Basics Of Statistics

Basics of Statistics Descriptive Statistics Measure of central tendency Mean,Median,Mode Measure Of Variability Range,Variance,S.d

Inferential Statistics Estimation and Test of Hypothesis

Scale of Measurement Nominal scale Ordinal (Rank) Scale Interval scale Ratio scale

Type Of Variables Discrete variable Ex: Gender

Continuous Variable Ex: Yield, Height

Frequency Distribution Histogram for continuous Variables If it is Symmetrical Mean and if it is Skewed Median should be used as a measure of central tendency

Bar chart for discrete or categorical variables S.e and Confidence Interval

Test Of Hypothesis Null Hypothsis(h0) Alternate Hypothesis(h1)

Type I Error Type II Error One tail and two tail Test One tail test H0 : u1=u2 H1: u1 < u2 or u1 > u2 Two tail Test H0 : u1=u2 H1: u1 # u2

Parametric and non-Parametric tests Assumptions for Parametric Tests • Observations are drawn from Normal Population • The sets of data being compared have approximately equal variance. If the groups are of same size this assumption is not so important • The data is measured on an interval or ratio scale If the data does not meet the above assumptions we can apply non-parametric tests

Parametric and non-parametric tests Parametric tests Z test T test F test Chi-square test

Non-Parametric Tests 1. 2. 3. 4. 5. 6.

Chi-Square Run Test Rank correlation Wilcoxin Mann-Whitness Kruskal-wallis

Selecting the Appropriate Test If the data is of Frequency count Cross-tabulation of two categorical variables : Two sample Chi square More than two categorical variables : Log linear Analysis Comparison between Observed and Expected Fre. : One sample Chi-square

If the data is an interval or Ratio type Differences with single Hypothesis value : One sample t-test If the two sets of scores come from the same respondents : Paired t-test (Wilcoxin) With three or More : MANOVA (Fridman) If the two sets of scores come from different respondents : Independent t-test (Mann-whitness) Three or More : One-Way ANOVA (Kruskal-Wallis)

Relationship between Variables Two Variables More than Two variables

: Pearson Correlation : MLR

Multivariate Analysis • • • •

Multiple Linear Regression (MLR) Discriminant Analysis Cluster Analysis Factor Analysis