References: Ymas, S.E. & Dayrit, B.C. (2012). College statistics with computer applications. Manila: Ymas Publishing House Mendenhall, W., Beaver, R.J., & Beaver, B.M. (2013). Introduction to probability and statistics. [14th Ed.]. Boston: Brooks/Cole
DESCRIPTIVE STATISTICS 1. Levels of Measurement *There are two types of data: quantitative and qualitative. *Qualitative Data may be Nominal or Ordinal. These are discrete data. *Quantitative Data may be Interval or Ratio. These may be discrete or continuous, but most often continuous. *NOMINAL Data – these are names or categories (ex. Gender) *ORDINAL Data – these are ranks or hierarchy (ex. Level of Customer Satisfaction) *INTERVAL Data – these are actual amounts. Zero (0) is just a place holder. (ex. age, a person with an age of “0” is not a person because he is not alive) *RATIO Data – these are values where zero (0) has meaning (ex. 0 votes in an election means the candidate did not get any vote) 2. Measures of Central Tendency *These are descriptions of the central point of a given data set. They show the middle value of a set of data. *For a data said to be of normal distribution, the mean, median, and mode are EQUAL. *Mean – average of the data. Used for INTERVAL/RATIO *Median – the center of the data. Used for ORDINAL *Mode – the highest occurring data. Used for NOMINAL 3. Measures of Variation *These are descriptions of how “far” given data are from one another. They show “scatteredness” of a set of data. *Range *Interquartile Range *Mean Deviation *Variance *Standard Deviation – most important *Coefficient of Variation *To interpret: -The larger the measure of variation, the more scattered a set of data is. The data are highly variable. The set is then considered heterogenous. -The smaller the measure of variation, the less scattered a set of data is. The data are less variable. The set is then considered homogenous. INFERENTIAL STATISTICS STATISTICAL TESTS and HYPOTHESIS TESTING Purpose of Hypothesis Testing: to make a judgement of the difference between the sample and the population. *Statistic – a value that describes the Sample *Parameter – a value that describes the Population *When the statistic has no significant difference from the parameter, the sample is representative of the population. *When the statistic has a significant difference from the parameter, the sample is not representative of the population. 1. Parts of a Statistical Test
a. Null Hypothesis: implies “there is no significant difference between variables” b. Alternative Hypothesis: implies “there is a significant difference between variables” 2. Errors in Conclusions a. Type I Error ( error): rejecting the null hypothesis when it should be accepted b. Type II Error ( error): accepting the null hypothesis when it should be rejected 3. Statistical Significance a. Level of Significance (): the maximum possibility of rejecting the null hypothesis when it is true. *For example, a level of significance of 0.05 means that the possible error we make in concluding about a hypothesis is only 5%. Therefore, we are 95% confident all the time that a certain relationship is true. *The lower the level of significance, the higher the possibility of getting an accurate observation. *Usually: = 0.05 in behavioral/psychological, epidemiological, sociological studies = 0.01 in RCTs, experimental, investigational studies b. P-value: the possibility of having a result that is as extreme as or too extreme than a set value *To interpret: -If the p-value is lower than the , reject the null hypothesis -If the p-value is higher than the , accept the null hypothesis -p-value is < 0.01 – reject the null hypothesis because the results are highly significant -p-value is between 0.01 to 0.05 – reject the null hypothesis because the results are moderately significant -p-value is between 0.05 to 0.10 – accept the null hypothesis because the results are moderately insignificant -p-value > 0.10 – accept the null hypothesis because the results are highly insignificant *For example, a study has an = 0.05. The results revealed a p-value of 0.04. It means that the maximum possible error is 5% (because is 0.05); since the p-value is less than , the decision should be to reject the null hypothesis. 4. Interpretation of Results of Statistical Tests a. If the computed value is GREATER THAN the tabulated value at a given degree of freedom and level of significance, reject the null hypothesis. There is a significant difference. b. If the computed value is LESS THAN the tabulated value at a given degree of freedom and level of significance, accept the null hypothesis. There is no significant difference. 5. Statistical Tests PARAMETRIC TESTS When to use Parametric Tests: a. The sample size is relatively small (each sample consists of 30 members or less). b. The sample must have been randomly selected. c. The population from which the sample has been obtained should be of normal
Conditions of the Data Under Consideration
NON-PARAMETRIC TESTS When to use Non-Parametric Tests: a. The sample size is relatively large (each sample consists of more than 30 members). b. The samples were not randomly selected. c. The population from which the sample has been obtained has a large
distribution (variability is small). d. Standards of observation over a population are set.
1. Z Test 2. T Test (Dependent)
3. T Test (Independent)
4. ANOVA/F-Test One Dep Variable: One Way Two Dep Variable: Two Way 5. Chi Square 6. Pearson’s Correlation Coefficient
One Sample (General) One/Two Samples (With Correlation; Dependent Groups) Two Samples (Without Correlation; Independent Groups) Several Samples
Categorical Samples (NOMINAL DATA) Relationship Between Variables
variability. The standard of observation is arbitrary, or researcherdependent.
1. (No Equivalent) 2. Wilcoxon Rank Sum Test Wilcoxon Rank Signed Test (ORDINAL DATA) 3. Mann-Whitney U Test
4. Kruskal-Wallis Test
5. Chi Square 6. Spearman’s Correlation Coefficient