soc data test 2

what is a normal curve?

bell shaped and symmetrical, mean, median, and mode are all at its peak

is the normal curve based on theory or real data?

Theory; real data approximates it.

what are the properties of normal distribution?

Symmetrical, bell-shaped, mean at peak, standard deviation changes the width

Where is the mean in a normal curve?

at the peak

What do standard deviations represent?

Distance from mean; larger SD = wider curve.

What is a Z score?

Number of SDs a score is from the mean.

Why is a Z score useful?

Finds probability, compares different distributions.

What is sampling? Why do we do it?

Selecting a subset from a population to study; saves time and resources.

what is a population

Entire group of interest.

what is a sample

Subset of the population.

what is a parameter

Value describing a population.

what is a sample statistic

Value describing a sample.

what is random sampling

Every member has equal chance of selection.

what is systematic sampling

Selects every Nth member after a random start.

what is stratified sampling

Population divided into subgroups, then sampled.

what is proportionate stratified sample

Sample size matches subgroup proportion in population.

what is sampling distribution

Theoretical distribution of all possible sample values.

what is sampling error

Difference between sample statistic and population parameter.

what is the central limit theorem

As sample size increases, the sampling distribution becomes normal. Larger sample size → smaller standard error (less variability).

What is estimation?

Using a sample statistic to estimate a population parameter.

What is the main goal of sampling theory and statistical inference?

To use sample data to make generalizations about a population.

What is a point estimate?

A sample statistic that estimates the exact value of a population parameter.

What is a confidence interval?

A range of values likely to contain the population parameter.

What does a 95% confidence interval mean?

There is a 95% probability that the interval contains the population mean.

What is a margin of error?

The range around a point estimate that accounts for sampling variability.

What confidence level is commonly used?

95% is standard, but 90% or 99% may be used depending on precision needed.

How can a researcher increase the precision of their estimate?

Increase sample size to reduce standard error.

What is statistical hypothesis testing?

Evaluating hypotheses about population parameters using sample statistics.

What are the assumptions of hypothesis testing?

Random sampling, interval-ratio level measurement, and normality (via CLT).

What is the research hypothesis (H₁)?

A claim that the population parameter differs from a specified value.

What is the null hypothesis (H₀)?

A statement of no difference, contradicting the research hypothesis.

What is a one-tailed test?

Tests for an effect in one direction (left or right tail).

What is a left-tailed test?

Tests if the sample outcome is in the left tail of the distribution.

What is a right-tailed test?

Tests if the sample outcome is in the right tail of the distribution.

What is a two-tailed test?

Tests for differences in both tails of the distribution.

What is a Z statistic?

a sample statistic converted into a Z score.

What is a p-value?

The probability of obtaining the test statistic under H₀.

What is alpha (α)?

The probability threshold for rejecting H₀ (e.g., .05, .01, .001).

What are the 5 steps of hypothesis testing?

1. Make assumptions
   2. State hypotheses, select α
   3. Choose distribution, test statistic
   4. Compute test statistic
   5. Make a decision, interpret results

What is a t statistic?

A test statistic used when the population standard deviation is unknown.

When do we use a t statistic instead of a z statistic?

When the population standard deviation is unknown and estimated from the sample.

What is the t distribution?

A family of curves based on degrees of freedom, used for small samples.

What is a Type I error?

Rejecting a true null hypothesis (false positive).

What is a Type II error?

Failing to reject a false null hypothesis (false negative).

Why is the t test useful?

Compares groups, such as gender or racial income differences.

What is bivariate analysis?

A method to detect and describe relationships between two variables.

What is cross-tabulation?

A table-based technique to analyze relationships between two categorical variables.

What is a bivariate table?

A table showing the distribution of one variable across categories of another.

What is a column variable?

The independent variable, shown in the table’s columns.

What is a row variable?

The dependent variable, shown in the table’s rows.

What is a cell in a bivariate table?

The intersection of a row and a column, showing the count or percentage.

What are marginals in a bivariate table?

The totals for rows and columns in a table.

How do you measure the strength of a relationship?

By examining the percentage difference across the categories of the independent variable.

What is a positive relationship?

When both variables increase or decrease together.

What is a negative relationship?

When one variable increases while the other decreases.

What is elaboration?

A process that introduces control variables to analyze a bivariate relationship.

What are control variables?

Additional variables used to test or clarify a relationship.

What are the three goals of elaboration?

1. Test for non-spuriousness
2. Clarify causal sequence
3. Identify conditions affecting the relationship

What is a spurious relationship?

When both variables are influenced by a third variable, with no direct causal link.

What is an intervening variable?

A variable that comes between the independent and dependent variable in a causal sequence.

What is a conditional relationship?

When the effect of the independent variable on the dependent variable depends on a control variable.

How do you test for non-spuriousness?

Introduce a control variable; if the original relationship remains after controlling for it, the relationship is non-spurious.