Applied Research Quiz 2

2/4 

Level of measurement

• Nominal - (lowest level of measurement) asking questions that cannot be ranked, can level it from low to high, only naming them

  • It must be made into new variables 

  • ex - color, gender, marital status, race, college major

  • Always discreet

  • Some are dichotomies 

• Ordinal variable - can rank it from low to high, but rank only, no other information 

  • ex. - not a discrete answer/ number like 3 meaning a couple times a month instead of 3 being the actual number

  • Always discreet 

  • Can be ranked or ordered 

• Interval ration - rank plus more, true 0 and knowable interval width, info between answers is more known

  • True zero point means we have an actual number  

  • Could be continuous or discrete 

The theory and logic of probability sampling 

• General term for samples selected in accord w probability theory

• Often used for large scale surveys 

• If all members of population were identical in respects there would be no need for careful sampling procedures, this is rarely the case 

• Sample of individuals from population must contain same variations that exists in the 

Population and sampling frames 

• Sampling frame would be the identifier for understanding the population, 

  • like ID numbers for all usc students, drivers licences, telephone numbers 

  • List of elements to closely approximate population  

• Population - pool from which sample is selected (targeted) 

  • All married people in the US 

  • All people born during the depression 

• Populations are abstract, need to estimate them

• Population parameters 

  • Summary description of a given 

• Statistic - the summary description of a variable in sample, used to estimate a population parameter 

Importance of randomization 

• Essential for replying on probability ]each sampling element has equal chance of being selected 

• Increases representativeness of the sample 

• Also allows for sampling error to be calculated 

  • Gap between sample results and pop. parameter 

• Types of randomized sampling methods 

  • Simple random 

  • Systematic 

  • Stratified 

  • Cluster (will have the most errors) will be on the quiz

• All of these samples will have errors, although clusters will have the most 

• Simple random sample 

  • Select cases randomly from sampling frame 

  • Randomly selected w no pattern 

• Systematic sample 

  • Randomly selected by the first one, and then the others after are selected in a variation 

    • Example: every 10th person from a directory 

• Yields the same results are simple random  

• Stratified sample 

  • Used for race to be able to get a little piece of every race

  • Divide the population into subpopulation/ strata

    • Strata usually based on some important characteristic 

    • Randomly selected cases from each strata

• Good for including proportionally small groups  

• Cluster sample 

  • More geographic

    • City block, county

  • Randomly select a cluster, then you randomly select from within that cluster 

    • Test he elements within the cluster, which keeps introducing more rounds 

  • Always has at least 1 more round of sampling 

    • This introduces another round of error 

  • Less accurate that simple random sampling and other forms because it introduces error every rounds it undergoes 

  • More clusters are better 

• Sample sizes

  • The larger the population is, the smaller the sampling ratio needs to be 

  • Larger samples are important if 

    • More accuracy is needed

    • Population is more heterogeneous 

    • More variables will be modeled

    • Subgroups will be analyzed 

• draw inferences

  • One of the key functions of sampling 

  • Smaller sampling error when sample is 

    • Larger 

    • More homogenous   

    • The larger the sample size leads to a smaller sample error, it narrows a confidence intervals  

• Central tendency, levels of measurements are about variables themselves 

  • Mode - least informations given, provides the common response, goes with nominal variables 

  • Median - the middle score, for ordinal variables 

  • Mean - interval ratio variables, every value of single scores are used to evaluate

• Mode 

  • Good for quick info

  • For nominal 

• Median 

  • Exact midpoint of the 2 middle cases 

• Mean 

  • Typical score 

  • Be aware of: 

    • Numerical middle meaning the value of all the scores have a mean 

    • The mean is affected by every score 

  • You anticipate additional statistical analyses 

• Dispersion : standard deviation 

  • Tells us that the mean can't 

  • Smaller the standard deviation the more similar the variables will be

Levels of Measurement:

• Nominal: Lowest level, categories that cannot be ranked (e.g. color, gender). Discreet variables only.

• Ordinal: Variables that can be ranked but don't specify the magnitude of difference (e.g. satisfaction ratings). Discreet and ordered.

• Interval Ratio: Incorporates ranking, true zero, and knowable intervals; can be continuous or discreet and provides comprehensive information between values.

Probability Sampling:

• A method where samples are selected according to probability theory, essential for large-scale surveys.

• Ensures all population variations are represented. Randomization is crucial for representativeness and allows for sampling error calculation.

Sampling Techniques:

1. Simple Random Sampling: Random selection from a sampling frame, equal chance for all.

2. Systematic Sampling: Begins with a random selection, followed by sampling at regular intervals (e.g., every 10th person).

3. Stratified Sampling: Divides the population into strata based on characteristics, ensuring small groups are represented.

4. Cluster Sampling: Randomly selects clusters (e.g., geographic areas) and samples within them, leading to higher error due to multiple rounds of selection.

Importance of Sample Size:

• Larger samples reduce sampling error and increase representativeness, essential for heterogeneous populations.