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Quantitative Data Analysis: Basic Approaches and Techniques for Dissertation Studies

Explore basic statistical approaches for analyzing quantitative data in studies, including phenomena description, behavior associations, subgroup differences, and concept relationships. Learn about category, ordinal, interval, and ratio data analysis, predictive modeling, and statistical significance testing.

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Quantitative Data Analysis: Basic Approaches and Techniques for Dissertation Studies

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  1. Dissertation Studies Quantitative Data Analysis

  2. Basic Analysis Approaches • description of a particular phenomena • associations of particular behaviours and conditions • differences between certain sub-groups or conditions • relationships between concepts

  3. Basic statistical approaches • Category / Discrete • nominal • Ordered • ordinal • Continuous • interval • ratio description of a particular phenomena associations of particular behaviours and conditions differences between certain sub-groups or conditions relationships between variables prediction of variables modelling of relationships

  4. What can we do with category type questions? • frequency analysis • occurrence of a response for a particular question or observation • expressed as a number or percentage 54.5% 45.5%

  5. What can we do with category type questions? • The respondents to the questionnaire comprised 74 males (33%) and 150 females (67%) of which 54.5% were full time • If you have a small number of participants don’t use percentages - absolute numbers are more meaningful! Example Text Hint!

  6. What can we do with category type questions? • Pie charts and Bar charts are the most appropriate figures to use.

  7. What can we do with category type questions? • If we want to know if there are significantly different numbers in each category – we use a one-way chi2 • An objective test to determine differences between group sizes • <5% chance of the result being a random occurrence The respondents to the questionnaire comprised 74 males (33%) and 150 females (67%). A one-way chi2 suggested that there was a significant difference in the size of these groups (chi2=25.786, df=1, p<0.001) Example Text

  8. What can we do with continuous type questions? • if the information is meaningful a frequency analysis can be undertaken for some numerical type variables (e.g. scales)

  9. What can we do with continuous type questions? • distribution charts are the most appropriate figure to indicate the frequency analysis for numerical type variables

  10. What can we do with numerical type questions? • central tendency • Mode • the most popular value • Median • is the middle case • Mean • the average of the cases

  11. What can we do with numerical type questions? • Mode - the most popular case

  12. what can we do with numerical type questions? • Median - is the middle case • Method of calculation • arrange the cases in order • the value of the middle case is the median • Mean - the mathematic average of the cases • only meaningful for interval and ratio variables

  13. What can we do with numerical type questions? • measures of dispersion • range • difference between highest and lowest cases • standard deviation (SD ) • the average deviation from the mean

  14. What can we do with numerical type questions? • The participants perceived their competence with playing the Cajon to be low. The mean competence was 2.794 with a standard deviation of 1.021. Example Text

  15. What can we do with numerical type questions? • sometimes a table can be used to present the descriptive statistics relating to several variables.

  16. Presenting Data

  17. Presenting Data

  18. Associations between two category questions • AKA: “crosstabulation”

  19. Associations between two category questions • The responses to the question about use teaching status were divided into two groups: full and part time. Ninety-one females and 31 males indicated that they worked full time, and 59 females and 43 males indicated that they worked part time Example Text

  20. Associations between two category questions • Stacked bar chart • Don’t use both tables and charts to present the same information Hint!

  21. Associations between two category questions • If we want to know if there are significantly different numbers in each category – we use a two-way chi2 • An objective test to determine differences between group sizes • <5% chance of the result being a random occurrence • The results of a 2-way chi2 suggested that there was an association between gender and full/part time teaching status (chi2=7.043; df=2,1; p=0.008) Example Text

  22. Differences between sub-groups on numerical questions • AKA: “Comparison of Means”

  23. Differences between sub-groups on numerical questions • The responses to the question regarding teaching competency were divided into two groups: male and female. Females indicated that they were moderately low in their ability (mean = 5.606; SD = 3.025). Males responded similarly (mean = 4.162; SD = 3.450). Example Text

  24. Differences between sub-groups on numerical questions • If we want to know if there are significantly different means for each sub-group – we use a t-test • An objective test to determine differences between group means • <5% chance of the result being a random occurrence • The results of a t-test indicated that Females (mean = 3.887; SD = 1.392) felt they were more competent than males (mean = 3.663; SD = 1.546) (t=3.206, p=0.002). Example Text

  25. Relationships between numerical questions • AKA: “scatter-plot”

  26. Relationships between numerical questions • How tightly the dots are bunched on the line indicate the strength of the relationship • It is positive if it raises to the right; negative if it falls to the right Hints!

  27. relationships between numerical questions • A scatterplot was constructed to see if there was a relationship between a competency in the use of the Cajon and their competency as a teacher. The scatter-plot (see Figure 1) suggested that there was a positive relationship between teaching ability and playing ability. Example Text If we want to know if the two concepts are significantly related we use a correlation

  28. Correlation • An objective test to determine relationships between variables/questions • <5% chance of the result being a random occurrence • is usually expressed by… • r = 0.824, p < 0.001 • correlation: • is it positive or negative? • strength is determined by its closeness to 1 • significance: • is it less than the selected value (0.05) • if so then it is significant

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