Introduction to Statistics

Introduction to Statistics

StatisticsStatistics is the science of the CollectionOrganization interpretation of data.

Uses of Statistics

1) Statistics helps in providing a better understanding and exact description of a phenomenon of nature. (Patients reactions towards novice nurses).(2) Statistics enable proper and efficient planning of a statistical inquiry in any field of study. (Is vitamin C effective in preventing cold )

(3) Statistics helps in collecting an appropriate quantitative data.(4) Statistics helps in presenting complex data in a suitable tabular, diagrammatic and graphic form for an easy and clear comprehension.(5) Statistics helps in understanding the nature and pattern of variability of a phenomenon through quantitative observations. (What are the important risk factors for heart disease, for bone cancer, for cot (crib) death?)

(6) Statistics helps in drawing valid inference, along with a measure of their reliability about the population parameters from the sample data.

Example:4 out of 5 dentists recommend DentyneAlmost 85% of lung cancers in men and 45% in women are tobacco-related.Condoms are effective in 94% of the time.

Statistical analysis: Purposes of statistical analysisTo summarize the large data in to understandable and meaningful form. Ex :.79.48% of all statistics are made up on the spot.

It exactly describes the data by using percentages and frequencies. Ex. There is an 80% chance that in a room full of 30 people that at least two people will share the same birthday.It promotes for identification of causal factors underlying complex phenomena by using inferential statistics.Data are collected and analyzed in order to predict or make inferences about situations that have been measured in full. It helps in making generalizations of the results from the collected data.

Levels / scales of measurement

Nominal Level: lowest level of measurement. Data can be placed in two or more classes or categories which are in descriptive form. Nominal data are categorized with different names for different groups as gender, blood type, and marital status. These categories are discrete and non continuous . The numeric codes are assigned for the decoding and describing the data like we classify males as 1 and females as 2.

Example: Sex Boy Girl Male Female Religion Hindu Muslim Christian etc. Activity Active Non ActiveExample: Census data of 678 villages:Census dataMenWomen197119813002161200378896825612The Ordinal Level Measurement

The second or ordinal level of measurement is characterized by variables that are assessed incrementally. For example: 1. Pain can be measured as slight, moderate, or intense. 2. Exercise can be measured in terms of frequency that is, often, sometimes, or never.

these intervals cannot be considered equal. It shows level of ranking there is no implication of equal distances between groups on scale.values of variables can be rank-ordered from highest to lowest

A ranking of patient behaviors accordingly to how often they occur during a given period.Example: Always, mostly, sometimes, rarely and never..Other variables that can be used as ordinal data: Depression, skin turger, helplessness, grief, stress, confusion, nausea, self-esteem, hope Ordinal data is used for graphical presentation

Example 1. Choice of screening among men & women:

ANDMenEg:5040302010ANDWomenBi variate dataExample: 2. Assessing nursing care , categories are ranked in order from highest, quality care to very poor care ranking from 1 to 5

12345Care is of highest, quality, could not be better.Care very good a few things could be improved but for most part time.Average care no better or worse than could be expected.Care is below average some services below poor.Very poor care, many services could be improved.The interval or ratio data can be converted into ordinal data.Example: 81 to100 Excellent 61 to 80 Good 41 to 60 Average. 21 to 40 Poor Below 21 Very poor data can be categorized in rank order cannot add up the categories or get mean or average. can compute percentiles and rank order correlation.

The Interval Level of Measurement: This level is quantitative in nature. Increments on the scale can be measured, and they are equidistant does not have an absolute or actual zero.

Between a temperature of 97 and 100 degrees Fahrenheit, there are three equal increments of one degree each. The interval between 10 degree F and 5degree F, or 10 5 = 5.

20Ratio Level of Measurement :- highest level of data The ratio level has a meaningful zero point. all arithmetic operations are permissible. One can meaningfully add, subtract, multiply, and divide numbers on a ratio scales. All the statistical procedures suitable for interval level data are also appropriate for ratio level data. Obvious ratio scales include time, length, and weight.

Ex: Monthly Income and occupational Back ground of respondents:Monthly Farmer Carpenter Black SmithTotal4001 5000 10 51163001 4000 70 35321372001 3000 15 3047922000 & less 10 2035 Total: 100 80 100 280

Measurement levels Weight RatioSex NominalEmotional status OrdinalBody temperature Interval

TYPES OF STATISTICS descriptive: describes what the data inferential statistics: to reach conclusions

Descriptive Statistics

to describe the basic features of the data in a study. numbers, percentages, averages (mean) or indication (variability and the relation ship among two sets of data (correlation). a population/parameters samples (or subsets) / statistics.

Types of Descriptive statistics The distribution : Frequency distribution, percentageMeasures of central Tendency: mean, median, mode.Measures of Variability: range, SD , average deviation and inter quartile rangeMeasures of relationship between 2 or more variables: correlation coefficient.

The Mean or average is probably the most commonly used method of describing central tendency.The Median is the score found at the exact middle of the set of valuesThe mode is the most frequently occurring value in the set of scores.

3. Measures of variability :- describe how spread out values is in a distribution of values. Range: The distance between the highest and lowest value in a group of values are called the range.Standard Deviation: This statistic describes how values vary about the mean of the distribution.

The quartile range: It determines the inter-quartile range, the score at the 25th percentile is subtracted from the score at the 75th percentile

The variance: It is the average of the squared differences of each score from the mean.

4 Measures of Relationship: Correlations are computed to determine how one variable on another variable. The Correlation co-efficient can vary between -100 and +100. These two numbers represent the extreme of perfect relationship. A Correlation co-efficient of -100 indicates a perfect positive relationship and 0.0 indicates the absence of any relationship.

Calculated by degree of relation between two variables.Charles Spearmans co-efficient of correlation determines the extent to which the two Karl Persons coefficient of correlation (or) simple correlation: measures the sets of ranking are similar or dissimilar.

Inferential statistics

For example: A Board of Examiners may want to compare the performance of 1000 students those completed an examination. Of these, 500 students are girls and 500 students are boys. The 1000 students represent our "population". Uses of Inferential statistics can:Provide more detailed information than descriptive statisticsInvestigate differences between and among groups.Yield insight into relationships between variablesReveal causes and effects and make predictionsGenerate convincing support for a given theoryLevel significance helps in applying the results to populationGenerally accepted due to widespread use in business and academics

Two areas of statistical inference. 1.Estimation 2.Hypothesis testingI step: Estimation of standard error of mean because sample distribution have some error as estimates of the population mean in order to make generalization with the study resultsThere are two types of errors: Type I error: Accepting experimental hypothesis when null hypothesis is true.Type II error: Accepting null hypothesis when experimental hypothesis is true

II step: Apply specified test:

Features of Null Hypothesis

III step : Probability:

ExampleWhat is probability of getting heads when you flip a coin?What is probability of rolling a 4 with a die?What is probability of not rolling a 4?

IV step Confidence levels:

Types of Inferential Statistics

Parametric major ones used if sample size large, used when the data is in interval and ratio level.

Nonparametric (less powerful) used with small sample size when data is at nominal, ordinal level of measurement

Parametric tests1. ANOVA 2. ANCOVA Non-Parametric tests1. Chi-square 2.Mann-Whitney u test: 3.Sign test:4.Median test: DESCRIPTIVE STATISTICSTypes of Descriptive statistics The distribution : Frequency distribution, percentageMeasures of central Tendency: mean, median, mode.Measures of Variability: range, SD , average deviation and inter quartile rangeMeasures of relationship between 2 or more variables: correlation coefficient.

Frequency distribution:

Example:Frequency distribution table (Only tells about number of sample fall into each category)

Percentage distribution table (Total no. of sample distribution per 100)

Frequency distribution - Unvaried table

Frequency Distribution of Weights by Age n=100

Wt in kgsF%80-84303075-79505070-741818