[06.03] Introduction to Statistics_ Inferential Statistics V2.1.pdf

Involves a characteristic about the population we target and the sample that we derive or collect

What does Statistical Inference involve?

Time and resource constraints and the need for information right away

What are the reasons researchers conduct sampling?

Gathering all information from the entire population (e.g., 120 million people divided by 5 into 25-30 million households) is difficult

Why is sampling necessary in censuses, which are conducted every 5 years?

Makes generalization from the result of the sample subjects to the general population

What is the main action of Inferential Statistics regarding sample results?

Whatever happens to the sample stays in the sample, or you do not sample at all because you are creating statistics from the population itself

What are the two possible outcomes if statistics are descriptive?

The target population

Where does the schematic diagram of the concepts of statistical inference begin and end?

A random sample

What is derived from the target population in statistical inference?

Information data

What is generated from the random sample in statistical inference?

Information

What is processed data called?

Statistics

What is obtained from processing data to information (small 's')?

The characteristics of your sample

What do small letter ‘s’ statistics represent?

The science and discipline of collecting, gathering and analyzing your information and data

What does capital letter ‘S’ Statistics represent?

The parameter

What does the statistics derived from the sample assume to represent?

The unknown parameter

What is the characteristic of your target population called?

Parameter Name, Population Parameter Symbol, Sample Statistic

What are the three columns in Table 1 regarding parameters and statistics?

N

What is the symbol for the number of cases in the Population Parameter?

n

What is the symbol for the number of cases in the Sample Statistic?

μ (mu)

What is the symbol for the Population Parameter mean?

x̄ (Sample mean)

What is the symbol for the Sample Statistic mean?

π (Pi)

What is the symbol for the Population Parameter proportion?

P (Sample proportion)

What is the symbol for the Sample Statistic proportion?

σ² (Sigma-square)

What is the symbol for the Population Parameter variance?

s² (Sample variance)

What is the symbol for the Sample Statistic variance?

σ (Sigma)

What is the symbol for the Population Parameter standard deviation?

s (sample standard deviation)

What is the symbol for the Sample Statistic standard deviation?

ρ (rho)

What is the symbol for the Population Parameter correlation?

r (Sample correlation)

What is the symbol for the Sample Statistic correlation?

β (beta)

What is the symbol for the Population Parameter regression coefficient?

b (sample regression coefficient)

What is the symbol for the Sample Statistic regression coefficient?

English letters (except number of cases)

What generally represents sample statistics in formulas?

Greek symbols

What generally represents population parameters?

Central tendency of a quantitative data

What does the mean measure?

Computing the percentage or proportion of a categorical variable

What is proportion used for?

Measures of variability or measures of dispersion of quantitative variables

What are variance and standard deviation?

Determine if there is a linear or strong relationship between two numerical or quantitative variables

What is the purpose of correlation?

A scatter plot

What graphical tool is used when performing correlation?

Regression

What statistical tool are coefficients later used for?

Estimation and Hypothesis Testing

What two main concepts of inferential statistics will the lecture focus on?

Using the sample statistics to represent an unknown parameter

What is the definition of Estimation?

To infer or generalize the sample statistic (e.g., mean BMI of 25.5) to the population parameter

What is the objective when estimating?

Point Estimation and Interval Estimation

What are the two types of estimation?

Calculation of a summary statistic from the sample that is used to estimate the value of the parameter of interest

What is Point Estimation?

Adaptation from the sample statistic or single point estimate to the parameter

What analogy is used to describe Point Estimation?

It will be adapted and assumed to be the same as the parameter mean (μ)

If you derive a sample mean (x̄) as a point estimate, assuming no bias, what is the inference?

Calculation of the range of values such that the parameter of interest is expected to be included in this range

What is Interval Estimation?

A measure of confidence (confidence interval)

What usually accompanies interval estimation?

We are unsure if we ‘hit the right spot’ or if we missed

Why do researchers create a range of values in interval estimation?

Interval Estimate = Point Estimate ± Margin of Error

What is the general equation for Interval Estimate?

μ = x̄ ± Zɑ/2 * (σ / √n)

What is the specific equation for the Interval Estimate of the population mean?

x̄

In the interval estimate equation for mean, what represents the point estimate?

Zɑ/2

In the interval estimate equation for mean, what represents the confidence level (Z-deviate)?

σ / √n

In the interval estimate equation for mean, what represents the margin of error?

Margin of error gets smaller

What happens to the margin of error if the sample size (n) is increased?

The variability will be less

What happens to the variability when interval estimation is done with a larger number of samples?

The confidence interval will be smaller

What happens to the confidence interval when interval estimation is done with a larger number of samples?

Symmetric data and more frequent near the mean

What two characteristics define a Normal distribution?

Almost all characteristics of the universe follow this probability distribution

Why do we study normal distribution?

Gaussian Distribution

What is another name for Normal distribution?

The z-score

What do the numbers -3 to 3 correspond to in the standard normal distribution graph?

For proportion and for means

For what two measures are the formulas for interval estimation different?

Standard deviation of the sample statistic

What is used to describe the error that is due to random chance?

Standard Error

What is the term for the standard deviation of the sample statistic?

Population parameter and sample size

What two factors does the Standard Error depend on?

(1-p)

What is the complement of p in the standard error formula for proportion, usually denoted as "q"?

Within 2 standard errors

In a normal distribution, 95% of sample statistics estimate the population parameters within what range?

Margin of Error

What is the term for the 95% range around the mean, representing 2 standard errors?

An interval that estimates the population parameter within a given value, usually 95%

What is the Confidence Interval?

A normal distribution model

What type of model do confidence intervals require?

At least 10 successes and failures

What condition is required for proportions to use a normal distribution model for confidence intervals?

Variable should be normally distributed OR sample size is more than 30

What two conditions are required for means to use a normal distribution model for confidence intervals?

-1.96 and +1.96

What are the actual z-score markers for the 95% confidence interval?

It gets narrower and more near to the mean

What happens to the accepted range of values when the confidence level is decreased (e.g., from 95% to 90%)?

Type 1 errors

What specific error increases when the confidence level is decreased (e.g., to 90%)?

It will show values for all the extreme data points and possibilities

Why is increasing the confidence level to extremes (e.g., 99.9%) not ideal?

It is unrealistic to interpret

What is the issue with interpreting an extreme confidence interval (e.g., 100%)?

p ± Zɑ/2 * √( (p(1-p))/n )

What is the interval estimate equation for Population Proportion?

The proportion vaccinated with BCG is between 84.3% and 91.7%

If a 95% interval estimate for BCG vaccination proportion is (0.843, 0.917), what is the interpretation?

The interval is narrow

If the standard error in a BMI interval estimate is low (<1), what does this imply about the interval?

The majority are within normal limits

What information does an interval estimate of population mean BMI (21.4 to 22.5) convey?

37% and 53%

If the 95% CI for the prevalence of hypertension is (0.372914 to 0.527086), what are the approximate percentage bounds?

Wide

How does Prof. Sto. Niño characterize the confidence interval (37% and 53%) for hypertension prevalence?

It suggests increasing sample size

What suggestion is made when the confidence interval is considered wide?

Standard error is not the same as standard deviation

What point does Prof. Sto. Niño repeatedly reiterate about standard error and standard deviation?

False

Is the statement "Point Estimation is a calculation of the range of values such that the parameter of interest is expected to be included in this range" True or False?

10%

90% confidence interval is equivalent to how many percent error?

A statement about the population, usually concerned with the parameters of the population

What is a Hypothesis?

Years of observation and researches

What may a hypothesis be formulated as a result of?

Is the population parameter equal to the hypothesized value?

What question does Hypothesis Testing answer?

To prove that a factor affects a particular outcome, and is not due to random error

What is the goal of hypothesis testing regarding factors and outcomes?

A set of procedures that leads to the rejection or non-rejection of a hypothesis

What is Hypothesis Testing?

To reject the null hypothesis

What is the usual objective in hypothesis testing when trying to establish a finding?

Tests for differences and tests for associations

What are the two common types of tests performed?

State the null hypothesis and alternative hypothesis

What is the first step in Hypothesis Testing?

Decide on the level of significance, ɑ

What is the second step in Hypothesis Testing?

Choose the appropriate alternative test statistic

What is the third step in Hypothesis Testing?

Determine the Critical Region

What is the fourth step in Hypothesis Testing?

Calculate the value of the test statistic and the p-value

What is the fifth step in Hypothesis Testing?

Make a statistical decision (using statistical programs)

What is the sixth step in Hypothesis Testing?

Draw conclusions about the population

What is the seventh step in Hypothesis Testing?

Descriptive statistics precede inferential

What type of statistics must precede inferential statistics?