STATISTICS FOR COMMUNICATION RESEARCH

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STATISTICS FOR COMMUNICATION RESEARCH

• PROF. MADYA DR. JUSANG BOLONG
• JABATAN KOMUNIKASI
• 03-8946 8780
• jusang_at_fbmk.upm.edu.my

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OBJEKTIF KURSUS

• Pada akhir kursus ini pelajar dapat
• Menerangkan peranan statistik dalam penyelidikan
• Menerangkan perbezaan dan kaitan antara statistik
  deskriptif dengan statistik inferensi
• Mengenalpasti dan menerangkan teknik yang boleh
  digunakan untuk menganalisis data kuantitatif
  dalam penyelidikan komunikasi
• Memilih teknik yang sesuai untuk menganalisis
  data dan membuat tafsiran yang betul daripada
  hasil analisis data.

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KANDUNGAN KURSUS

1. Definisi, jenis dan peranan statistik
2. Jenis data, tahap pengukuran, sampel dan populasi
3. Statistik deskriptif dan persembahan data
4. Indeks kecenderungan memusat dan serakan
5. Statistik inferensi dan taburan normal

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KANDUNGAN KURSUS (Samb.)

• 6. Ujian hipotesis jenis hipotesis, jenis
  ralat, paras keertian, langkah-langkah ujian
  hipotesis dan keputusan
• 7. Ujian signifikan satu sampel satu pemboleh
  ubah
• 8. Ujian perbandingan Membandingkan kumpulan dan
  membandingkan pemboleh ubah
• 9. Ujian perkaitan dan analisis regrasi

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Penilaian Kursus

• Kerja Kursus (4 tugasan) 40
• Peperiksaan Pertengahan 20
• Peperiksaan Akhir 40

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Statistics

• Scientific methods for collecting, organizing,
  summarizing, presenting, and analyzing data as
  well as with drawing valid conclusions and making
  reasonable decision on the basis of such
  analysis.
• A branch of applied mathematics that specializes
  in procedures for describing and reasoning from
  observations of phenomena

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Purpose of Statistics

1. To describe phenomena,
2. To organize and summarize our result more
   conveniently and meaningfully,
3. To make inference or make certain predictions,
4. To make explain, and
5. To make conclusion.

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Type of Statistics

• 1. Descriptive Statistics
• - Concerned with summarizing the distribution of
  single variable or measuring relationship between
  two or more variables (Eg Frequency
  distribution, measure of central tendencies,
  measures of dispersion, correlation coefficient
  and deriving regression equation (prediction
  equation)

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Type of Statistics (cont.)

• 2. Inferential Statistics
• - Concerned with making generalization from
  sample to population (Eg T-test, Analysis of
  Variance and Chi-square).

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Concepts in Statistics

• Population
• The entire group being observed, almost always
  assumed to be infinite in size
• The total collection of all cases in which the
  researcher is interested and wishes to
  understanding.
• Group or set of human subjects or other entities
  (Ex all student at the UPM, all members at
  Jabatan Komunikasi)

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Concepts in Statistics (Cont.)

• Sample
• The sub-group of population
• Generalizations based on samples can accurately
  represent the population

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Concepts in Statistics (Cont.)

• Population
• Basic unit of interest
• Known as universe
• Large in numbers
• Difficult to observed
• Dynamic

• Sample
• A portion of defined population
• Small in numbers
• Observable
• Can draw inference about population

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Concepts in Statistics (Cont.)

• Variable
• As an observable characteristic of an object or
  event that can be described according to certain
  classification or scales of measurement
• Independent Variable In bivariate relationship,
  the variable is taken as cause, normally
  represented by symbol X

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Concepts in Statistics (Cont.)

• Dependent variable In a bivariate relationship,
  the variable is taken as the effect, normally
  represented by symbol Y
• Continuous variable/data A variable/data with a
  unit of measurement that can be subdivided
  infinitely. Eg Height 150.3 cm

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Concepts in Statistics (Cont.)

• Discrete variable/data A variable with a basic
  unit of measurement that cannot be subdivided.
• Eg sex
• 1 Male
• 2 Female

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Measurement

• The process of assigning a number to object,
  place or person
• Level of Measurement
• - The mathematical characteristic of a variable
  as determined by the measurement process. A major
  criterion for selecting statistical procedures or
  techniques.

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Level of Measurement (Type of Data)

• 1. Nominal
• Sorting elements with respect to certain
  characteristics
• Sort into categories that are at homogenous as
  possible
• Lowest level of measurement
• classification, naming, labeling

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Level of Measurement (Type of Data)

• 2. Ordinal
• Grouping or classification of elements with
  degree of order or ranking
• May not be able say exactly how much they possess
• Can be arrange or placed in single continuum
• Eg Likert scale

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Level of Measurement (Type of Data)

• 3. Interval
• Ordering elements with respect to the degree to
  which they possess certain characteristics
• Indicates the exact distance between them
• Zero does not means absence
• Eg 0 degrees Celsius (Suhu rendah)

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Level of Measurement (Type of Data)

• 4. Ratio
• - Ordering elements with respect to the degree to
  which they possess certain characteristics
• Indicates the exact distance between them
• Zero means absence absolute
• Eg RM0 (tiada pendapatan)

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Level of Measurement (Type of Data)

• These four scale of measurement can be
  generalized into two categories
• Non-metric includes the nominal and ordinal
  scales of measurement.
• Metric include interval and ratio scales of
  measurement.

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Descriptive Statistics

• Frequency distribution
• Measure of central tendency
• Measure of dispersion
• Measure of association

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Data Presentation

• Basic function of statistics to organize and
  summarize data
• Frequency table
• Graphic presentation
• - Pie chart
• - Bar Chart
• - Histogram
• - Polygon
• - Line graph

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General guides

• Use mode when variable are nominal you want to
  present quick and easy measure for ordinal,
  interval and ratio data/variables.
• Use median when variable are ordinal you want to
  report the central score and the scores measured
  at interval and ratio levels have badly skewed
  distribution

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• Use mean when variables are interval or ratio
  (except for badly skewed distribution) you want
  to report the typical score and you anticipate
  additional statistical analysis.

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• Range The highest score minus the lowest score
• Standard Deviation The square root of the
  squared deviation of the score around the mean
  divided by N (number of cases). Represented by
  the symbol s
• Variance The squared deviations of scores around
  the mean divided by N. Represented by the symbol
  s²

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Inferential Statistics

• To enable researcher to make statement or summary
  or decision about the population based on the
  sample
• To enable researcher to make statement or summary
  or decision on the unseen data based on the
  empirical data
• To enable researcher to make statement or summary
  or decision on the large group based on data from
  the small group.

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Two main procedures of Inferential Statistics

• Estimates
• Hypothesis Testing

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Statistical Assumption

• A set of parameters, guidelines indicating the
  conditions under which the procedures can be most
  appropriately used.
• Every test has own assumption that should not be
  violated
• Four main assumption of Inferential Statistics

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1. Random sample
2. Characteristics are related to true population
3. Multiple random sample from same population yield
   similar statistics that cluster around true
   population parameters
4. Can calculate the sampling error associated with
   a sample statistics

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Normal Distribution

• The normal probability distribution is a
  continuous probability distribution (Ref.
  Equation pg 70)
• Data in the normal distribution are measured in
  terms of standard deviation from mean and are
  called standard scores or Z score.
• Characteristics of Normal Distribution
• 1. It is a continuous probability distribution
• 2. Symmetrical or bell-shaped with the mode,
  median and mean are equal

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• 3. The distribution contains an infinite number
  of cases
• 4. The distribution is asymptotic the tails
  approach abscissa range from negative to
  positive infinity
• 5. About 95 of distribution lies within 2
  standard deviation from the mean.

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Hypothesis Testing

• Hypothesis is a tentative statement about
  something.
• Statement concerning
• Differences between groups
• Relationship or association between variables
• Changes that occurs

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• Statement related to our prediction about
  population characteristics or relationship
• Statement related to research question
• Statement must be testable or verifiable

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• Hypothesis statement and testing help us on
• Drawing conclusion
• Making implication
• Making suggestion

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• We are not going to prove the hypothesis is true,
  but we are to prove that is not true or false
• Statistical test is to test the hypothesis
• Two types of hypothesis
• Null Hypothesis (Ho)
• Alternative or Research Hypothesis (Ha or H1)

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• Null Hypothesis A statement of no difference or
  no association (among variables, samples etc)
• Alternative or Research hypothesis A statement
  asserting that there is difference or association
  (among variables, samples, etc)

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• Two forms of hypothesis
• 1. Directional Hypothesis. Eg
• Ha µ gt230 or
• Ha µ lt 230
• 2. Non-directional Hypothesis. Eg
• Ha µ 230

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FIVE STEP Model for Hypothesis Testing

• Step 1making assumption
• Samples selected randomly
• Defined population
• Interval-ratio data
• Sampling distribution normal

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• Step 2 State the null and research hypothesis
• Step 3 Selecting the appropriate distribution
  such as z, t, f and ?² and establishing the level
  of significance as well as critical region.
• Step 4 Calculate the test statistics
• Step 5 State the level of significance and
  critical region
• Level of significance or alpha level commonly
  used 0.05
• Critical region will determine the rejection or
  failure to reject the null hypothesis

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• Step 6 Making decision
• If test statistic falls in the critical region,
  reject the null hypothesis.
• If test statistic does not fall in the critical
  region, we fail to reject the null hypothesis at
  predetermined alpha level

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• Step 7 State the conclusion
• Type I and Type II Error (Ref Pg. 86-module)
• Type I Error (Alpha Error)
• The probability of rejecting a null hypothesis
  that is in fact true
• Type II Error (Beta Error)
• The probability of failing to reject the null
  hypothesis in fact false

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Level of Significance (Alpha Level)

• The probability of area under the sampling
  distribution that contains unlikely sample
  outcomes given that the null hypothesis is true.
  Also, the probability of type I error
• Commonly expressed as 90, 95 or 99 or written
  as alpha 0.10, 0.05 or 0.01
• 95, refers to alpha 0.05 which means that we are
  95 sure of making the right decision and 5
  error.

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Critical Region

• The area under the sampling distribution that, in
  advance of the test itself, is defined as
  including unlikely sample outcome given that the
  null hypothesis is true.
• Critical value of the test statistic to reject
  null hypothesis
• Critical value is defined from the test statistic
  table corresponding to its level of significance
  and degree of freedom.

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• The null hypothesis is rejected when the value of
  test statistics exceed the critical value and
  lies in the critical region

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One-tailed and Two-tailed Test

• Critical region on one side or both sides of the
  distribution depending on the nature of
  alternative or research hypothesis.
• Eg Ho a b (Two-tailed)
• Ha a ?b
• Ha a gt b (One-tailed)
• Ha a lt b

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Two-tailed Test

• A type of hypothesis test used when direction of
  difference between variables or samples cannot be
  predicted (Non-directional hypothesis)
• Two-tailed test has a two critical regions on
  both sides of the distribution

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One-tailed Test

• A type of hypothesis test used when the direction
  of the difference between variables or samples
  can be predicted (Directional hypothesis)
• One-tailed test has a one critical region that
  correspond to the direction of the research
  hypothesis.