Descriptive Statistics Quiz

Descriptive Statistics

• This unit focuses on relating population and sample to scientific inquiry for problem-solving.
• It involves computing sample sizes from given populations.
• Different sampling techniques and their properties are differentiated.
• Differentiating data collection techniques based on procedure, data reliability, ethical concerns, and resources, is also covered.
• Understanding how to construct various graphs, using MS Excel, is addressed.
• Measures of central tendency, variation, and location need to be calculated using scientific calculators for both ungrouped and grouped data.
• Frequency distributions, histograms, polygons, and ogives are to be constructed using graphing paper.
• Appropriate correlation techniques for determining relationships between variables are explored.

Definition and Importance of Statistics

• Statistics are both numerical data and a scientific investigation process.
• The investigation process involves collecting, organizing, presenting, analyzing, and interpreting data.

Sampling Techniques

• Probability Sampling includes Simple Random Sampling, Systematic Sampling, Cluster Sampling, and Stratified Sampling.
• Non-Probability Sampling includes Purposive Sampling, Quota Sampling, and Convenience Sampling.

Sampling Techniques Detail

• Simple Random Sampling: Elements are selected randomly without a specific order.
• Systematic Sampling: Elements are selected using a fixed interval (e.g., every 10th element).
• Cluster Sampling: The population is divided into clusters, and a random sample of clusters is chosen.
• Stratified Sampling: The population is divided into strata, and a sample is taken from each stratum.
• Purposive Sampling: Researcher selects elements based on specific criteria.
• Quota Sampling: Researcher ensures certain characteristics are proportionally represented in the sample.
• Convenience Sampling: Samples are selected based on ease of access.

Simple Random Sampling (Lottery method)

• Number each element in the population.
• Create slips of paper representing each number.
• Randomly select the desired number of slips.

Simple Random Sampling (Electronic Method)

• Number each element in the population.
• Use a calculator to generate random numbers.

Systematic Sampling (Method 1)

• Select a starting point.
• Choose elements at a constant interval.
• Continue until the desired number of samples is reached.

Sampling Methods (Method 2)

• Number each element in the population.
• Decide on a time interval or specific location.
• Collect elements based on the interval/location.

Cluster Sampling (Method 1)

• Divide population into clusters
• Randomly select clusters to form sample

Cluster Sampling (Method 2)

• Divide population into clusters based on specified criteria.
• Randomly choose clusters for samples
• Collect members from the selected clusters

Stratified Sampling

• Divide Population into homogeneous groups (strata)
• Randomly draw proportionate samples from each stratum.

Multi-stage Sampling

• Multiple stages of sampling (e.g., regions, provinces, barangays)

Data Collection Techniques

• Direct Methods: Interview, Observation, Experiment
• Indirect Methods: Questionnaire, Registration

Nominal Variables

• Categorical values (e.g., gender, colors)

Ordinal Variables

• Ranked values with meaningful order (e.g., rankings, satisfaction levels)

Interval Variables

• Numerical values with equal intervals but no true zero (e.g., temperature)

Ratio Variables

• Numerical values with equal intervals and a true zero point (e.g., height, weight)

Quantitative Variables

• Numerical values that can be measured.

Qualitative Variables

• Non-numerical values that can be categorized.

Discrete Variables

• Numerical values that can only take on whole number values (e.g., number of students)

Continuous Variables

• Numerical values that can take on any value within a given range (e.g., height, weight)

Measures of Central Tendency

• Mean: Average of a set of scores.
• Median: Middle score in a sorted set.
• Mode: Most frequent score(s) in a set.

Measures of Variation

• Standard Deviation: Average measure of how spread out the scores are from the mean.
• Variance: The average of the squared differences from the mean.
• Quantiles (Quartiles, Deciles, Percentiles): Values that divide a distribution into equal parts.

Correlation

• Used to determine the degree of association between two variables.
• Correlation coefficient (r) indicates the strength and direction of the relationship.

Inferential Statistics

• Used to draw conclusions about a population based on sample data.
• Including hypothesis testing, symbolic representation of hypotheses, and hypothesis testing procedures for diverse data types are included.

Hypothesis Testing

• Formulating null and alternative hypotheses.
• Selecting a significance level.
• Determining the appropriate test statistic.
• Computing the test statistic.
• Comparing the computed value to the critical value.
• Drawing conclusions with respect to the null and alternative hypotheses.

Test Statistics

• z-test: Used for large sample sizes when population variance is known.
• t-test: Used for smaller sample sizes when population variance is unknown.

Repeated t-test: One-way ANOVA (Analysis of Variance)

• To determine if there is a significant difference on the means of three or more groups.

Post Hoc Tests for ANOVA

• Scheffe's test.

Significance of Correlation Coefficient

• Assessing if the degree of relationship is statistically significant.