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ANALYSING AND INTERPRETING QUANTITATIVE DATA 76.00 32.00 70.00 34.00 68.00 42.00 66.00 65.00 43.00 58.00 44.00 57.00 45.00 47.00 56.00 50.00 54.00 55.00 HJ. SHAWAL KASLAM INTRODUCTION ONE OF THE MAJOR THING IN RESEARCH IS THE DATA. THEREFORE UNDERSTANDING THE DATA IS A CRUCIAL PART IN RESEARCH. Some of the fundamental questions have to be considered are: 1. What is the nature of data? 2. How to gather the data? 3. What is the instrument used to gather the data? 4. How to measure the data? 5. How to analyze the data? 6. How to interpret the output? The Objective of this presentation is to describe the fundamental process of analyzing quantitative data. By the end of this session, the participants should be able to:• describe, combine, and make inferences from numbers. • understand the procedures used to obtain several statistical values. • use, present and interpret the statistical outputs to produce a report. • make conclusion based on the statistical findings. WHAT IS QUANTITATIVE DATA ANALYSIS? QUANTITATIVE DATA ANALYSIS IS A PROCESS OF TRANSFORMING THE RAW DATA OBTAINED FROM QUESTIONNAIRES INTO MEANINGFUL INFORMATION SUCH AS STATISTICAL VALUES [e.g: % value, mean value etc..] AND TO TEST STATISTICAL SIGNIFICANT OF THE DATA. THE STEPS IN DATA ANALYSIS SELECT THE SOFTWARE [SPSS] CREATING DATA FILE KEY IN DATA EXPLORING DATA EDITING FILE ANALYSING DATA INTERPRETING THE RESULT/OUTPUT DATA ANALYSIS TECHNIQUES AND THE STATISTICAL VALUES DESCRIPTIVE MEASURE OF FREQUENCY DISTRIBUTION . Percentage value % MEASURE OF CENTRAL TENDENCY . Mean . Mode . Media SKEWNESS & KURTOSIS Exploration of the variables INFERENTIAL Chi-square Test T-Tests . One Sample Test . Paired T-Test . Independent T-Test ANOVA Z-Test To test statistical significant of the variables PREDICTIVE Correlation Analysis Regression Analysis To test relationship, statistical significant and predict the impact or changes of the variables BASIC DESCRIPTIVE STATISTICS used to explore the data collected and to summarise and describe those data. MEASURES OF FREQUENCY DISTRIBUTION - is a display of the frequency of occurrence of each score value. The frequency distribution can be represented in a tabular form or, with more visual clarity, in graphical form. Gender Valid Male Female Total Frequency 4 6 10 Percent 40.0 60.0 100.0 Valid Percent 40.0 60.0 100.0 Cumulative Percent 40.0 100.0 Support from pee r Valid Undec ided Agree St rongly Agree Total Frequency 11 107 37 155 Percent 7.1 69.0 23.9 100.0 Valid Perc ent 7.1 69.0 23.9 100.0 Cumulative Percent 7.1 76.1 100.0 Ma rita l Status Valid Bachelor Married wi dower Total Frequency 19 134 2 155 Percent 12.3 86.5 1.3 100.0 Valid P erc ent 12.3 86.5 1.3 100.0 Cumul ative Percent 12.3 98.7 100.0 70 widower 60 Bachelor 50 40 30 20 Std. Dev = .58 10 Mean = 2.7 Married N = 100.00 0 1.0 2.0 What is your cgpa? 3.0 4.0 5.0 BASIC DESCRIPTIVE STATISTICS MEASURES OF CENTRAL TENDENCY – INTERVAL or RATIO DATA STATISTICAL VALUES - MEAN - MODE - MEDIA - STANDARD DEVIATION - MAKSIMUM - MINIMUM Statistics N Mean Median Mode St d. Deviation Minimum Maximum Valid Missing Support from peer 155 0 4.1677 4.0000 4.00 .53232 3.00 5.00 Support from peer 155 0 3.2710 4.0000 4.00 .92097 1.00 5.00 Support from peer 155 0 4.3419 4.0000 4.00 .57478 3.00 5.00 Support from peer 155 0 3.0581 3.0000 4.00 .95509 1.00 5.00 Support from peer 155 0 4.2323 4.0000 4.00 .62231 2.00 5.00 Support from peer 155 0 3.8452 4.0000 4.00 .65606 2.00 5.00 MEASURE OF CENTRAL TEDENCY COMPARE MEAN Descriptive Statistics N Tahap pengurus an kualiti Tahap program kualiti Tahap s okongan s taf Tahap kepuas an pelanggan Ceramah kualiti Valid N (lis twis e) 121 120 120 Minimum 2.00 2.00 2.00 Maximum 5.00 5.00 5.00 Mean 3.8182 3.8250 4.1250 Std. Deviation .67082 .68185 .76216 119 2.00 5.00 3.9664 .70028 128 119 1.00 9.00 2.8906 1.50712 BASIC DESCRIPTIVE STATISTICS MEASURES OF SKEWNESS & KURTOSIS – refer to the shape of distribution and are used with interval and ratio level data. 100 120 100 80 80 60 60 40 40 20 20 Std. Dev = .87 Std. Dev = .53 Mean = 3.6 Mean = 4.17 N = 155.00 0 3.00 3.50 Support f rom peer 4.00 4.50 5.00 N = 155.00 0 1.0 2.0 Work Environment 3.0 4.0 5.0 5 4 3 2 1 Std. Dev = 22.74 Mean = 72.8 N = 20.00 0 20.0 30.0 V AR00001 40.0 50.0 60.0 70.0 80.0 90.0 100.0 BASIC DESCRIPTIVE STATISTIC CROSS TABULATION – to explore the intersection of two variables Ma rita l Status * I NCOME GROUP Crosstabulati on Count B Marital St atus Total Bachelor Married widower 11 25 36 INCOME GROUP C D 7 1 71 33 2 80 34 E 5 5 Total 19 134 2 155 INTERPRETING BASIC DESCRIPTIVE STATISTICS BASIC DESCRIPTIVE STATISTICAL VALUES CAN BE USED TO EXPLORE AND EXPLAIN THE RESEARCH QUESTIONS. Example: Research question “is there any different of mean score between the group [male and female] of sample study? Re port W hat is your gender Post-s core MALE Mean 76.4000 N 15 St d. Deviat ion 9.53040 FE MALE Mean 72.8000 N 15 St d. Deviat ion 14.78030 Total Mean 74.6000 N 30 St d. Deviat ion 12.35565 Pre-sc ore 54.2667 15 10.79330 51.8667 15 13.22264 53.0667 30 11.92197 Descriptive Statistics N beneficial to new s tudents run smoothly lecture hall was comfortable s atisfied with the room guidance by the librarian Valid N (lis twis e) Item Minimum Maximum Mean Std. Deviation 80 1.00 5.00 3.2750 .87113 80 1.00 4.00 2.8500 .91541 80 1.00 5.00 3.5625 .82437 80 80 80 1.00 1.00 5.00 5.00 3.4625 3.6875 .91325 .77286 Mean SD Rank Guidance by the Librarian 3.6875 .77286 1 Lecture hall 3.5625 0.82437 2 Satisfaction with room 3.4625 0.91325 3 INFRENTIAL STATISTICS - tests for difference of means and tests for statistical significance. The purpose of difference of means tests is to test hypotheses. The most common techniques are called - T-Test - ANOVA - CHI-SQUARE Hypothesis Ho : ∂1 = ∂2 No significant different H1 : ∂1 ≠ ∂2 There is significant different Rule of significant test SPSS Calculated Test value ρ Critical value α [alfa] By convention, in social science α = .05 or 0.01 CRITERIA OF REJECTION or ACCEPTANCE If significant test value ρ < α [0.05 / 0.01] reject Ho [ There is significant difference] If significant test value ρ > α [0.05 / 0.01] fail to reject Ho [No significant difference] T-TEST – used to determine whether there is a significant difference between two sets of scores One-sample T-test – is used when you have data from a single sample of participants and you wish to know whether the mean population from which the sample is drawn is the same as the standard mean. e.g: test whether the mean of students test score is the same as the standard mean = 70 One-Sample Statistics N Tes t s core 1 30 Mean 67.7000 Std. Deviation 12.50145 Std. Error Mean 2.28244 DATA Test score 65 56 58 79 80 65 65 67 68 69 The Result from the study is One-Sample Test Tes t Value = 70 Tes t s core 1 t -1.008 df 29 Sig. (2-tailed) .322 Mean Difference -2.3000 95% Confidence Interval of the Difference Lower Upper -6.9681 2.3681 T (29) = -1.008, ρ = 0.322, ρ > 0.05 ∴ Fail to reject Ho Conclusion there is no significant difference between the sample mean of population with the standard mean [Test value]. Independent T-Test – is used to test whether the difference between means for the two sets of scores is significant. A study was done to compare job stress between two employee groups (administrative and support). Data were solicited from a randomly selected sample. Test the hypothesis on the difference at .05 level of significance. Group Statistics Job s tress Employee groups Adminis trative Support N 10 10 Mean 22.8000 22.1000 Std. Deviation 2.39444 2.68535 Std. Error Mean .75719 .84918 The result of independent sample T-Test Independent Samples Test Levene's Test for Equality of Variances F Job s tress Equal variances ass umed Equal variances not as sumed .640 Sig. .434 t-tes t for Equality of Means t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper .615 18 .546 .7000 1.13774 -1.69030 3.09030 .615 17.768 .546 .7000 1.13774 -1.69253 3.09253 T(18) = .615, ρ = .545 ρ > 0.05 ∴Fail to reject Ho Conclude that there is no significant difference in job stress between administrative and support groups at .05 level of significance. Paired T-Test – used to determine whether the difference between means for the two sets of scores is the same or different. A training program was conducted to improve participants participants’ knowledge on ICT. Data were collected from a selected sample both before and after the ICT training program. Test the hypothesis that the training is effective to improve participants knowledge on ICT at 0.05 level of significant. Paired Samples Statistics Pair 1 Pos t-Test scores Pre-Tes t s cores Mean 15.1000 12.3000 N 10 10 Std. Deviation 2.99815 1.88856 Std. Error Mean .94810 .59722 The result of Paired T-Test Paired Samples Test Paired Differences Mean Pair 1 Pos t-Test scores - Pre-Test scores 2.8000 Std. Deviation Std. Error Mean 1.81353 .57349 95% Confidence Interval of the Difference Lower Upper 1.5027 4.0973 T(9) = 4.882, ρ = .001 ρ < 0.05 ∴Reject Ho [Null hypothesis] Conclude that the training program was effective to improve participants knowledge on ICT at .01 level of significance t 4.882 df Sig. (2-tailed) 9 .001 ANOVA One Way Analysis of variance – wish to compare means of more than two groups. ANOVA is also provide post hoc analysis to determine pair of groups that are significantly difference Data on perception toward management was gathered from a randomly selected sample comprising of three from a randomly selected sample comprising of three employee groups (supervisory, line and support). Test the difference in perception among the three groups at .05 level of significance. The result of INOVA Descriptives Perception towards management N Supervis ory Line Support Total 9 10 10 29 Mean 30.3333 21.1000 19.6000 23.4483 Std. Deviation 3.50000 3.07137 3.56526 5.75442 Std. Error 1.16667 .97125 1.12744 1.06857 95% Confidence Interval for Mean Lower Bound Upper Bound 27.6430 33.0237 18.9029 23.2971 17.0496 22.1504 21.2594 25.6371 Test of Homogeneity of Variances Minimum 25.00 17.00 14.00 14.00 Maximum 35.00 25.00 24.00 35.00 F (2, 26) = 27.542, p = .000 Perception towards management Levene Statis tic .194 df1 df2 2 26 Since sig-F (.000) < α (.05) Sig. .825 ∴Reject the null hypothesis ANOVA Perception towards management Between Groups Within Groups Total Sum of Squares 629.872 297.300 927.172 df 2 26 28 Mean Square 314.936 11.435 F 27.542 Sig. .000 Conclude that there is a significant difference in perception towards management between the three employee groups at .05 level of significance. Post-hoc Analysis – which pair is significance different? Multiple Comparisons Dependent Variable: Perception towards management Tukey HSD (I) Employee groups Supervis ory Line Support (J) Employee groups Line Support Supervis ory Support Supervis ory Line Mean Difference (I-J) 9.2333* 10.7333* -9.2333* 1.5000 -10.7333* -1.5000 *. The mean difference is significant at the .05 level. Std. Error 1.55370 1.55370 1.55370 1.51226 1.55370 1.51226 Sig. .000 .000 .000 .588 .000 .588 95% Confidence Interval Lower Bound Upper Bound 5.3726 13.0941 6.8726 14.5941 -13.0941 -5.3726 -2.2578 5.2578 -14.5941 -6.8726 -5.2578 2.2578 Chi-Square Test for independence or relatedness – nonparametric techniques A study was conducted to determine whether job stress is significantly related with employees group. Chi-Square Tests Pears on Chi-Square Likelihood Ratio Linear-by-Linear Ass ociation N of Valid Cas es Value 4.667 a 6.225 9 9 Asymp. Sig. (2-s ided) .862 .717 1 .532 df .391 20 a. 20 cells (100.0%) have expected count les s than 5. The minimum expected count is .50. The result Pearson Chi-square = 4.667, p = .862 X2 ( 9, N = 20) = 4.667, p > .05 ∴ Fail to reject Ho Conclude that there is no significance relatedness of job stress with employees group. PREDECTIVE STATISTICAL ANALYSIS TECHNIQUES – CORRELATION ANALYSIS CORRELATION ANALYSIS – used to look at the relationship between two variables in a linear fashion. The correlation coefficient has a range of possible values from -1 to +1. The value indicates the strength of the relationship, while the sign ( + or - ) indicates the direction. Guildford Rule of Thumb x The result of Correlation analysis Correlations Anxiety Team cohes ivenes s Pears on Correlation Sig. (2-tailed) N Pears on Correlation Sig. (2-tailed) N Team Anxiety cohes ivenes s 1 -.783** . .000 21 21 -.783** 1 .000 . 21 21 **. Correlation is significant at the 0.01 level (2-tailed). R = -.783 Sign r = .000 , p < 0.01 There is a negative and high relationship between anxiety (X) and team cohesiveness (Y) PREDECTIVE STATISTICAL ANALYSIS TECHNIQUES – REGRESSION ANALYSIS Regression analysis – The result of regression is an equation that represents the best prediction of a dependent variable from several independent variables. Regression analysis is used when independent variables are correlated with one another and with the dependent variable. The purpose of regression analysis Determine relationship between one or more IVs and one DV Predict value of the dependent variable on value of independent variables (X’s) CONCLUSION Analyzing quantitative data is the most interesting part of a research. It is important that the presentation of the data is effective in bringing the objectives of the study to the forefront and in stating clearly the research outcome. That all, Thank you very much.