Research Seminars in IT in Education (MIT6003) Quantitative Educational Research Design 2 Dr Jacky Pow

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

Data analysis  Descriptive statistics  Correlation –As a measure of relationship  Inferential statistics –Making inferences from samples to populations  Parametric analyses  Nonparametric analyses  Correlational analyses

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

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)

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

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

Descriptive statistics  Describing a distribution of scores –To provide information about its location, dispersion, and shape 1. Means 2. Standard deviation (s.d.) 3. Normal distribution (i.e., bell shape)

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

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

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

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

Shapes of distribution Distributions with like central tendency but different variability Distributions with like variability but different central tendency

Correlation (measure of relationship)  The correlation coefficient is a measure of the relationship between tow variables. It can take on values from 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

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

Inferential statistics  Significance level or level of significance ( α - 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

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

Assumptions of parametric analyses 1. Measurement of the dependent variable is on at least an interval scale 2. The scores are independent 3. 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 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

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

Inferential statistics - nonparametric  The Chi-Square (X 2 ) test and distribution –Unlike t-distribution, the X 2 distribution is not symmetrical –It tests hypotheses about how well a sample distribution fits some theoretical or hypothesized distribution (goodness of fit)

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

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

Choosing the appropriate test Relationship between variables About means, and parametric assumptions are met About frequencies, etc., and parametric assumptions are met Correlation Coefficient Nonparametric X 2 - test for contingency table Parametric analyses Nonparametric analyses X 2 - test contingency table Goodness of fit t-tests ANOVA Analysis of Covariance Magnitude of Relationship Hypothesis of independence only

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

Type I and Type II errors Conclusion about null hypothesis from statistical test Fail to rejectReject Truth about null hypothesis TrueCorrectType I error FalseType II errorCorrect

Introduction of statistical tools  Statistical Package for Social Sciences (SPSS)  Excel – data analysis  SAS  MINITAB

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

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

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