EDU 702 RESEARCH METHODOLOGY Quantitative Data analysis Presented by : NORAZLIYATI YAHYA 2009905123 NURHARANI SELAMAT 2009324059 NUR HAFIZA NGADENIN 2009720649
QUANTITATIVE DATA ANALYSIS DATA ANALYSIS STATISTICS IN PERSPECTIVE DESCRITIVE STATISTICS INFERENTIAL STATISTICS
QUANTITATIVE DATA Histogram & Stem-leaf Plots Skewed polygons Frequency polygons Techniques for summarizing quantitative data Normal Curve Correlation Standard scores & Normal Curve Average Spreads
FREQUENCY POLYGONS Constructing a frequency polygon List all scores in order of size, group scores into interval Label the horizontal axis by placing all the possible scores at equal intervals Label the vertical axis by indicating frequencies at equal interval Find the point where for each score intersect with frequency, place a dot at the point Connect all the dots with a straight line. l
SKEWED POLYGONS Positively Skewed Polygon Negatively Skewed Polygon The tail of the distribution trails off to the right, in the direction of the higher score value The longer tail of the distribution goes off to the left
HISTOGRAM Histogram facts Bars arranged from left to right on horizontal axis Width of the bar indicate the range of value in each bar Frequencies are shown in vertical axis, point of intersection is always zero Bars in the histogram touch, indicate they illustrate quantitative rather than categorical data
STEM-LEAF PLOTS Constructing a Stem-Leaf Plot Separate number into a stem and a leaf Group number with the same stem in numerical order Mathematics Quiz Score Reorder the leaf values in sequence
NORMAL CURVE Normal Distribution The smooth curve (distribution curve) shows a generalized distribution of scores that is not limited to one specific set of data Majority of the scores are concentrated in the middle of the distribution, scores decrease in frequency the farther away from the middle The normal curve is symmetrical and bell-curved, commonly used to estimate height and weight, spatial ability and creativity.
AVERAGES Measure of Central Tendency Mode Mean Median The most frequent score in a distribution Average of all the score in a distribution The midpoint - middlemost score or halfway between the two middlemost score
SPREADS Variability Standard Deviation Facts 34% 34% Represents the spreads of a distribution, describe the variability based on how greater or smaller the standard deviation 68% 13.5% 13.5% 95% 2.15% 99.7% 50% of all observation fall on each side of the mean -2 SD -1 SD Mean 1 SD 2 SD 27% of the observation fall between one or two standard deviation away from the mean 68% of the score fall within one standard deviation of the mean 99.7% fall within three standard deviations of the mean
STANDARD SCORE & NORMAL CURVE Standard score & Normal Curve z-score How far a raw score is from the mean in standard deviation units .3413 .3413 Probability Percentage associated with areas under a normal curve, stated in decimal form .0215 .1359 .1359 .0215
CORRELATION Correlation Coefficient and Scatterplots Correlation Coefficient Scatterplots Express the degree of relationship between two sets of scores Used to illustrate different degrees of correlation Positive relationship is indicated when high score on one variable accompanied by high score on the other and when low score on one accompanied by low score on the other
CATEGORICAL DATA Bar Graphs and Pie Charts Frequency Table Techniques for summarizing categorical data Crossbreak Table
CROSSBREAK TABLE Reported a relationship between two categorical variables of interest Grade Level and Gender of Teachers (Hypothetical Data) Junior high school teacher is more likely to be female. A high school teacher is more likely to be male. Exactly one-half of the total group of teachers are female. If gender is unrelated to grade level, the same proportion of junior high school and high school teachers are would be expected female.
A researcher administered a study on the average IQ of primary school students at Shah Alam district and findstheir average IQ score is 85. I don’t want to obtain data for entire population but how am I going to estimate how closely the average sample IQ scores with population IQ scores? If different, how are they different? Are their IQ scores higher or lower? Does the average IQ score of students in entire population is also equal to 85 or this sample of students differ from other students in Shah Alam district?
INFERENTIAL STATISTIC • What is inferential statistic? • It is the Statistical Technique/Method using obtained sample data to infer the corresponding population. • Type of inferential statistics POPULATION μ =? SAMPLE = 10.14 • 1. Estimation • Using a sample mean to estimate • a population mean • Example: • Interval Estimation: Confidence Intervals • 2. Hypothesis testing • Comparing 2 means • Comparing 2 proportions • Association between one • variable and another variable
1. INTERVAL ESTIMATION • RESEARCH OBJECTIVE : • To identify the average IQ of primary school students at Shah Alam district. • Population: 1,000 students of Shah Alam primary schools • Sample: 65 primary school students • Sample Mean : 85 • Standard Error of Mean : 2.0 • Interval Estimation : • 95% Confidence Interval = 85 1.96(2) • = 85 3.92 = 81.08 or 88.92 • Interpretation: Researcher has 95% confidence that the average IQ of primary students at Shah Alam district is between 81.08 or 88.92
SAMPLING ERROR • What is sampling error? • The difference between the population mean and the sample mean • Why does sampling error occurs? • Different samples drawn from the same population can have different • properties • How can we quantify sampling error? • Using standard error of mean. • It is useful because it allows us to represent the amount of sampling error associated with our sampling process—how much error we can expect on average. S S P S
1. HYPOTHESIS TESTING • What is hypothesis testing? • A hypothesis is an assumption about the population • parameter. • A parameter is a characteristic of the population; mean or relationship. • The parameter must be identified before analysis. • Steps in conducting hypothesis testing • State the null hypothesis and research hypothesis. • Identify the appropriate test. • State the decision rule for rejecting null hypothesis.
NULL HYPOTHESISThe average IQ score of primary school students at Shah Alam district EQUAL to 85 • This test is called one sample t test. • At the end of the hypothesis testing, we will get a P value. • If the P value is less than 0.05, we reject the Null Hypothesis and conclude as Research Hypothesis. • If the P value is more than or equal to 0.05, we cannot reject the Null Hypothesis. • In above example, if we get P =0.01, we reject the null • hypothesis, then we conclude Research Hypothesis “the average IQ score of primary school students at Shah Alam district is GREATER 85 ”.
TYPE OF TESTS PARAMETRIC TEST • Quantitative data • t-test for means • ANOVA • ANCOVA • MANOVA • MANCOVA • t-test for r • Categorical data • t-test for difference in proportion NON PARAMETRIC TEST • Quantitative data • Mann-Whitney U test • Kruskall-Wallis one way analysis of variance • Sign test • Friedman two ways analysis of variance Categorical data Chi-square test
Comparing GroupsQuantitative Data • Frequency polygons → central tendency
Interpretation • Information of known groups • Effect size, ES: • Inferential statistics
Comparing GroupsCategorical Data • Crossbreak tables Table 1 Felony Sentences for Fraud by Gender
Table 1 Felony Sentences for Fraud by Gender (frequencies added)
Interpretation • Place data in tables • Calculate contingency coefficient c = √