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Social Statistics and Data Analysis-Lecture 12-Sociology-Dr David Hall, Lecture notes of Social Statistics and Data Analysis

Nipissing University Social Statistics and Data Analysis

From Descriptive to Inferential Statistics.Inferential Statistics, Descriptive Statistics, Normal Curve, Sampling distribution, Central Limit Theorem, Mean, Mode, Median, Statistical Estimation, Confidence Intervals,Social Statistics and Data Analysis, Lecture Slides, Sociology, Dr David Hall, Nipissing University, Canada

Typology: Lecture notes

2011/2012

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From Descriptive to Inferential

Statistics….

•Tables, Graphs, & Measures of Central

Tendency/ Variability are Descriptive

Statistics.

•Inferential Statistics estimate population

characteristics, test hypotheses, & measure

relationships.

•The Normal Curve (and standard scores)

link up descriptive & inferential

statistics….and add to the interpretation of

the standard deviation.

Partial preview of the text

Download Social Statistics and Data Analysis-Lecture 12-Sociology-Dr David Hall and more Lecture notes Social Statistics and Data Analysis in PDF only on Docsity!

From Descriptive to Inferential

Statistics….

Tables, Graphs, & Measures of Central Tendency/ Variability are Descriptive Statistics.
Inferential Statistics estimate population characteristics, test hypotheses, & measure relationships.
The Normal Curve (and standard scores ) link up descriptive & inferential statistics….and add to the interpretation of the standard deviation.

Key aspects of the normal curve:

Normal curve is symmetrical or bell-shaped.
Average ( mean ) is the most frequently occurring value ( mode ), & the value that

splits the distribution in half ( median )… so

that 50% of the cases have values

greater than the mean, and 50% of the

cases have values lower than the mean

(Mean = Mode = Median).

Assuming a variable is normally distributed we can say more about the standard deviation.

If the mean IQ is 100 and the standard deviation is 25 , 34% of our 1000 cases ( 340 people ) will have IQs between 75 & 100 ; 34% ( 340 people ) will have IQs between 100 & 125 ; and 68% ( people) will have IQs between 75 & 125 …. within 1 standard deviation of the mean.

Only 2.1% or 21 people have IQs between 150 & 175 (2- 3 standard deviations above mean), while another 2.1% or 21 people have IQs between 50 & 25 (2-3 standard deviations below mean). Adding everything up (2.1 + 13.5 + 34.1 + 34.1 + 13.5 + 2.1) we can see that 99% of our sample of 1000 ( people) have IQs between 25 & 175….or within 3 standard deviations of the mean IQ of 100!

The percentages associated with areas under the normal curve can also be interpreted as probabilities !!!

z = standard score Xi = any raw score or value Xbar = sample mean S = sample standard deviation

Why convert original values or scores on

a variable into standard scores?

1. Converting variable scores into

standard scores allows us to compare

original scores from different

distributions.

2. Converting variable scores into

standard scores allows us to express

variable scores in probabilities.

Statistical Estimation

“A poll found 31% of voters would support the Liberals if an election were held today, 35% would vote for the Conservatives, 15% for the NDP. The remainder of those polled

were undecided. The results are based

on a sample of 1000 respondents and

are accurate to within 5 percentage

points 99 times out of 100.”

And surveys are not just limited to political polling. A survey of sex in the U.S. found that:

“The average number of times per week that a married couple have sex is 2.3 times per

Social Statistics and Data Analysis-Lecture 12-Sociology-Dr David Hall, Lecture notes of Social Statistics and Data Analysis

Related documents

Partial preview of the text

Download Social Statistics and Data Analysis-Lecture 12-Sociology-Dr David Hall and more Lecture notes Social Statistics and Data Analysis in PDF only on Docsity!

From Descriptive to Inferential

Statistics….

splits the distribution in half ( median )… so

that 50% of the cases have values

greater than the mean, and 50% of the

cases have values lower than the mean

(Mean = Mode = Median).

Why convert original values or scores on

a variable into standard scores?

1. Converting variable scores into

standard scores allows us to compare

original scores from different

distributions.

2. Converting variable scores into

standard scores allows us to express

variable scores in probabilities.

Statistical Estimation

were undecided. The results are based

on a sample of 1000 respondents and

are accurate to within 5 percentage

points 99 times out of 100.”

week. The results are accurate to plus

or minus .2 sex acts 99 times out of