A232 SMS3123 ASSIGNMENT 1 (PART 1) Statistics DESCRIPTIVE Statistics Descriptive statistics is a concise informative coefficients that summarise a particular data collection, which might represent the full population or a subset of it. 2 types of data which is Quantitative and Qualitative data Measures include mean, median, mode, range, variance, and standard deviation. INFERENTIAL Statistics Involves making inferences or predictions about a population based on a sample from that population Utilizes probability theory and hypothesis testing. POPULATION The entire group that is the subject of interest. All individuals, items, or data under study. SAMPLE A subset of the population. Used to make inferences about the population. RANDOM SAMPLE A sample where each member of the population has an equal chance of being selected. Minimizes bias and ensures representativeness. Examples of random sampling: Simple, Stratified, Cluster, Systematic NON- RANDOM SAMPLE Method of selecting units from a population using a subjective (i.e. nonrandom) method. Fast, easy, and inexpensive way of obtaining data Examples of nonrandom sampling: Snowball, Convenience, Purposive RANDOM VARIABLE A variable is a characteristic under study that assumes different values for different elements. due to randomness where it can be discrete or continuous. Example: outcomes of a coin toss, heights of individuals in a population. HYPOTHESIS TESTING A statistical method used to make inferences about a population parameter based on sample data. Involves formulating null and alternative hypotheses and using sample data to assess the likelihood of these hypotheses. Type I error occurs when the null hypothesis is rejected when it is actually true. Type II error occurs when the null hypothesis is not rejected when it is actually false. PARAMETER A characteristic or numerical measure obtained from a population. Example: population mean, population standard deviation. STATISTIC A characteristic or numerical measure obtained from a sample. Example: sample mean, sample standard deviation. ESTIMATION The process of using sample data to estimate population parameters. POINT ESTIMATION Point estimation involves estimating a single value For instance, a sample mean is a point estimate of a population mean INTERVAL ESTIMATION Interval estimation involves estimating a range of values. An interval estimate gives you a range of values where the parameter is expected to lie. A confidence interval is the most common type of interval estimate CONFIDENCE INTERVAL A range of values that is likely to contain the true population parameter. Calculated from sample data and a specified level of confidence.
5 WAYS TO INCREASE STATISTICAL POWER 5 WAYS TO INCREASE STATISTICAL POWER INCREASE SAMPLE SIZE (THE MOST PRACTICAL WAY) USE Z DISTRIBUTION DECREASE STANDARD DEVIATION What is Power? Power is the abilityto detect aneffect ina statistical test. It refers to a statistical test'scapacityto accurately reject thenullhypothesis whenthe alternativehypothesis is true. A highstatisticalpowerprovides a better chance ofidentifyingactualeffects, whereas a low power indicateshigher risk offailingto detecteffects, resultingin falsenegatives or TypeIIerrors. INCREASE SIGNIFICANCE LEVEL ALPHA SWITCH FROM A 2- TAILED TEST TO A 1- TAILED TEST INCREASE MEAN DIFFERENCE Usinga z distribution makes iteasier to achievestatistical significance becausea ithas ahigherkurtosis (z is taller thanthet distribution) and smaller tails. By modifyingtheshape, it also effect increasespower. Another wayto modifytheshape of the distributionis to lower Standard Error (SE) by decreasing Standard Deviation(SD). Itcan beachieve by: 1) Use moreprecise measurements whenaskingforuserfeedbacksurveys. 2) Perform apaired samples t-test Larger samplesizes oftenresult in higher statisticalpower. It reduces thevariability(SD) in estimates and increases theprecision oftheresults. increasingalpha isgoingto increasetheprobability of makinga typeIerror One-tailed testsconcentrate statisticalpower onfindingeffects in a single direction, rather thanacross bothtails ofthe distribution. This may beuseful whenthereis a priori reasonto assumeaninfluencein one directionexclusively. Mean differenceis onetype ofeffect size, so byincreasingtheeffect size, itcanlead to increaseinstatistical power becauseit makes the difference betweengroups morepronounced and easier to detect. A232 SMS3123 ASSIGNMENT 1 (PART 2) DEFINITION WRONG WAY INSTEAD OF T DISTRIBUTION 1 2 3 4 5 M ODIFIY SHAPE SHAPE M ODIFIY MOST PRACTICAL WAY SINGLE DIRECTION EFFECT SIZE