PXGZ6102 BASIC STATISTICS FOR RESEARCH IN EDUCATION Chap 2 - Descriptive and Inferential Statistics (Introduction) - Level of Measurement, - Measures of Central Tendency

Descriptive & Inferential Statistics Descriptive statistics can be used to summarize the data, either numerically or graphically, to describe the sample. Basic examples: mean and standard deviation. Graphical summarizations:various kinds of charts and graphs.

Descriptive Statistics Involves transformation of the raw data into a form that will make them easy to understand and interpret. Describing responses or observations is a form of analysis The calculation of averages, frequency distributions, and percentages distributions is the most common form of summarizing data. Descriptive Statistics is used when no inferences are made about the population based on the sample

Inferential Statistics Inferential statistics is used to model patterns in the data, accounting for randomness and drawing inferences about the larger population. These inferences may take the form of answers to yes/no questions (hypothesis testing), estimates of numerical characteristics (estimation), descriptions of association (correlation), or modeling of relationships (regression). Other modeling techniques include ANOVA

Scales /levels of measurements of variables Nominal (categorical) – Ordinal Interval Ratio

Nominal (categorical) Scale Simple Classification in Categories without any order or reference to quantity e.g. Variable Classification Gender Male (1) and Female (2) Race Malay, Chinese, Indians Football Jersey No 10, 7, 3 etc. Your IC No.

Ordinal Scale Has order or rank ordering, e.g. called LIKERT SCALE Reflects relative position not distance (quantity) Strongly agree, Agree, Undecided, Disagree, Strongly disagree

Interval Scale Do not have true 0 points. Has order as well as equal distance or interval between judgements (Social Sciences) e.g. IQ score of 95 is better than IQ 85 by 10 IQ points E.g. Fahrenheit Scale

Ratio Scale Have true 0 points. Has high order, equal distance between judgements, a true zero value (Physical Sciences) e.g.age, no. of children, 9 ohm is 3 times 3 ohm and 6 ohm is 3 times 2 ohm

Descriptive Statistics for different levels/types of measurement Types of Measurement Type of descriptive analyses Nominal Mode Ordinal Median Interval Mean Ratio Mean

Types of Measurement Scales and their Statistical Analyses Tests Characteristics Type of Data Simple Classification in Categories without any order e.g Boy / Girl Happy / Not Happy Muslim / Buddhist / Hindu Non- parametric Association Nominal Chi-square Ordinal Has order or rank ordering e.g. Strongly agree, agree, undecided, disagree, strongly disagree (LIKERT SCALE) RELATIONSHIP: Spearman’s rho COMPARISON: Mann-Whitney Wilcoxon Non- parametric

Types of Measurement Scales and their Statistical Analyses Tests Characteristics Type of Data Do not have true 0 points. Has order as well as equal distance or interval between judgements (Social Sciences) e.g. IQ score of 95 is better than IQ 85 by 10 IQ points Parametric COMPARISON: t-tests ANOVA RELATIONSHIP: Pearson r Interval Ratio Have true 0 points. Has high order, equal distance between judgements, a true zero value (Physical Sciences) e.g.age, no. of children, 9 ohm is 3 times 3 ohm and 6 ohm is 3 times 2 ohm But IQ 120 is more comparable to IQ 100 than to IQ 144, although ratio IQ 120 /100 = 144 /120 = 1.2 Parametric COMPARISON: t-tests ANOVA RELATIONSHIP: Pearson r

Types of Measurement Scales and their Statistical Analyses Higher order of measurement --> lower order e.g. Interval ---> ordinal, nominal But not ordinal, nominal ----> interval

Measures of Central Tendency Mode Median Mean

Median, Mod and Mean Median is the score at the center of the series when the scores are arranged in increasing order. Example: 30, 45, 48, 48, 54, 55, 60, 62, 68 The median is 54 30, 45, 48, 48, 54, 55, 60, 62, 68, 78 The median is (54 + 55)/2 = 54.5

Mode Mode is the most common score 30, 45, 48, 48, 54, 55, 60, 62, 68 The mode is 48

Upper and lower Quartile Upper quartile is the score obtained by the top 25% of the students Lower quartile is the score obtained by the bottom 25% of the students

Interquartile Range Is the range between the lower quartile and the upper quartile

Exercise 2

Calculating Mean using Frequency distribution 7 6 6 6 5 5 4 4 4 4 4 3 3 3 3 2 1 x xf f 7 6 5 4 3 2 1 1 3 2 5 4 7 18 10 20 12 2 1 n = Σf = 17 Σxf= 70 Σxf= 70 = 4.12 Mean, X = --------------- Σf = 17

Measures of Variability Range - Variance Standard Deviation

Range Refers to the overall span of the scores Eg. 18, 34, 44, 56, 78 The range is 78 – 18 = 60

Mean Deviation Is the degree to which scores deviate from the mean Shows the variability of a distribution Eg. Shoes sizes in Ali’s home: 11,12,13,14,15,16,17 the mean is 14 In Ahmad’s home: 5,8,11,14,17,20, 23 the mean is also 14 But the distribution in Ahmad’s home is greater

Calculation of Mean Deviation (MD) Ali Scores Mean (x - mean) |X – mean| 11 14 -3 3 12 14 -2 2 13 14 -1 1 14 14 0 0 15 14 1 1 16 14 2 2 17 14 3 3 N = 7 |x – Mean| =12 Σ |x – Mean| 12 MD = ---------------------- = ------- = 1.71 n 7

End of Chap 2