Basic statistics cut.ppsx

Basic statistics cut.ppsx

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  BASIC STATISTICS By Vishnu AchuthaMenon Research Scholar Department of Media and Communication CUTN
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  Basic Terms andDefinitions ⚫Descriptive Statistics - are the methods that help collect, summarise, present and analyse a set of data. ⚫Inferential Statistics - are methods that use the data collected from a small group to draw conclusions about a larger group. Jayanth Jacob, DoMS, Anna University 2
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  Basic Terms -Contd ⚫A variable is a characteristic of an item or individual ⚫Data are different values associated with a variable. ⚫Variable values are meaningless unless their corresponding variables have operational definitions. These definitions are universally accepted meanings that are clear for the analysis and the objective. Jayanth Jacob, DoMS, Anna University 3
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  Basic Terms -Contd ⚫A population consists of all the items or individuals about which we want to draw a conclusion. ⚫A parameter is a measure that describes a characteristic of a population. Jayanth Jacob, DoMS, Anna University 4
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  Basic Terms andDefinitions ⚫A sample is the portion of a population selected for analysis ⚫ A statistic is a measure that describes a characteristic of a sample. Jayanth Jacob, DoMS, Anna University 5
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  Basic Terms -Contd ⚫Degrees of Freedom (df) ◦ df = Total no of observations – Number of estimated parameters ◦ Lower df lesser predictability ⚫Level of Significance (α) ◦ Probability of wrongly rejecting null hypothesis H0, when it is true ◦ Generally chosen to be 0.05 (5%) Jayanth Jacob, DoMS, Anna University 6
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  Steps in Research(DCOVA) ⚫Define the variables for the study ⚫Collect the data from appropriate sources ⚫Organize the data collected by developing tables ⚫Visualize the data through charts ⚫Analyze the data by examining the relevant charts and tables to draw inferences. Jayanth Jacob, DoMS, Anna University 7
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  Types of Variables ⚫Categorical/Qualitativevariable ◦ Nominal variable ◦ Dichotomous variable ◦ Ordinal variable ⚫Continuous variable ◦ Interval variable ◦ Ratio variable Jayanth Jacob, DoMS, Anna University 8
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  Types of Analysis ⚫Univariateanalysis ◦ Single variable in terms of the applicable unit of analysis ⚫Bivariate analysis ◦ Analysis of two variables ◦ Covariance is a measure to see if the variables are related to one another ◦ Help in testing simple hypotheses of association ⚫Multivariate analysis ◦ Analysis of more than one statistical outcome variable at a time Jayanth Jacob, DoMS, Anna University 9
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  Variance ⚫Variance measures howfar a set of numbers is spread out. A variance of zero indicates that all the values are identical. Variance is always non-negative: a small variance indicates that the data points tend to be very close to the mean (expected value) and hence to each other, while a high variance indicates that the data points are very spread out around the mean and from each other. Jayanth Jacob, DoMS, Anna University 10
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  Homoscedascity and Heteroscedascity ⚫In statistics,a sequence of random variables is homoscedastic if all random variables in the sequence have the same finite variance. This is also known as homogeneity of variance. The lack of homogeneity of variance results in heteroscedasticity. Jayanth Jacob, DoMS, Anna University 11
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  p-value ◦ Probability ofobtaining a test statistic result at least as extreme as the one that was actually observed ◦ p ≤ 0.01 very strong presumption against H0 ◦ 0.01 < p ≤ 0.05 strong presumption against H0 ◦ 0.05 < p ≤ 0.1 low presumption against H0 ◦ p > 0.1 no presumption against H0 Jayanth Jacob, DoMS, Anna University 12
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  Hypothesis ◦ A proposedexplanation for a phenomenon ◦ Null Hypothesis H0 ◦ Alternate Hypothesis H1 ●One-tailed directional ●Two-tailed directional Jayanth Jacob, DoMS, Anna University 13 ERROR TYPE H0 H1 I True but rejected False but accepted II False but accepted True but rejected
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  Chi-Square Test ⚫Used toassess two types of comparisons ◦ Test of goodness of fit ◦ Test of independence ⚫Assumptions ◦ Simple random sample ◦ Sample size ◦ Expected cell count ◦ Independence Jayanth Jacob, DoMS, Anna University 14
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  Analysis of Variance(ANOVA) ⚫Test whether there are any significant differences between the means of two or more independent groups ⚫Assumptions ◦ DV – interval or ratio scale ◦ IDV – two or more categorical variable ◦ Independence of observation ◦ No significant outliers ◦ DV normally distributed (Shapiro-Wilk test) ◦ Homogeneity of variance (Levene's test) Jayanth Jacob, DoMS, Anna University 15
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  Independent t-test ⚫Compares themeans between two unrelated groups on the same continuous, dependent variable ⚫Assumptions ◦ DV – interval or ratio scale ◦ IDV – two or more categorical variable ◦ Independence of observation ◦ No significant outliers ◦ DV normally distributed ◦ Homogeneity of variance (Levene's test) Jayanth Jacob, DoMS, Anna University 16
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