DATA ANALYSIS Indawan Syahri

Descriptive Statistics Inferential Statistics Data Analysis Qualitative Data Words Typology Quantitative Data Descriptive Statistics Mode Mean Median Inferential Statistics t-test Correlation ANOVA Regression

Qualitative Data - Words Recording Data: Transcripts from taped Interview Field-notes of Observation Diaries Photographs Documents

Qualitative Data - Typologies Types of errors Errors in Addition Errors in Omission etc. Social variables: Gender Ages Occupations Ethnic groups

Reminders: The data appear in words rather than in numbers. The data may have been collected in a various ways: Observation Interviews Extracts from documents Tape recordings Numbers used have no arithmetic values. Numbers may be used for coding the data. e.g.: Male (1), Female (2), Teachers (3), Bankers (4), Policemen (5) Qualitative data exist dominantly in descriptive studies

Stages in Qualitative Data Analysis Observation Interviews Document Recording Data Collection Selecting Focusing Simplifying Abstracting Transforming Data Reduction Matrices Graphs Networks Charts Data Display Give meanings Confirming Verifying Conclusion Drawing

Quantitative Data – Descriptive Statistics MEASURE OF CENTRAL TENDENCY MODE (the most frequently occurring scores) MEDIAN (the middle score) MEAN (the average of all scores)

Measures of Central Tendency 26/04/2017 Measures of Central Tendency Central tendency is used to talk about the central point in the distribution of value in the data. Indawan Syahri

Measures of variability 26/04/2017 Measures of variability In order to describe the distribution of interval data, the measure of central tendency will not suffice. To describe the data more accurately, we have to measure the degree of variability of the data of the data from the measure of central tendency. There are 3 ways to show the data are spread out from the point, i.e. range, variance, and standard deviation. Indawan Syahri

Range Range = X highest – X lowest 26/04/2017 Range Range = X highest – X lowest E.g. The youngest student is 17 and the oldest is 42, Range = 42 – 17 = 25 The age range in this class is 25. If range is so unstable, some researchers prefer to stabilize it by using the semi-interquartile range (SIQR) SIQR = Q3 – Q1 / 2 Q3 is the score at the 75th percentile and Q1 is the score at the 25th percentile. E.g., the score of the toefl score at the 75th percentile is 560 and 470 is the score at the 25th percentile. SIQR is 560 – 470 / 2 = 45 Indawan Syahri

Variance To see how close the scores are to the average for the test. 26/04/2017 Variance To see how close the scores are to the average for the test. E.g., if the mean score on the exam was 93.5 and a student got 89, the deviation of the score from the mean is 4.5. If we want a measure that takes the distribution of all scores into account, it is variance. To compute variance, we begin with the deviation of the individual scores from the mean. Stages: Compute the mean: X Subtract the mean from each score to obtain the individual deviation scores x = X – X. Square each individual deviation and add: ∑ x² Divide by N – 1: ∑ x²/ N - 1 Indawan Syahri

26/04/2017 Standard Deviation Variance = standard deviation are to give us a measure that show how much variability there is in the scores. They calculate the distance of every individual score from the mean. Standard deviation goes one step further, to take the square root of the variance. S =√ ∑ (X –X)²/ N – 1 or s = √ ∑x² / N - 1 Indawan Syahri

QUANTITATIVE DATA –Inferential Statistics 26/04/2017 QUANTITATIVE DATA –Inferential Statistics Correlation is that area of statistics which is concerned with the study of systematic relationships between two (or more) variables. It attempts to answer questions such as: Do high values of variable X tend to go together with high values of variable Y? (positive correlation) Do high values of X go with low values of Y? (negative correlation) Is there some more complex relationship between X and Y, or perhaps no relationship at all? Indawan Syahri

Visual representation of correlation: Scatter diagram 26/04/2017 Visual representation of correlation: Scatter diagram Y Y Y X X High positive r X High negative r Lower positive r Y Y Y X X X Nonlinear r Lower negative r No r Indawan Syahri

Correlation coefficients: 26/04/2017 Correlation coefficients: To supplement the information given by a scatter diagram a correlation coefficient is normally calculated. The expressions for calculating such coefficients are so devised that a value of +1 is obtained for perfect positive correlation, a value of -1 for perfect negative correlation, a value of 0 for no correlation at all. For interval variables, the appropriate measure is the so-called Pearson product-moment correlation coefficient. For ordinal variables (scattergraghs are not really appropriate), they use the Spearman rank correlation coefficient. For nominal variables, they use the phi coefficient. Indawan Syahri

t-test t-test is used to compare two means of sets of scores: Pre-test vs. posttest Test scores in experimental group vs. test scores in control group It means to observe the differences between the scores obtained by Group A and those obtained by Group B