# Southampton Education School Southampton Education School Dissertation Studies Quantitative Data Analysis.

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Southampton Education School Southampton Education School Dissertation Studies Quantitative Data Analysis

Southampton Education School Southampton Education School Basic Analysis Approaches description of a particular phenomena associations of particular behaviours and conditions differences between certain sub-groups or conditions relationships between concepts

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

Southampton Education School Southampton Education School 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%

Southampton Education School Southampton Education School 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!

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

Southampton Education School Southampton Education School 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)

Southampton Education School Southampton Education School 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)

Southampton Education School Southampton Education School What can we do with continuous type questions? distribution charts are the most appropriate figure to indicate the frequency analysis for numerical type variables

Southampton Education School Southampton Education School 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

Southampton Education School Southampton Education School What can we do with numerical type questions? Mode - the most popular case

Southampton Education School Southampton Education School 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

Southampton Education School Southampton Education School 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

Southampton Education School Southampton Education School 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.

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

Presenting Data Type of Data Frequency/ Percentage MeanModeMedian Nominal (Discrete unordered) Ordinal (Discrete ordered) ? Scale (Ordered continuous)

Presenting Data Type of DataTables Pie Charts Bar Graph Line chart / histogram Nominal (Discrete unordered) Ordinal (Discrete ordered) Scale (Ordered continuous)

Southampton Education School Southampton Education School Associations between two category questions AKA: “crosstabulation”

Southampton Education School Southampton Education School 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

Southampton Education School Southampton Education School Associations between two category questions Stacked bar chart Don’t use both tables and charts to present the same information

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

Southampton Education School Southampton Education School Differences between sub- groups on numerical questions AKA: “Comparison of Means”

Southampton Education School Southampton Education School 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).

Southampton Education School Southampton Education School Differences between sub- groups on numerical questions If we want to know if there are significantly different means for each sub-group – we use at-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).

Southampton Education School Southampton Education School Relationships between numerical questions AKA: “scatter-plot”

Southampton Education School Southampton Education School 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

Southampton Education School Southampton Education School 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. If we want to know if the two concepts are significantly related we use a correlation

Southampton Education School Southampton Education School 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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