dependent variable. "Define" - Transfer variables, "Plots" - Transfer independent variable (such as time) into horizontal axis. "continue"... "Options" - Transfer independent variable to "Display Means For" Tick: compare main effects, and select "Bonferroni" from drop down menu in "Confidence Interval Adjustment" Tick: descriptive statistics, estimates of effect size,

Factorial ANOVA SPSS

Analyze - general linear model - univariate input "Dependent Variable" Input "Fixed Factor(s)" = independent variables "options" - transfer the (3?4?) way interaction from the "Factors and Factor Interactions" box to the "Display Means For" box. Select "Descriptive Statistics" and "Homogeneity Test". "continue" "Ok"

Multiple Regression SPSS

Analyze - regression - linear Transfer dependent and independent variables to respective boxes. Click "statistics" button. Tick: Confidence intervals. "Continue" "Ok"

Five Stages of Research Process

1. Initial Observation and Research Question 2. Generate Theory 3. Generate Hypothesis 4. Collect Data to Test Theory 5. Analyse Data

Factorial ANOVA Main Effect and Interaction

A main effect is an outcome that can show consistent difference between levels of a factor. An interaction effect is said to exist when differences on one factor depend on the level of other factor. However, it is important to remember that interaction is between factors and not levels. We know that there is no interaction between the factors when we can talk about the effect of one factor without mentioning the other factor.

Repeated Measures ANOVA SPSS

Analyze- general linear model - repeated measures replace "factor1" with a name that is more meaningful name for your independent variable, like "time". Enter into "number of levels" the number of times dependent variable has been measured. like "3" representing pertaining, 2 weeks, and post training. Click "Add" button "Measure Name" - put appropriate name for your dependent variable. Click "Add" button Click "Define" button Transfer variables to "Within-Subjects Variables (time): Click "Plots" button. Transfer "time" factor into "Horizontal Axis" and click "Add" click "Continue" Click "Options" and transfer "Time" to "Display means for" Tick: compare main effects, and select "Bonferroni" from drop down menu in "Confidence Interval Adjustment" Tick: descriptive statistics, estimates of effect size, Click "Continue" and "OK"

Exact or Approximate Normality of Observations

Averages of samples of observations of random variables independently drawn from independent distributions converge in distribution to the normal, that is, become normally distributed when the number of observations is sufficiently large.

One Way ANOVA SPSS

BEFORE THE TEST Just like we did with the paired t test and the independent samples t test, we'll want to look at descriptive statistics and graphs to get picture of the data before we run any inferential statistics. Analyze > Descriptive Statistics > Descriptives Analyze > Compare Means> Means Analyze - Compare Means - One Way ANOVA Dependent List - This is the variable whose means will be compared between the samples (groups). You may run multiple means comparisons simultaneously by selecting more than one dependent variable. Factor -The independent variable. The categories (or groups) of the independent variable will define which samples will be compared. The independent variable must have at least two categories (groups), but usually has three or more groups when used in a One-Way ANOVA. Options - Descriptive, Means Plot OK If p < .05, may want to run post-hoc test to see which specific means are significantly different

Importance of Meeting Assumptions Prior to Conducting Analysis

Common assumptions that must be met for parametric statistics include normality, independence, linearity, and homoscedasticity. Failure to meet these assumptions, among others, can result in inaccurate results, which is problematic for many reasons. When testing hypotheses, running analyses on data that has violated the assumptions of the statistical test can result in both false negatives and false positives, depending on the particular assumption violated. Statistics does not infer valid conclusions from nothing. Inferring interesting conclusions about real statistical populations almost always requires some background assumptions. Those assumptions must be made carefully, because incorrect assumptions can generate wildly inaccurate conclusions.

Factorial ANOVA

Experiments where the effects of more than one factor are considered together are called 'factorial experiments' and may sometimes be analyzed with the use of factorial ANOVA. For instance, the academic achievement of a student depends on study habits of the student as well as home environment. We may have two simple experiments, one to study the effect of study habits and another for home environment. But these experiments will not give us any information about the dependence or independence of the two factors, namely study habit and home environment. In such cases, we resort to Factorial ANOVA which not only helps us to study the effect of two or more factors but also gives information about their dependence or independence in the same experiment. Example: Let us claim that blonde women have on average longer hair than brunette women as well as men of all hair colors. We find 100 undergraduate students and measure the length of their hair. A conservative statistician would then state that we measured the hair of 50 female (25 blondes, 25 brunettes) and 25 male students, and we conducted an analysis of variance and found that the average hair of blonde female undergraduate students was significantly longer than the hair of their fellow students. A more aggressive statistician would claim that gender and hair color have a direct influence on the length of a person's hair. Most statisticians fall into the second category. It is generally assumed that the factorial ANOVA is an 'analysis of dependencies.'It is referred to as such because it tests to prove an assumed cause-effect relationship between the two or more independent variables and the dependent variables.

Multiple Regression report findings

Look at the following tables for "F", "df - regression and residual", "Sig./p" and "Rsquared": Model Summary ANOVA a Coefficients a A multiple regression was run to predict VO2max from gender, age, weight and heart rate. These variables statistically significantly predicted VO2max, F(4, 95) = 32.393, p < .0005, R2 = .577. All four variables added statistically significantly to the prediction, p < .05.

Qualitative Research Design

Narrative, phenomenology, ethnography, case study, and grounded theory. Researchers might study individuals (narrative, phenomenology), explore processes, activities, and events (case study, grounded theory), or learn about broad culture-sharing behavior of individuals or groups (ethnography).

p > .05

Not Statistically Significant

5. Analyse Research Data

Qualitative: Thematic Analysis: organize and prepare data for analysis - transcribing interviews, scanning material, field notes, cataloguing visual material, sorting and arranging data into types. read or look at all data - what are general ideas, what is the tone, impression of overall depth, credibility, and use of info. Coding data - organize data by bracketing chucks and describing with one word. Quantitative: Conduct appropriate statistical analysis and interpret the results. single sample t test, independent samples t test, dependent samples t test, one way anova, factorial anova, repeated measures anova, multiple regression.

2. & 3. Generating Theories and testing them (hypothesis)

The research design refers to the overall strategy that you choose to integrate the different components of the study in a coherent and logical way, thereby, ensuring you will effectively address the research problem; it constitutes the blueprint for the collection, measurement, and analysis of data. Your design should be determined by the research problem. The function of a research design is to ensure that the evidence obtained enables you to effectively address the research problem logically and as unambiguously as possible. Decide between qualitative, quantitative, or mixed methods design. A prediction from a theory - hypothesis Methods: techniques and tools used to collect, analyze, and interpret your data.

One Way ANOVA

PROBLEM STATEMENT In the sample dataset, the variable Sprint is the respondent's time (in seconds) to sprint a given distance, and Smoking is an indicator about whether or not the respondent smokes (0 = Nonsmoker, 1 = Past smoker, 2 = Current smoker). Let's use ANOVA to test if there is a statistically significant difference in sprint time with respect to smoking status. Sprint time will serve as the dependent variable, and smoking status will act as the independent variable. Just like we did with the paired t test and the independent samples t test, we'll want to look at descriptive statistics and graphs to get picture of the data before we run any inferential statistics. The One-Way ANOVA is commonly used to test the following: Statistical differences among the means of two or more groups. Statistical differences among the means of two or more interventions. Statistical differences among the means of two or more change scores. Both the One-Way ANOVA and the Independent Samples t Test can compare the means for two groups. However, only the One-Way ANOVA can compare the means across three or more groups. The null and alternative hypotheses of one-way ANOVA can be expressed as: all k population population means are equal, at least one of the k population means is not equal to the others, where: µi is the population mean of the ith group (i = 1, 2, ..., k) Stated another way, this says that at least one of the means is different from the others. However, it does not indicate which mean is different. Your data should include at least two variables (represented in columns) that will be used in the analysis. The independent variable should be categorical (nominal or ordinal) and include at least two groups, and the dependent variable should be continuous (i.e., interval or ratio). Each row of the dataset should represent a unique subject or experimental unit.

Extra info: Report Findings

Qualitative: Briefly reiterate the goals of your study and the ways in which your research addressed them. Discuss the benefits of your study and how stakeholders can use your results. Also, note the limitations of your study and, if appropriate, place them in the context of areas in need of further research. Quantitative: Interpretation of results - reiterate the research problem being investigated and compare and contrast the findings with the research questions underlying the study. Did they affirm predicted outcomes or did the data refute it? Describe any trends that emerged from your analysis and explain all unanticipated and statistical insignificant findings. What is the meaning of your results? Highlight key findings based on the overall results and note findings that you believe are important. How have the results helped fill gaps in understanding the research problem? Describe any limitations or unavoidable bias in your study and, if necessary, note why these limitations did not inhibit effective interpretation of the results.

4. Collect Data to test theory

Qualitative: Data - observations yield a detailed, "thick description"; interviews capture direct quotations about people's personal perspectives and lived experiences; often derived from carefully conducted case studies and review of material culture. Personal experience and engagement - researcher has direct contact with and gets close to the people, situation, and phenomenon under investigation; the researcher's personal experiences and insights are an important part of the inquiry and critical to understanding the phenomenon. Empathic neutrality - an empathic stance in working with study respondents seeks vicarious understanding without judgment [neutrality] by showing openness, sensitivity, respect, awareness, and responsiveness; in observation, it means being fully present [mindfulness]. Dynamic systems -- there is attention to process; assumes change is ongoing, whether the focus is on an individual, an organization, a community, or an entire culture, therefore, the researcher is mindful of and attentive to system and situational dynamics. Quantitative: data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques. Data are in the form of numbers and statistics, often arranged in tables, charts, figures, or other non-textual forms.

p < .05

Statistically Significant

Repeated Measures ANOVA

Studies that investigate (1) changes in mean scores over three or more time points, or (2) differences in mean scores under three or more different conditions. For example, for (1), you might be investigating the effect of a 6-month exercise training programme on blood pressure and want to measure blood pressure at 3 separate time points (pre-, midway and post-exercise intervention), which would allow you to develop a time-course for any exercise effect. For (2), you might get the same subjects to eat different types of cake (chocolate, caramel and lemon) and rate each one for taste, rather than having different people flavour each different cake. The important point with these two study designs is that the same people are being measured more than once on the same dependent variable (i.e., why it is called repeated measures).

Quantitative Research Design

Surveys and experiments. Survey design provides a quantitative or numeric description of trends, attitudes, or opinions of a population by studying a sample of that population. Experiment design tests the impact of a treatment (or an intervention) on an outcome, controlling for all other factors that might influence that outcome. As one form of control, researchers randomly assign individuals to groups. When one group receives a treatment and the other group does not, the experimenter can isolate whether it is the treatment and not other factors that influence the outcome. Quantitative research designs are either descriptive [subjects usually measured once] or experimental [subjects measured before and after a treatment]. A descriptive study establishes only associations between variables; an experimental study establishes causality.

Repeated Measures ANOVA report findings

The Tests of Within-Subjects Effects table tells us if there was an overall significant difference between the means at the different time points. From this table we are able to discover the F value for the "time" factor, its associated significance level and effect size ("Partial Eta Squared"). As our data violated the assumption of sphericity, we look at the values in the "Greenhouse-Geisser" row (as indicated in red in the screenshot). We can report that when using an ANOVA with repeated measures with a Greenhouse-Geisser correction, the mean scores for CRP concentration were statistically significantly different (F(1.171, 22.257) = 21.032, p < 0.0005). The results presented in the previous table informed us that we have an overall significant difference in means, but we do not know where those differences occurred. This table presents the results of the Bonferroni post hoc test, which allows us to discover which specific means differed. Remember, if your overall ANOVA result was not significant, you should not examine the Pairwise Comparisons table. Looking at the table above, we need to remember the labels associated with the time points in our experiment from the Within-Subject Factors table. This table gives us the significance level for differences between the individual time points. We can see that there was a significant difference in CRP concentration between post-training and pre-training (p = 0.0005), and between post-training and after 2 weeks of training (p = 0.001), but no significant differences between pre-training and after 2 weeks of training (p = 0.149). From the "Mean Difference (I-J)" column we can see that CRP concentration was significantly reduced at this time point. A repeated measures ANOVA with a Greenhouse-Geisser correction determined that mean CRP concentration differed statistically significantly between time points (F(1.171, 22.257) = 21.032, P < 0.0005). Post hoc tests using the Bonferroni correction revealed that exercise training elicited a slight reduction in CRP concentration from pre-training to 2-weeks of training (3.09 ± 0.98 mg/L vs 2.97 ± 0.89 mg/L, respectively), which was not statistically significant (p = .149). However, post-training CRP had been reduced to 2.24 ± 0.50 mg/L, which was statistically significantly different to pre-training (p < .0005) and 2-weeks training (p = .001) concentrations. Therefore, we can conclude that a long-term exercise training program (6 months) elicits a statistically significant reduction in CRP concentration, but not after only 2 weeks of training.

One Way ANOVA Report Findings

We conclude that the mean sprint time is significantly different for at least one of the smoking groups (F2, 350 = 9.209, p < 0.001).