EXECUTIVE DIPLOMA IN BUSINESS MANAGEMENT

Module Title Lecturer

: Module 5- Research Methods & Statistic : Inferential Statistic : Prof. Madya Dr. Sabitha Binti Marican

Presented by: EDBM07-49

: Mohd Hisham Bin Ramlee

Date: 22 April 2012

Inferential Statistics

Inferential statistics are used to draw conclusions about a population by examining the sample POPULATION Sample

Inferential StatisticsAccuracy of inference depends on representativeness of sample from population random selection equal chance for anyone to be selected makes sample more representative

Inferential Statistics

Inferential statistics help researchers test hypotheses and answer research questions, and derive meaning from the results a result found to be statistically significant by testing the sample is assumed to also hold for the population from which the sample was drawn the ability to make such an inference is based on the principle of probability

Inferential Statistics

Researchers set the significance level for each statistical test they conduct by using probability theory as a basis for their tests, researchers can assess how likely it is that the difference they find is real and not due to chance

Two Types of Techniques1.

Parametric Technique Non-Parametric Technique

2.

Parametric Technique

makes various assumptions about the nature of the population from which the sample for study is drawn capable of determining the actual difference or relationship in the study

Non-Parametric Technique

makes few, if any, assumptions about the nature of the population useful in measurements of nominal and ordinal data cannot determine the relationships in a study

Common Parametric and NonParametric Tests in Inferring Quantitative DataAssociation Pearson r Two Groups Independent t One Independent Variable Parametric Between Subjects Two Independent Variables Difference Two Groups Within Subjects > Two Groups Repeated Measures ANOVA Correlated t-test Two-Way ANOVA > Two Grps One-Way Anova

Association Spearman rho Two Independent Groups Between Subjects Nonparametric > Two Independent Groups Kruskal-Wallis Chi-Square, Mann-Whitney U

Difference

Two Groups Within Subjects > Two Groups

Sign Test, Wilcoxon Friedman

Alternative and Null Hypotheses

Inferential statistics test the likelihood that the alternative (research) hypothesis (H1) is true and the null hypothesis (H0) is not in testing differences, the H1 would predict that differences would be found, while the H0 would predict no differences by setting the significance level (generally at .05), the researcher has a criterion for making this decision

Correlated t-testParametric Samples are correlated when two or more samples are taken from the same group Correlated t-test checks for significance of difference between two means of correlated samples Example: Compare pretest and posttest exam means of a single programming class that was given a new software tool

Independent t-testParametric Test the significance of the difference of means of two samples drawn from independent groups Example: Test whether means of exams of two independent classes are significantly different where the classes each used different software tools

One-Way ANOVAParametric A composite test of the significance of difference of means of multiple independent groups, each getting a different treatment Example: Three different software tools are used in three independent classes then the means of the exam scores are tested to see if there is one that is significantly different from the others

Pearson r Correlation CoefficientTest the significance of the relationship of two variables calculated on the same group Determine the function for predicting one variable given the other For prediction, r should be significant and r2 should explain most of the variance of the dep. variable

Parametric

y (r

y x

)x (r

y x

)X Y

Example: A study of the relationship

Repeated Measures ANOVAParametric MANOVA An analysis of variance for two dependent variables Note that a separate ANOVA for each dep variable could be run and analyzed Example: The final exam score and the time of completion of programming assignment are dep variables in a comparison of two programming classes having different treatments

Two Way ANOVAParametric ANOVA with one dependent variable on multiple groups with multiple treatments Minimum of four groups:Group Characteristic A Group Characteristic B Treatment A Group 1 Group 3 Treatment B Group 2 Group 4

Example: The effects of two treatments and gender are studied for different final exam scores from treatments or gender, as well as interaction effects

Sign TestNonparametric correlated t-test A test of simple changes (up or down) within group using ordinal data Example: Students are taught C# after being taught C++ then are asked to evaluate their abilities in problem solving using: 1 better, 2 no change, 3 worse

WilcoxonNonparametric sign test & correlated t-test changes within a group are tested using ranks based on magnitude of change Example: Students in computer literacy are asked to rank response to training as:1.2. 3. 4.

If I can solve a problem on a computer, I will. I will use a computer for problem solving, I will. Sometimes I will use a computer for problem solving and some times not. I will rarely use a computer for problem solving.

Chi-SquareNonparametric independent t-test Test for significant differences of observed and expected frequencies Expected frequencies should be >= 10 Example: Is there a significant difference in user preference of IBM PC vs McIntosh?

Mann-Whitney UNonparametric independent t-test Test significant difference between independent groups using ordinal data Example: An instructor teaches both a graduate and an undergraduate computer science class. The students in each class evaluate the instructors teaching on a Likert scale. The Mann-Whitney U is applied to see if there is a significant

Kruskal-WallisNonparametric one-way ANOVA A composite test of the difference of means of multiple independent groups, each getting a different treatment using ordinal data Example: Three different socioeconomic groups within a class are asked to evaluate a new software tool using a Likert scale. The results are tested to see is there is a socioeconomic level that is significantly

Spearman rhoNonparametric Pearson r Correlation coef. for rank-order data Example: A study seeks to establish a relationship and possible prediction between a students rank in the current computer science graduating class and his/her starting salary after graduation

FriedmanNonparametric repeated measures ANOVA Rpt. Meas. ANOVA for ordinal data Example: Students rank a software product on the Likert scale at the beginning, middle and end of the semester. The study seeks to find if there is any significant change in the rankings due to experiences in the class

Alternative and Null HypothesesIf the .05 level is achieved (p is equal to or less than .05), then a researcher rejects the H0 and accepts the H1 If the the .05 significance level is not achieved, then the H0 is retained

Degrees of Freedom

Degrees of freedom (df) are the way in which the scientific tradition accounts for variation due to error

it specifies how many values vary within a statistical test

scientists recognize that collecting data can never be error-free each piece of data collected can vary, or carry error that we cannot account for by including df in statistical computations, scientists help account for this error there are clear rules for how to calculate df for each statistical test

Inferential Statistics: 5 Steps

To determine if SAMPLE means come from same population, use 5 steps with inferential statistics 1. State Hypothesis

Ho: no difference between 2 means; any difference found is due to sampling error any significant difference found is not a TRUE difference, but CHANCE due to sampling error

results stated in terms of probability that Ho is false findings are stronger if can reject Ho therefore, need to specify Ho and H1

Steps in Inferential Statistics2. Level of Significance Probability that sample means are different enough to reject Ho (.05 or .01)

level of probability or level of confidence

Steps in Inferential Statistics3. Computing Calculated Value

Use statistical test to derive some calculated value (e.g., t value or F value)

4. Obtain Critical Value

a criterion used based on df and alpha level (.05 or .01) is compared to the calculated value to determine if findings are significant and therefore reject Ho

Steps in Inferential Statistics5. Reject or Fail to Reject Ho

CALCULATED value is compared to the CRITICAL value to determine if the difference is significant enough to reject Ho at the predetermined level of significance If CRITICAL value > CALCULATED value --> fail to reject Ho If CRITICAL value < CALCULATED value --> reject Ho If reject Ho, only supports H1; it does not prove H1

Testing Hypothesis

If reject Ho and conclude groups are really

different, it doesnt mean theyre different for the reason you hypothesized may be other reason Since Ho testing is based on sample means, not population means, there is a possibility of making an error or wrong decision in rejecting or failing to reject Ho Type I error Type II error

Testing Hypothesis

Type I error -- rejecting Ho when it was true (itshould have been accepted) equal to alpha if = .05, then theres a 5% chance of Type I error Type II error -- accepting Ho when it should have been rejected If increase , you will decrease the chance of Type II error

Identifying the Appropriate Statistical Test of DifferenceOne variable

One-way chi-square

Two variables (1 IV with 2 levels; 1 DV) Two variables (1 IV with 2+ levels; 1 DV) Three or more variables

t-test

ANOVA

ANOVA

Summary Descriptive

stats summarize measures of central tendency and variability Inferential determine how likely it is that results based on sample are the same in population Must know level of measurement of variables to choose correct statistics

Parametric

and non-parametric two types of statistics requiring analysis of assumptions Pearson r, t tests and ANOVA examples of parametric Pearson r measure relationship or Association between 2 variables T test determines if there is a significant difference between 2 group means ANOVA determines if there is a