Statistical Package Statistical Package for the Social for the Social

SciencesSciencesSPSS for windows is a relatively SPSS for windows is a relatively

comprehensive data analysis package comprehensive data analysis package for use in research and businessfor use in research and business

Statistics and Statistical Statistics and Statistical inferenceinference

StatisticsStatistics- is a method for analyzing data, - is a method for analyzing data, for describing and drawing inferences from for describing and drawing inferences from data. Statistics can also be viewed as the study data. Statistics can also be viewed as the study of variation.of variation.

StatisticalStatistical inferenceinference-scientific -scientific inference, which is in turn is inductive inference, which is in turn is inductive inference, the making of general statements inference, the making of general statements from the study of particular cases. Statistics from the study of particular cases. Statistics attempts to make induction thorough/precise.attempts to make induction thorough/precise.

Review of Basic ConceptsReview of Basic Concepts

Definition of terms and conceptsDefinition of terms and concepts

PopulationPopulation-any group or aggregation that comprises -any group or aggregation that comprises the totality of cases of interest in the study. E.g. the totality of cases of interest in the study. E.g. people, animals, plants.people, animals, plants.

SampleSample-any subgroup or subaggregate drawn by -any subgroup or subaggregate drawn by some appropriate method from a population.some appropriate method from a population.

ParameterParameter-a property descriptive of the population.-a property descriptive of the population. Estimate/StatisticEstimate/Statistic-a property of a sample drawn at -a property of a sample drawn at

random from a population.random from a population.

ConstantConstant-observations that do not vary. E.g. lighting -observations that do not vary. E.g. lighting condition, time of the day the experiment was condition, time of the day the experiment was conducted.conducted.

VariableVariable-Observations that vary. E.g. Age, scores.-Observations that vary. E.g. Age, scores. Discrete/Discontinuous variable-Discrete/Discontinuous variable- observations have observations have

a finite number of values. Includes whole numbersa finite number of values. Includes whole numbers Continuous Variable-Continuous Variable- observations have an infinite observations have an infinite

number of values, wherein measurements of varying number of values, wherein measurements of varying degrees of precision can be made. E.g. Height, degrees of precision can be made. E.g. Height, temperature, length.temperature, length.

Levels of Measurement

Nominal-Numbers are used simply to classify and label observations.Ordinal scale- Numbers reflect the rank order of the individuals or objects.Interval scale- Distances between levels on the scale can be specified although the zero point is arbitrary.E.g. I.Q., TemperatureRatio Scale-highest type of scale. Ratios can be formed with levels of the scale because it has a true zero point. E.g. length and weight.

• Categorical Variables-Categorical Variables- are also are also referred to as Nominal Level Data. referred to as Nominal Level Data. (Gender)(Gender)

• ContinuousContinuous VariableVariables-are also s-are also referred to as Interval Level Data. referred to as Interval Level Data. (age in years, scores in scales)(age in years, scores in scales)

Important concepts in Important concepts in Descriptive StatisticsDescriptive Statistics

Measures of Central tendencyMeasures of Central tendency

-Mode--Mode- the observation in the sample the observation in the sample that occurs most frequently.that occurs most frequently.

-Median--Median- the point in the distribution the point in the distribution above which are found one-half of the above which are found one-half of the cases and below it the other half.cases and below it the other half.

-Mean--Mean- the center of gravity of the the center of gravity of the distribution.distribution.

Measures of Measures of Dispersion/VariabilityDispersion/Variability

provide information on how the data is distributed provide information on how the data is distributed around the typical scorearound the typical score

RangeRange- difference between the - difference between the highest and lowest values of a data highest and lowest values of a data set.set.

Standard DeviationStandard Deviation-this is the -this is the measure of the average variability in measure of the average variability in the distribution of scores.the distribution of scores.

VarianceVariance-squared SD-squared SD

Distribution of Scores on Distribution of Scores on Continuous VariablesContinuous Variables

►Skewness Value-Skewness Value- provides an provides an indication of the symmetry of the indication of the symmetry of the distribution.distribution.

- Positively skewed-Positively skewed- most scores are relatively low most scores are relatively low but there are few unusually high scoresbut there are few unusually high scores

Negatively skewed-Negatively skewed- majority of the scores are majority of the scores are high, but a few outliers score lowhigh, but a few outliers score low

Importance of identifying Importance of identifying skewnessskewness

►We may wish to identify more closely We may wish to identify more closely the outliers, what accounts for their the outliers, what accounts for their unusual scores.unusual scores.

►Skewed Data can distort outcomes of Skewed Data can distort outcomes of many commonly used statistical many commonly used statistical procedures (even the mean)procedures (even the mean)

Kurtosis- The flatness or peakedness of Kurtosis- The flatness or peakedness of one distribution in relation to anotherone distribution in relation to another

►Three typesThree types

a.) Platykurtic-exceptionally flata.) Platykurtic-exceptionally flat

Leptokurtic-unusually peaked; tails are Leptokurtic-unusually peaked; tails are more elevated above baselinemore elevated above baseline

►Normal curve- bell shaped, assumes Normal curve- bell shaped, assumes that the data handled are normally that the data handled are normally distributeddistributed

Important reminder!!Important reminder!!

If the distribution is perfectly normal, you If the distribution is perfectly normal, you would obtain a skewness and kurtosis would obtain a skewness and kurtosis value of “0”.value of “0”.

General assumptions that apply to General assumptions that apply to all parametric techniques all parametric techniques

Level of measurements- Each of these approaches assumes Level of measurements- Each of these approaches assumes that the dependent variable is measured at the interval or ratio that the dependent variable is measured at the interval or ratio scalesscales

Random Sampling-These tests assume that the scores are Random Sampling-These tests assume that the scores are obtained using a random sample from the population.obtained using a random sample from the population.

Normal Distribution-it is assumed that the populations from Normal Distribution-it is assumed that the populations from which samples are taken are normally distributed.which samples are taken are normally distributed.

Homogeneity of variance- it is assumed that samples are Homogeneity of variance- it is assumed that samples are obtained from populations of equal variances. This means that obtained from populations of equal variances. This means that the variability of scores for each of the groups is similar.the variability of scores for each of the groups is similar.

““No matter how well versed you are with the software, focus No matter how well versed you are with the software, focus on examining first the data, it does not pay to run the analysis on examining first the data, it does not pay to run the analysis

then ooooops, you chose the wrong tool”then ooooops, you chose the wrong tool”