Research Seminars in IT in Education MIT6003 Quantitative Educational Research Design 2

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Research Seminars inIT in Education(MIT6003)Qu
antitative Educational Research Design 2

• Dr Jacky Pow

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Agenda

• Data analysis/statistical analysis
• Introduction of statistical tools
• Data interpretation
• Significance, generalization and presentation of
  findings

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Data analysis

• Descriptive statistics
• Correlation
• As a measure of relationship
• Inferential statistics
• Making inferences from samples to populations
• Parametric analyses
• Nonparametric analyses
• Correlational analyses

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Data analysis

• Concepts of measurement
• Measurement is a process of assigning numerals
  according to rules. The numerals are assigned to
  events or objects, such as responses to items, or
  to certain observed behaviours
• A numeral is a symbol, such as 1, 2, 3 assigned
  by a rule

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Data analysis

• Types of measurement scales
• Nominal
• Categorization without order (e.g., sex)
• Ordinal
• Indicate difference and order of the scores on
  some basis (e.g., attitude toward the government)
• Interval
• Same units throughout the scale (e.g., time)
• Ratio
• Equal unit with a true zero point (e.g., the
  government expenditures birth weight in pounds)

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Data analysis

• Data preparation
• To facilitate data input
• To facilitate tabulation of data
• To make data machine-readable (coding)
• Data Input
• Are the data on machine-scored answer sheets?
• Manual input of data?
• Check for input errors

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Descriptive statistics

• List of data is not enough or helpful
• A frequency count or constructing related
  histograms are not enough in any research report
• A mathematical summary of the data collected is
  needed
• Provide a general impression of the data
  collected
• Provide background information for interpretation

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Descriptive statistics

• Describing a distribution of scores
• To provide information about its location,
  dispersion, and shape
• Means
• Standard deviation (s.d.)
• Normal distribution (i.e., bell shape)

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Descriptive statistics

• Measures of central tendency (average)
• Locators of the distribution on the scale of
  measurement
• Mean, median, mode are the most commonly used
  measures of central tendency

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Descriptive statistics

• Measures of variability
• Describe the dispersion or spread of the scores
• Range
• Gives the highest and lowest scores on the scale
• Variance
• The difference between an observed score and the
  mean of the distribution

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Variance and Standard deviation

• Var(S) Sum i (Si - E(S))2 / N where Sum i means
  to sum over all elements of set S
• N is the number of elements in S
• Si is the ith element of the set S
• E(S) is the mean over the values of set S

S1 10, 10, 10, 10, 10, mean 10 S2 0, 5,
10, 15, 20, mean 10 The first set though has
a variance of zero all numbers are the same. The
second set has a variance of 50
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Variance and Standard deviation

• The standard deviation is the square root of the
  variance and is kind of the mean of the mean,
  which can help you find the story behind the data

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Shapes of distribution
Distributions with like central tendency but
different variability
Distributions with like variability but different
central tendency
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Correlation (measure of relationship)

• The correlation coefficient is a measure of the
  relationship between tow variables. It can take
  on values from -1.00 to 1.00, inclusive. Zero
  indicates no relationship (i.e., by random)
• Prediction is the estimation of one variable from
  a knowledge of another. Accuracy of prediction is
  increased as the correlation between the
  predictor and criterion variables increases

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Inferential statistics

• Making inferences from samples to populations
• Inferences are made and conclusions are drawn
  about parameters from the statistics of sample
  hence, the name inferential statistics
• The most common procedure of inferential
  statistics is testing hypothesis

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Inferential statistics

• Significance level or level of significance (a-
  level) is a probability (e.g., 0.05 and 0.01) or
  a criterion used in making a decision about the
  hypothesis (i.e., rejecting the null hypothesis)
• Significance level is set before the study

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Inferential statistics - parametric

• t-distribution (difference between two means)
• Analysis of variance (ANOVA)
• F-distribution
• Two-way ANOVA - when 2 independent variables are
  included simultaneously in an ANOVA

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Assumptions of parametric analyses

• Measurement of the dependent variable is on at
  least an interval scale
• The scores are independent
• The scores (dependent variable) are selected from
  a population distribution that is normally
  distributed. This assumption is required only if
  sample size is less than 30
• When two or more populations are being studied,
  they have homogeneous variance. This means that
  the population being studied have about the same
  dispersion in their distributions

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Inferential statistics - nonparametric

• Require few if any assumptions about the
  population under study
• Can be used with ordinal and nominal scale data
• Not emphasizing means, they use other statistics
  such as frequencies

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Inferential statistics - nonparametric

• The Chi-Square (X2) test and distribution
• Unlike t-distribution, the X2 distribution is not
  symmetrical
• It tests hypotheses about how well a sample
  distribution fits some theoretical or
  hypothesized distribution (goodness of fit)

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Correlational Analyses

• Correlation can be used to measure relationship
  (descriptive) but can be also used to test
  hypothesis and therefore can be inferential
  statistics
• The hypothesis of independence or no correlation
  in the population can use tested directly using
  the sample correlation coefficient

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Correlational Analyses

• Analysis of Covariance
• A procedure by which statistics adjustments are
  made to a dependent variable. These adjustments
  are based on the correlation between the
  dependent variable and another variable, called
  the covariate
• F-distribution

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Choosing the appropriate test
About means, and parametric assumptions are met
Relationship between variables
About frequencies, etc., and parametric
assumptions are met
Hypothesis of independence only
Magnitude of Relationship
Parametric analyses
Nonparametric analyses
t-tests
ANOVA
Correlation Coefficient
X2 - test contingency table Goodness of fit
Nonparametric X2 - test for contingency table
Analysis of Covariance
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Type I and Type II errors

• If we reject the null hypothesis when it is true
  and should not be rejected, we have committed a
  Type I error
• If we accept the null hypothesis as true when it
  is false and should be rejected, we have
  committed a Type II error
• Unfortunately, Type I and Type II errors cannot
  be eliminated. They can be minimised, but again
  unfortunately, minimising one type of error will
  increase the probability of committing the other
  error

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Type I and Type II errors
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Introduction of statistical tools

• Statistical Package for Social Sciences (SPSS)
• Excel data analysis
• SAS
• MINITAB

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Data interpretation

• Making sense of it
• Help us in decision making
• Data interpretation is an intellectual exercise
  of using sampling and related data to
  inform/evaluate/correlate the phenomena under
  studied

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Significance and generalization of findings

• Significance
• Comment on the contribution of the research
• Fit the research in the larger context of the
  field of knowledge
• Provide insights to future research
• Generalization
• Context sensitivity
• Applicability of the findings
• Comment on the limitations to generalize the
  findings

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Presentation of findings

• In summarizing, use graphics/figures/tables as
  far as possible
• When comparing groups of data, use tables/figures
• Highlight the findings
• In abstract
• In conclusion